Answer:
1. See Explanation for Sample Space
2. [tex]P(10) = \frac{1}{12}[/tex]
3. [tex]P(6) = \frac{5}{36}[/tex]
Step-by-step explanation:
Given
Roll of Two die
Solving (1): The Sample Space
Represent the first dice with S1 and the second with S2
[tex]S_1 = \{1,2,3,4,5,6\}[/tex]
[tex]S_2 = \{1,2,3,4,5,6\}[/tex]
The sample space of both die is:
[tex]S = (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)[/tex][tex](4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(55,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)}\}[/tex]
Solving (2): Probability of Sum being 10
First, we need to add the outcome of each roll in (1) above:
[tex]S = \{2,3,4,5,6,7, 3,4,5,6,7,8, 4,5,6,7,8,9, 5,6,7,8,9,10, 6,7,8,9,10,11 7,8,9,10,11,12\}[/tex][tex]n(S) = 36[/tex]
[tex]n(10) = 3[/tex]
The required probability is:
[tex]P(10)= \frac{3}{36}[/tex]
[tex]P(10) = \frac{1}{12}[/tex]
Solving (3): Probability of Sum being 6
[tex]n(S) = 36[/tex]
[tex]n(6) = 5[/tex]
The required probability is:
[tex]P(6) = \frac{5}{36}[/tex]
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for x=-3 and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Never mind I got it. mtan=6x+4. Sub in x values, for x=-2, take 6(-2)+4 = -8, and for x=1.5. 6(1.5)+4=13.
Complete Question
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for [tex] x = 3[/tex] and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Answer:
The generally expression for the slope of [tex]y = 2x^2 + 4x[/tex] is [tex]y' = 4x +4[/tex]
The graph is shown on the first uploaded image
The generally expression for the slope of [tex]y=2x^2+4[/tex] is [tex]y' = 4x[/tex]
Step-by-step explanation:
From the question we are told that
The equation of the curve is [tex]y = 2x^2 + 4x[/tex]
First we differentiate the equation
So
[tex]y' = 4x +4[/tex]
Therefore the generally expression for the slope tangent to the curve [tex]y=2x^2+4x[/tex] is [tex]y' = 4x +4[/tex]
The next step is to substitute for x = 3 and x = 0.5
So for [tex]x_1 = 3 [/tex]
[tex]y' = 4(3) +4[/tex]
[tex]y' =m_1= 16[/tex]
And for [tex]x_2 = 0.5[/tex]
[tex]y' = 4(0.5) +4[/tex]
[tex]y' =m_2= 6[/tex]
Here m_1 and m_2 are slops of the curve
Next we obtain the coordinates of the tangent lines
So at [tex]x_1 = 3 [/tex]
[tex]y_1 = 2(3)^2 + 4(3)[/tex]
[tex]y_1 = 21[/tex]
So the coordinate for the first tangent line is
[tex](x_1 , y_1 ) = (3 , 21)[/tex]
At [tex]x_2 = 0.5 [/tex]
[tex]y_2 = 2(0.5)^2 + 4(0.5)[/tex]
=> [tex]y_2 = 2.5[/tex]
So the coordinate for the second tangent line is
[tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex]
Next we obtain the equation for the tangent lines
So generally the slope is mathematically represented as
[tex]m = \frac{y - y_1 }{x-x_1}[/tex]
For [tex](x_1 , y_1 ) = (-3 , 21)[/tex] and [tex]y' =m_1= 16[/tex]
[tex] 16 = \frac{y -21 }{x-3)}[/tex]
=> [tex]y = 16x - 27[/tex]
For [tex](x_2 , y_2 ) = (0.5 , 2.5)[/tex] and [tex]y' =m_2= 6[/tex]
[tex] 6 = \frac{y -2.5 }{x-0.5}[/tex]
[tex]y = 6x -0.5[/tex]
Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows
[tex]y' = 4x[/tex]
Answer the following questions using the table below.
-2
-1
0
-10
-8
-6
-4
1
Is this a linear function?
<
What is the slope?
h
What is the y-intercept?
What is the equation of the linear function?
Answer:
the - are the x or y
Step-by-step explanation:
Does seth or briana walk faster
Answer:
PLEASE GIVE BRAINLIST
you need to be more pacific on your question so that can other people can help you.
HOPE THIS HELPED
Use linear equation to calculate intercepts. x minus one-half y = negative 4 Complete the table with values for a and b. A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.
Answer:
Use linear equation to calculate intercepts.
x minus one-half y = negative 4
Complete the table with values for a and b.
A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.
a =
✔ 8
b =
✔ –4
Step-by-step explanation:
those are ur correct answers
Answer:
Use linear equation to calculate intercepts.
x minus one-half y = negative 4
Complete the table with values for a and b.
A 2-column table with 3 rows. Column 1 is labeled x with entries 0, negative 2, b. Column 2 is labeled y with entries a, 4, 0.
a =
✔ 8
b =
✔ –4
Step-by-step explanation:
Which statement is true? Question 7 options: A) |–3| = 3 and –|–4| = –4 B) |–3| = 3 and –|4| = 4 C) –|3| = 3 and |4| = 4 D) |–3| = 3 and |–4| = –4
Answer:
option A is correct
Step-by-step explanation:
mod's has a simple function -
if |x| is given it simply means that the value of "X" can't be negative
Option A is correct, |–3| = 3 and –|–4| = –4 is true statement.
What is Number system?A number system is defined as a system of writing to express numbers.
The absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.
|-x|=x
For option A
|–3| = 3 and –|–4| = –4 is true
For option B
|–3| = 3 and –|4| = 4 is not true because –|4| is -4.
For option C
–|3| = 3 and |4| = 4 is not true because –|3| is -3
For option D
|–3| = 3 and |–4| = –4 is not true because |-4| is 4
Hence, option A is correct, |–3| = 3 and –|–4| = –4 is true statement.
To learn more on Number system click:
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Find the value of x for which l is parallel to m. The diagram is not to scale.
Answer:
x= 41
Step-by-step explanation:
3x-43= 80 is the equation since they are alternate interior angles.
Step 1- Add 43 to both sides.
3x-43= 80
+43 +43
Step 2- Divide both sides by 3.
3x= 123
3 3
x= 41
The given angles are the alternate interior angles formed by a common
transversal to two parallel lines.
The value of x for which line l is parallel to line m is c. 41°.
Reasons:
When line l is parallel to line line m, we have;
The alternate interior angles will be equal
Therefore;
(3·x - 43)° = 80°
Which gives;
[tex]x = \dfrac{80^{\circ} + 43^{\circ} }{3} =41^{\circ}[/tex]
The value of x is 41°Learn more here:
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Use the given conditions to write an equation in slope-intercept form. passing through (-2, 0) & (0, 2)
Answer:
Step-by-step explanation:
(2 - 0)/(0 + 2)= 2/2= 1
y - 0 = x + 2
y = x + 2
What is the prime factorization of 36
Answer:
[tex]2^{2} x 3^{2}[/tex]
Step-by-step explanation:
Answer:
2^2*3^2
Step-by-step explanation:
You can break down 36 through ways down to its prime factors through multiple ways like a facor tree
36
4 9
2 2 3 3
Since two and three cannot be broken down anymore, they are prime factors. Also, because you are left with two 2s and two 3s, you would mark that as squared when giving an answer.
Juan baked 5 dozens of cupcakes which cost her a total of PHP 2675.How much should she sell each cupcake if she wants to get a 25% profit?
Step-by-step explanation:
5 cupcakes = PHP 2675
25% profit =
25/100 × 2675 = 668.75
Selling price for 25% profit = 2675 + 668.75 = 3343.75
Cost of each cupcake for 25% profit = 3343.75/5
= 668.75
please help me fr tho
Answer: y=2x+1
Step-by-step explanation:
To solve for y, we want to use our algebraic properties to isolate y.
16x+9=9y-2x [add both sides by 2x]
18x+9=9y [divide both sides by 9, divide to each term]
2x+1=y
Now, we know that y=2x+1.
Answer:
no thx and thx for the points
Step-by-step explanation:
Twice the sum of a number and 7 is more than 6 or at most -3. Which compound inequality can represent this relationship
Answer:
C
Step-by-step explanation:
The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation so option (C) will be correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
Let's say that number is x
Then,
sum of a number and 7 = x +7
Twice the sum of a number and 7 is more than 6
So,
2(x + 7) > 6
And
Twice the sum of a number and 7 is at most -3, it means it can go up to -3 not more than.
So,
2(x + 7) ≤ -3
Hence "The inequality 2(x + 7) > 6 and 2(x + 7) ≤ -3 will represents the given situation".
For more about inequality,
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Can anyone help me with my algebra homework ?
Answer: No, it is not possible
Why not? Because of the phrasing "share an arm AB". If two angles share a common line, segment or ray, then they are considered adjacent angles by definition. You can think of two rooms sharing the same wall. Those rooms are adjacent. So we cannot have nonadjacent angles sharing the same arm AB.
In a particular class of 22 students, 18 are men. What fraction of the students in the class are men
Answer:
9/11
Step-by-step explanation:
The fraction that are men are
men/total
18/22
Divide the top and bottom by 2
9/11
If
3x^2+ 9x + 11
X – 1 =
3x2 + 3x + a + 23
X-1
what is the value of a?
Answer:
a = -6 - 6x + 3x^2
Step-by-step explanation:
A
Para resolver los siguientes casos, plantea sistemas de
ecuaciones en tu cuaderno y encuentra los valores de las
incógnitas.
1. Horacio quiere poner una hamaca en su jardín. Tiene una cuer-
da que mide 14 metros para amarrar los dos extremos de la
hamaca, por lo que decide cortar la cuerda en dos. Si un pedazo
de cuerda mide 4 metros más que el otro, ¿cuánto miden las
nuevas cuerdas?
2. Imagina que vas a la tienda con un amigo y compras 6 paletas
y 2 gomitas. Tu amigo pide 1 paleta y 10 gomitas. Si tú pagas
$24 y tu amigo $33, ¿cuánto cuestan las gomitas y las paletas?
porfavor ayuda es para una tarea de mañana antes de las 8
Answer:
1 La longitud de las nuevas cuerdas = 5 metros y 9 metros
2 El costo de las paletas = $ 3
El costo de las gomitas = $ 3
Step-by-step explanation:
1) Sea la primera mitad de la cuerda representada por = a
Deje que la segunda mitad de la parte superior esté representada por = b
a + b = 14 metros
De la pregunta, se nos dice que ok, la mitad es 4 metros más larga que la otra
a = b + 4
Por lo tanto
b + 4 + b = 14 metros
2b + 4 = 14 metros
2b = 14 - 4
b = 10/2
b = 5 metros
a = b + 4
a = 5+ 4
a = 9 metros
Por lo tanto, la longitud de las nuevas cuerdas = 5 metros y 9 metros
2)
Representemos el costo de las paletas = p
Costo de gomitas = g
De la pregunta 2 se nos dice que:
Tu vas a la tienda con un amigo y compras 6 paletas y 2 gomitas. Si tú pagas $ 24
Por tanto: 6p + 2g = 24 ....... Ecuación 1
Tu amigo pide 1 paleta y 10 gomitas. y tu amigo $ 33
p + 10g = 33 ....... Ecuación 2
p = 33 - 10g
Sustituya p por 33 - 10g en la Ecuación 1
6p + 2g = 24 ....... Ecuación
6 (33-10 g) + 2 g = 24
198 - 60 g + 2 g = 24
-58g = 24-198
-58g = - 174
g = -174 / -58
g = $ 3
Para encontrar p
p = 33 - 10g
p = 33 - 10 × 3
p = 33 - 30
p = $ 3
Por lo tant,
El costo de las paletas = $ 3
El costo de las gomitas = $ 3
Choose the algebraic expression that represents the area of a triangle that has a base 4 inches less than 5 times wider than the height.
a (1/2)(5h)(h – 4)
b (1/2)(5b + 4)(b)
c (1/2)(5h – 4)(h)
Answer:
c (1/2)(5h – 4)(h)
Step-by-step explanation:
Area of a triangle = 1/2 × base × height
Let
Height of the triangle = h
Base 4 inches less than 5 times wider than the height.
Base of the triangle = 5h - 4
Area of a triangle = 1/2 × base × height
= (1/2)(5h-4)(h)
The algebraic expression that represents the area of a triangle that has a base 4 inches less than 5 times wider than the height is (1/2)(5h-4)(h)
Option C is the correct answer
Answer:
c
Step-by-step explanation:
i had this same question a while ago
A landscape architect wants to plant a circle of flowers around a triangular garden. She has sketched the triangle on a coordinate grid with vertices at A (0, 0), B (8, 12), and C (18, 0). Explain how the architect can find the center of the circle that will circumscribe triangle ABC. Then find the radius of the circumscribed circle.
Answer:
The center of the circle is the point (6,3)
I don’t get thiss so can someone help me
Step-by-step explanation:
use algabraic expreshens it will help trust me
SOMEONE HELP I NEED THE ANSWERS TO THIS PROBLEM
Answer:
Step-by-step explanation:
∠6 = 45 {Vertically opposite angles are equal}
∠6 + 5x + 35 = 180 {Co interior angles}
45 + 5x + 35 = 180 {add like terms}
80 + 5x = 180
5x = 180 - 80
5x = 100
x = 100/5
x = 20
5x + 35 = 5*20 + 35 = 100 + 35 = 135
∠8 = 5x + 35 { Corresponding angles}
3) ∠8 = 135
4) ∠ 3 = ∠6 {Alternate interior angles are equal}
∠3 = 45
5) ∠6 = 45
any help please, asap
J = 0 because it is the midpoint of K and P.
Since we know that K is at -5 and P is at 5, KP = 10
Both KP and JQ are equal to 10, therefore, they are equal.
Answer:
14. j=0
15. KP=10
16. yes
Step-by-step explanation:
(The two letters next to each other means that the question is asking for the distance between the points. For example, KP is the distance from K to P, or P to K.)
14.:
If P is the midpoint of J and Q, that means that there is an equal distance between Q and P and J and Q. So, you can see this because
Q-P=5 and 5*2= J
So the distance from J to Q is 10, but to find what J is, subtract the distance from Q, leaving you with 0. So, J=0.
15.:
Since each line represents 5 and the distance from -5 to 5 is 10, KP = 10.
16.:
Since KP = 10 and JQ = 10, then yes, they are the same.
helphelphelphelphelphelph
Answer:
first 2 are right and last is right, but 3 is 30 not 66
Step-by-step explanation:
Answer:
you got 1 and 2 and 4 right but 3 is 30
Step-by-step explanation:
3 is 30 because you have to multiply before you add due to pemdas
Find the base for the following items.
4 is 1% of what number?
Answer:
400
Step-by-step explanation:
Does the following number belong to the interval (1.5, 2.4) ?
Square root of 2
Square root of 3
Square root of 5
Square root of 6
Yes or no
Answer:
Square root of 2: No
Square root of 3: Yes
Square root of 5: Yes
Square root of 6: No
Step-by-step explanation: Verified by RSM
Consigna:
Resuelve el siguiente problema:
Para comprar un juego de mesa para divertirnos en familia durante la pandemia. yo aporté un quinto (6)
del total del precio, mi hermana María aportó la sexta parte (') y mi papá aporto el resto que faltaba.
¿Qué parte del costo del del juego aportó mi papá? Si pagamos el total de $90, ¿Cuánto dinero puso
cada uno?
DATOS
GRÁFICOS O DIBUJOS OPERACIONES
RESULTADOS
Answer:
El padre pago el 63% del valor del juego, es decir, $57.
Step-by-step explanation:
Si el valor total del juego es de $90, y el redactor aportó una quinta parte del total del precio, el total aportado por él es de $18 (90 / 5 = 18). A su vez, su hermana María aportó una sexta parte del valor, es decir $15 (90 / 6 = 15). Por ende, el padre de los niños aportó $57 (90 - 18 - 15 = 57), es decir, el 63% del valor total.
Solve for k.
k/4 + 8 = 12
Answer:
k = 16
Step-by-step explanation:
To solve this we must isolate k. Let's first simplify this equation by subtracting 8 from both sides:
k/4 = 4
Next, remove the fraction by multiplying both sides by 4:
k = 16
Both of the equations below have the same solution when solved for x. What is the value of t?
Answer:
-.75x-6
Step-by-step explanation:
Step 1: simplify the first equation
1/4(x-28)=2x, or .25x-7=2x.
Step 2: simplify the second equation so that one side equals 2x
13-5x=-7.5x-t. Add 7x to either side to get 13+2x=-.5x-t. Then, subtract 13 from either side and then you have 2x=-.5x-t-13
Step 3: make both equations into one equation
Since 2x=.25x-7, and 2x=-.5x-t-13, then it's safe to say .25x-7=-.5x-t-13.
Step 4: Simplify this final equation
Add .5x to both sides to get .75x-7=-t-13. Then add 13 to both sides to get .75x+6=-t. Then multiply everything by -1 to get -.75x-6=t
Multiply (6x^3+8)(7x^2+8x+7)
MATH QUESTION... NEED HELP
Answer:
C. 7 inches I hope this helps
1. Ms. Scott raised $4,763 for the local charity. Find the opposite of this integer.
Answer:
D
Step-by-step explanation:
Shsgbsbdh
Barbara’s soccer team selected 15 girls from 75 girls who tried out for the team. What decimal is equivalent to the fraction of girls selected from the group
Answer:
.2
Step-by-step explanation:
15 /75
Divide the top and bottom by 15
1/5
Changing to decimal form
1/5 * 2/2 = 2/10
.2