Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y ), hence
F(- 1, 9) → F'(- 1, - 9)
G(- 2, 1) → G'(- 2, - 1)
H(- 7, 4) → H'(- 7, - 4)
Find. F(g(d))
F(d)=d-15
G(d)=0.8d
Since f(d) and g(d) represent two types of discounts that you will receive off of the price, the composite function is f(g(d)) = 0.8d - 15.
In Mathematics and Geometry, a function composition is an operation (∘) that combines two functions f(x) and g(x), in order to produce a composite function h(x) = (g∘f)(x), such that h(x) = g.
In this exercise, we would determine the corresponding output values for the composite functions by using the substitution method as follows;
f(g(d)) = 0.8d - 15
In this context, we can reasonably infer and logically deduce that the composite function is f(g(d)) = 0.8d - 15.
Complete Question:
You go to a store to buy sneakers f(d) and g(d) represent two types of discounts that you will receive off of the price of the sneakers that you want.
Find f(g(d))
f(d)=d-15
g(d)=0.8d
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
Answer:
Theoretical P(3) = 1/6
Experimental P(3) = 67/450
Step-by-step explanation:
A die has 6 possibilities that can come up {1,2,3,4,5,6} They are all equally likely, so each has a probability of 1/6
a P(getting a 3) = 1/6
We rolled a 3 67 times out of 450. This is our experimental probability
b P (getting a 3) = 67/450
This does not simplify
As your math teacher, let's solve this problem together step by step.
a. Theoretical Probability of Rolling a 3:
A standard number cube, often referred to as a die, has six faces numbered 1 through 6. Since all faces are usually designed to be equally probable, the theoretical probability of rolling a three (or any specific number) is the ratio of the number of successful outcomes (rolling a 3) to the total number of possible outcomes (any number from 1 to 6).
So,
Theoretical Probability = Number of successful outcomes / Total number of possible outcomes
= 1 / 6
This is already in the simplest form since 1 and 6 have no common divisors other than 1.
b. Experimental Probability of Rolling a 3:
The experimental probability, in contrast to the theoretical probability, is determined based on actual trials or experiments. In this case, the cube was rolled 450 times, and the number 3 appeared 67 times.
So,
Experimental Probability = Number of times a 3 was rolled / Total number of rolls
= 67 / 450
Now, to simplify the fraction, you would find the greatest common divisor (GCD) of 67 and 450 and divide both numerator and denominator by that GCD.
Looking at the numbers, they do not immediately suggest a common factor, and since 67 is a prime number, we can reasonably conclude that the fraction is already in its simplest form. Therefore, the experimental probability is:
= 67 / 450
So there you have it, answers to both questions in their simplest form:
a. The theoretical probability of rolling a 3 on a number cube is 1/6.
b. The experimental probability of rolling a 3 given the cube is rolled 450 times and 3 comes up 67 times is 67/450.
Calculate the approximate mean absolute deviation of the given data set.
5, 7, 8, 10, 11, 17, 19, 24
8
12.625
5.53
10.5
Answer:
12.625
mean=total sum value /total data set
The mean of given data set is: 12.625.
The correct option is (B)
What is mean?
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean = (Sum of all the observations/Total number of observations)
Given data: 5,7,8,10,11,17,19,24.
Mean=
sum of observation/ Total number of observation
=5+7+8+10+11+17+19+24/8
=101/8
=12.625.
Hence, the mean is 12.625.
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What number is missing from the number pattern? 1,2,5,10,__,26,37
Answer:
17 is the missing the number
Step-by-step explanation:
Pattern: +1, +3, +5, +7, etc.
solve the system .....................
Answer:
The correct answer is first option
(2, 3)
Step-by-step explanation:
It is given that,
3y = -x + 11 and
x + 4y = 14
To find the solutions
The given equation can be written as,
x + 3y = 11 --------(1)
x + 4y = 14 -------(2)
Subtract (1) from (2) we get
y = 3
Substitute vale of y in eq(1)
x + 3*3 = 11
x = 11 - 9 = 2
Therefore x = 2 and y = 3
The correct answer is first option
Answer:
first option
(2, 3)
Step-by-step explanation:
We have the following system of linear equations
[tex]\left \{{{3y=-x+11} \atop {x+4y=14}} \right.[/tex]
This is the same as
[tex]\left \{{{x + 3y=11} \atop {x+4y=14}} \right.[/tex]
To solve the system multiply the first equation by -1 and then add it to the second equation.
[tex]-1*(x+3y)=11*(-1)[/tex]
[tex]-x -3y=-11\\x+4y=14[/tex]
-----------------
[tex]y = 14-11[/tex]
[tex]y = 3[/tex]
substitute [tex]y = 3[/tex] in any of the two equations and then solve for x
[tex]x+4(3)=14\\x+12=14\\x =14-12\\x = 2\\[/tex]
[tex]x =2[/tex]
The answer is the first option
(2, 3)
Which of the following pair(s) of circles have / as a common external tangent? Select all that apply.
A and B
A and C
B and C
Answer with explanation:
A tangent to a circle is a Line which touches a circle at a single point.
There can be Infinite number of tangents to a circle which are external only.
In the given figure:
⇒ There are three circles having Centers A, B and C.Circle having Center B lies inside the circle having center C.
⇒The three circles intersect at point T.
⇒The common tangent of these three circles passes through Point T.
⇒Circles having Center B and Center C , have a common external Tangent.
Option A,B and C:
→A and B
→A and C
→B and C
Tangent is the line that intersects the circle at a single point. Thus, Option A, B, and C all apply.
Three different circles are given in the question that is A, B, and C.
We have to determine the pair of circles that have a common external tangent.
Therefore, take circles A and B from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option A applies.
Now, take circles A and C from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option B applies.
Further, take the circles B and C from the given figure.
Line " L " is the common tangent to both circles. It is clear from the figure that it is an external tangent to both circles.
Hence, Option C applies.
Thus, Option A, B, and C all apply.
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Which expression is equivalent to the expression below?
Answer:
A
Step-by-step explanation:
Given
[tex]\sqrt{-108}[/tex] - [tex]\sqrt{-3}[/tex]
= [tex]\sqrt{36(3)(-1)}[/tex] - [tex]\sqrt{3(-1)}[/tex]
= 6[tex]\sqrt{3}[/tex] i - [tex]\sqrt{3}[/tex] i
= 5[tex]\sqrt{3}[/tex] i
Answer:
Step-by-step explanation:
√(-108) - √(-3)
= √(-3*36) - √(-3)
= √[(-3)*36] - √(-3)
= √(-3)*(√36 - 1)
= √[(-1)*(3)]*(6-1)
= i*√(3)*(5)
= 5√3i
A swim teacher sells lesson packages. The best deal has the highest ratio of lessons to total cost.
Swim Lesson Packages
Number of Lessons Total Cost
$10
$40
10 1 $80
15
$80
Which package is the best deal?
l lesson for $10
5 lessons for $40
10 lessons for $80
15 lessons for $80
Mark this and return
Save and Exit
Answer:
the best package is 15 lessons for $80
Answer:
Which package is the best deal? Option D
(D) 15 lessons for $80 100% Answer
Step-by-step explanation:
The two-way table below describes the attendance at a movie theater at various times of the day.
Which statement best describes the relationship between the two variables?
There is an association because the relative frequencies by column are different.
There is an association because the relative frequencies by column are similar.
There is no association because the relative frequencies by column are different.
There is no association because the relative frequencies by column are similar.
Answer:
There is an association because the relative frequencies by column are different.
Step-by-step explanation:
For checking the association of a two-way table we have to calculate the relative frequency of the table. Here we see that there is an association between timing and day pf watching the movie. Also here relative frequencies of both columns are similar.
This time make a simple coaster that bumps the axis at x=500. Remember to make sure that the track rises before it falls
Answer:
y=-ax(x-500)^2(x-1000)
Step-by-step explanation:
(2x + 3).x (4x + 1)
Answer:
8x^2 +14x +3
Step-by-step explanation:
(2x + 3)* (4x + 1)
FOIL
first 2x *4x = 8x^2
outer 2x*1 = 2x
inner 3*4x =12x
last = 3*1 =3
Add them together
8x^2 +2x+12x +3 = 8x^2 +14x +3
What is the solution to the system of equations?
Answer:
[tex]\large\boxed{\left(7,\ \dfrac{13}{3}\right)}[/tex]
Step-by-step explanation:
You must use the algebraic method: substitution or elimination.
I will solve a given system of equations the substitution method.
[tex]\left\{\begin{array}{ccc}y=\dfrac{1}{3}x+2&(1)\\\\y=\dfrac{4}{3}x-5&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\\dfrac{4}{3}x-5=\dfrac{1}{3}x+2\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}x-(3)(5)=3\!\!\!\!\diagup^1\cdot\dfrac{1}{3\!\!\!\!\diagup_1}x+(3)(2)\\\\4x-15=x+6\qquad\text{add 15 to both sides}\\\\4x=x+21\qquad\text{subtract x from both sides}\\\\3x=21\qquad\text{divide both sides by 3}\\\\x=7\\\\\text{put the value of x to the first equation}\\\\y=\dfrac{1}{3}\cdot7+2\\\\y=\dfrac{7}{3}+\dfrac{6}{3}\\\\y=\dfrac{13}{3}[/tex]
Will give brainliest!! Part of me thinks the answer is D but I just want to double check.
Answer: C) 6.0025
Step-by-step explanation:
The equation for the area of a circle requires the radius, you put in the full diameter. Just divide 4.9 by 2, which gives you 2.45. 2.45 squared is equal to 6.0025 and then slap your pi on to the end of it.
Answer:
[tex]6.0025\pi \: {m}^{2} [/tex]
Step-by-step explanation:
The formula for the area of a circle:
[tex]\pi \times {r}^{2} [/tex]
We are given the diameter of the circle, which is two times its radius. To find the radius, we divide the diameter by 2.
4.9 ÷ 2 = 2.45 m^2.
Now we need to square the radius:
[tex] {2.45}^{2} = 6.0025[/tex]
So, the area in terms of pi would be
[tex]\pi \ \times {6.0025}^{2} \: {m}^{2} [/tex]
Or
[tex]6.0025 \times \pi \: {m}^{2} [/tex]
Hope this helps!
What is the simplified form of sqrt 10,000
Answer:
100
Step-by-step explanation:
10,000 is merely 100 x 100 = 100²
so √10,000 = √100² = 100
Hector keep close tabs on his bank account. His account had a balance of -$22.80. The next day, he made a deposit of $56.60. His account balance changed to $.
In the triangle below, what is the measure of Angle z
Answer:65
Step-by-step explanation:
The triangle is isosceles triangle and the base angles must be the same
The measure of angle z is 65°.
Given that, in ΔXYZ XZ=XY=7 cm.
We need to find the value of ∠Z.
What is the isosceles triangle?In an isosceles triangle with two equal sides. The angles opposite the equal sides are also equal.
Since XZ=XY=7 cm.
Here, ∠Y=∠Z=65°
Therefore, the measure of angle z is 65°.
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Solve the following word problems using your knowledge
9 word problems using your knowledge of fractions. Be sure to express your answers
in simplest form.
Mike had 9 1/2 cups of Gatorade in a bottle. After he darom 2 3/4 cups of Gatorade, how much was left in the bottle?
can you please help me and I will get you brainliest.
Answer:
27/4 or 6 3/4
Step-by-step explanation:
( 19 x 4 ) - ( 11 x 2 )
------------------------------
2 x 4
=54/8
54/2
-------------
8/2
what two integers is √42 between? explain
[tex]\sqrt{36}=6[/tex] and [tex]\sqrt{49}=7[/tex], so it stands to reason that [tex]\sqrt{42}[/tex] lies somewhere between 6 and 7.
Can someone pls answer this?
255 square centimeters
Step-by-step explanation:First, break this into two shapes: a triangle and a rectangle.
The rectangle is 22 cm by 10 cm. [tex]22 * 10 = 220[/tex] square centimeters
The triangle's base is 10 cm ([tex]22-12=10[/tex]) and its height is 7 cm ([tex]17-10=7[/tex]). [tex]\frac{1}{2} * 10 * 7 = 5 * 7 = 35[/tex] square centimeters
Add the areas together. [tex]220 + 35 = 255[/tex] square centimeters
is x 2 = y a function?
Answer:
yes
Step-by-step explanation:
a
The answer is:
Yes, the given equation is also a function. (it's a quadratic function)
Why?We know a function exists when there is only one value of y (output) for each x (input).
We can easily know if an equation (relation) is also a function using the graphic method:
To know if a relation is a function, we need to graph it a draw a vertical line, if the line cut the graph in only one point, the relation is a function, otherwise, if the vertical line cuts the graph in two or more points, the relation is a not a function. Remember, the condition for a function is that there is only one output for each input.
Note: I have attached a picture for better understanding.
Have a nice day!
How do you do right Triangle
Answer:
right triangles should have one right angle (90 degrees) and it should liik like an L, and then draw a line connecting the gap (the hypotenuse)
Step-by-step explanation:
Answer:
make a 90 degree angle and connect the two points to finish the shape of the triangle.
Step-by-step explanation:
HINT: the corner of a piece of paper is a 90 degree angle
Which expression is the factorization of x2 + 10x + 21?
You must remember that a polynomial is written like so...
ax^2 + bx + c
In this case...
a = 1
b = 10
c = 21
To factor you must find two numbers who both add up to b (10) AND multiply to c (21)
3 + 7 = 10
3 * 7 = 21
so...
(x + 3 )(x + 7)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: 12x + 21 or C. F(x) = (x - 2)(x + 2)
Step-by-step explanation:
x2 + 10x + 21
2x + 10x + 21
Rearrange to put the coefficient in front/move it in front of the term.
Ex. (× · 4 ⇒ 4×)
(×( 7 ) ⇒ 7×)
Identify and group like terms.
(2x + 10x) + 21
Group the coefficients together.
(2+ 10)x + 21
Combine 2 + 10 to get 12.
12x + 21
= 12x + 21
You're Welcome! :))
Find the value of Q in the following system so that the solution to the system is (2,3)
x-2y=-4
3x+5y=Q
Answer:
Q = 21Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x-2y=-4&(1)\\3x+5y=Q&(2)\end{array}\right\\\\\text{From (2, 3), put x = 2 and y = 3 to (2):}\\\\Q=3(2)+5(3)=6+15=21[/tex]
Which of the following is needed to construct the figure below?
A. 8 Acute triangles
B. 5 isosceles triangles
C. 6 Equilateral triangles
D. 10 obtuse triangles
Answer:
C. 6 equilateral triangles
6 Equilateral triangles needed to construct the hexagon option (C) 6 Equilateral triangles is correct.
What is hexagon?A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.
We have a given a hexagon in the figure.
As we know hexagon is a polygon made up from six sides also hexagon can be made using six equilateral triangles by joining them.
Thus, 6 Equilateral triangles needed to construct the hexagon option (C) 6 Equilateral triangles is correct.
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what is the equation of a line that goes through the point (0,5/6) and has a slope of 1
The slope is given as 1.
The Y-intercept is where the line crosses the Y axis when X is 0. This is also given by the point (0,5/6). X is 0 and Y is 5/6, so the Y-intercept is 5/6.
The equation of a line is given as y = mx +b where m is the slope and b is the y-intercept.
The equation is: y = x +5/6
Answer:
y = x+5/6
Step-by-step explanation:
The slope intercept form of the equation of a line is
y = mx +b
We are given the slope of 1 and the y intercept of 5/6 (The y intercept is when x=0)
y = 1x+5/6
y = x+5/6
What value of b will cause the system to have an infinite number of solutions?
y = 6x – b
–3x + y = –3
Solving for b by simplifying both sides of the equation, then isolating the variable.
b = −y + 6x
----
Choosing three values for x and substitute in to find the corresponding y values.
(0,−3) , (1,0) , (2,3)
____
I hope this helps, as always. I wish you the best of luck and have a nice day, friend..
Answer:
Step-by-step explanation:
y = 6x -b
and -3x +y =-3
on simplifying equation 2 ,we have y = 3x -3
System of equation has infinite number of solution if one equation can be obtained by multiplying by suitable non zero number
if we multiply equation by 2 we get y =6x -6
Since coefficient of x and y is same therefore comparing the value of x b with constant in another equation which is 6 .
therefore b =6
demand for a brand of clock radio is given by p+3q=390 , and the supply for these radios is given by p=7q=90 , where is the price and is the quantity demanded at price . Solve the system containing these two equations to find the price at which the quantity demanded equals the quantity supplied and the equilibrium quantity.
Answer:
p=$300 and q=30 clock radio
Step-by-step explanation:
we have
p ----> is the price
q ----> is the quantity
[tex]p+3q=390[/tex] ----> equation A
[tex]p-7q=90[/tex] ----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The intersection point is (300,30)
see the attached figure
therefore
The solution is
p=$300
q=30 clock radio
A line is defined by the equation y = 2/3 x - 6 The line passes through a point whose y-coordinate is 0. What is the x-coordinate of this point?
Answer:
x = 9
Step-by-step explanation:
Use the equation of the line, and let y = 0. Then solve for x.
y = 2/3 x - 6
Let y = 0:
0 = 2/3 x - 6
Add 6 to both sides.
6 = 2/3 x
Multiply both sides by 3/2.
3/2 * 6 = x
x = 9
List the following numbers from least to greatest: -4, |-6|, 3, -2, |5
-4, -2, 3, |5|, |-6
|-6|, -4, -2, 3, |5
|-6|, 5, -4, 3, -2
-6|, |5|, 3, -2, -4
Answer:
-4,-4,-4,-4,-2,-2,-2,-2,3,3,3,3,3,|5|,|5|,|5|,5,|6||6||-6||-6|
Numbers' absolute values are outputted as non-negative numbers. The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|
What is modulus of a real number?Modulus of a real number, also called absolute value, is non-negative result of the input value.
This is defined as:
[tex]|x| = x ; \text{ (x is non-negative)}\\\\|x| = -x ; \text{ (x is negative)}[/tex](so that the outer negative makes the negative number positive).
Example:
[tex]|5| = 5\\|-5| = -(-5) = 5[/tex]
What is magnitude and sign?A number has both magnitude(its absolute value) and its sign(positive or negative).
If numbers are negative, the more their magnitude increases, the lesser they become.
If numbers are positive, the more their magnitude increases, the greater they become.
Thus, for -5, the magnitude is 5, and sign is –ve.
Also, positive numbers > 0 > negative numbers.
For given case, we get:
-4 = -4|-6| = 63 = 3-2 = -2|5| = 5Arranging, we get:
-4 < -2 < 3 < 5 < 6
or
-4 < -2 < 3 < |5| < |-6|
Thus,
The arrangement of given numbers from least to greatest is: Option A: -4, -2, 3, |5|, |-6|
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find the nature of the quadratic equation 2x^2+5x+8=0
[tex]
2x^2+5x+8=0 \\
x=\dfrac{-5+\vee-\sqrt{5^2-2\cdot2\cdot8}}{2\cdot2} \\
x=\dfrac{-5+\vee-\sqrt{25-64}}{4} \\
x=\dfrac{-5+\vee-\sqrt{-39}}{4}\Longrightarrow x\notin\mathbb{R} \\
x\notin\mathbb{R}\Longrightarrow x\in\mathbb{C}
[/tex]
So no real solutions for x. But two complex solutions for x.
[tex]
x_1=\boxed{\dfrac{-5-39i}{4}} \\ \\
x_2=\boxed{\dfrac{-5+39i}{4}}
[/tex]
Hope this helps.
r3t40