The value of P(S or T) is 71/110.
What is mutually exclusive event?
If two events cannot happen simultaneously, they are mutually exclusive or discontinuous. The results of a single coin flip, which can result in either heads or tails but not both, serve as an obvious illustration.
As given,
S and T are mutually exclusive events. P(S)= 6/11 , P(T)= 1/10.
By using,
P(S ∪ T) = P(S) + P(T) - P(S ∩ T)
= 6/11 + 1/10 - P(S ∩ T)
= 71/110 - P(A ∩ T)
But the events S and T are mutually exclusive events.
therefore, P(S ∩ T) = 0.
So,
P(S ∪ T) = 71/110
Therefore, value of P(S or T) is 71/110.
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Determine if the triangles are similar. If similar, state how and complete the similarity statement.
Answer:
SAS (Both sides share common angle n, and the sides, 40 : 65 and 32 : 52 have the same ratio)
▲LMN ~ ▲GHN
Steve drives an electric car. He can drive 425 kilometres before he needs to stop and re-charge his car. It takes 10 minutes to charge 50 kilometres. How long does Steve have to wait for his car to fully charge?
Steve has to wait for 1 hour 25 minutes
Answer: 1 h 25 min
Step-by-step explanation:
Let us make the proportion:
10 min - 50 km
x min - 425 km
Hence,
[tex]\displaystyle\\x=\frac{425(10)}{50} \\\\x=\frac{85(5)(10)}{5(10)} \\\\x=85 \ min\\\\x=(60+25) \ min\\\\x=1\ hour\ 25\ min[/tex]
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 30 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer:
largest angle = 90°
Step-by-step explanation:
let the smallest angle be x then and other 2 angles are 3x and x + 30
the sum of the 3 angles in the triangle sum to 180° , that is
x + 3x + x + 30 = 180
5x + 30 = 180 ( subtract 30 from both sides )
5x = 150 ( divide both sides by 5 )
x = 30
3x = 3 × 30 = 90
x + 30 = 30 + 30 = 60
the 3 angles are 30° , 60° , 90°
with 90° being the largest
The picture won't load but it's a problem that asks: use the picture to determine which inequality represents the graph
First, we find the slope of the line using the points the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (-1, -1) and (0, 1). Where
[tex]m=\frac{1-(-1)}{0-(-1)}=\frac{1+1}{1}=\frac{2}{1}=2[/tex]Given that the slope is 2, then the answer is in the first column.
Observe that the region of solutions is above the solid line, which means the answer is
[tex]y\ge2x+1[/tex]The right answer is D.x/5 = 15
please quick now now now faults hurry
Answer:
x=75
Step-by-step explanation:
Answer:
x = 75
Step-by-step explanation:
x/5 = 15
Multiply 5 on both sides
x = 75
Use the following function rule to find f(–3a + 7). Simplify your answer.
f(b) = – 8b
f (–3a + 7) = ?
The functional value of f(-3a + 7) is 24a - 56
What is a function?
A rule that assigns a specific element of B to each element of A is known as a function from A to B. Both A and B are referred to as the function's domain and codomain, respectively. A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
There are different operations on functions like addition, subtraction, multiplication, division, and composition of functions.
Here we have,
the given function is
f(b) = -8b
f(-3a + 7) = -8(-3a + 7)
= 24a - 56
Hence, the functional value of f(-3a + 7) is 24a - 56
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Find the volume of a cone with a height of 9 cm and a base diameter of 6 cm. Use the value 3.14 for , and do not do any rounding. Be sure to include the correct unit in your answer. Explanation Check cm 6 cm 0 A cm X cm² cm³ ?
Given:
Required:
We need to find the volume of given cone
Explanation:
Take
[tex]\begin{gathered} r=\frac{6}{2}=3\text{ cm} \\ \\ h=9\text{ cm} \\ \pi=3.14 \end{gathered}[/tex]The volume of cone is
[tex]V_c=\frac{1}{3}\pi r^2h[/tex]Plug the values
[tex]V_c=3.14*\frac{1}{3}*3*3*9=84.78\text{ cm}^3[/tex]Final answer:
Volume of cone is 84.78 cubic cm
two boats leave a dock at the same time. boat a goes due north 500 feet and stops. boat b goes due east 400 feet and stops and turns directly towards boat a. what angle must b turn to face and proceed directly to boat a
By using Trigonometry, it is obtained that
The boat must turn by 51.34° to face and proceed directly to boat A
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
Here,
The diagram has been attached here.
Let C be the starting point A and B be the position of boat A and boat B respectively
Boat A goes due north 500 feet and stops
Boat B goes due east 400 feet and stops
Let the angle by which B turn to face and proceed directly to boat A be [tex]\theta[/tex]
By using Trigonometry,
[tex]tan\theta =\frac{500}{400}\\\\tan\theta =\frac{5}{4}\\\\\theta = 51.34^{\circ}[/tex]
The boat must turn by 51.34° to face and proceed directly to boat A
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Solve the following quadratic equation using the zero product property.
3(7-x)(x+1)=0
Answer:
x = - 1 , x = 7
Step-by-step explanation:
3(7 - x)(x + 1) = 0
equate each factor to zero and solve for x
7 - x = 0 ⇒ x = 7
x + 1 = 0 ⇒ x = - 1
Alpha Company sells their product for $ 1 each. The variable costs are $ 7 per unit and the fixed costs are $ 30,000 per year. How much should we sell the unit to: 1- Reach the break-even point 2- Achieve a net profit of $ 21,000 3- Achieve a net profit equal to $ 21,000.
we have that
Part 1
Remember that breakpoint is when the revenue (R) is equal to the cost (C)
so
C=7x+30,000
R=10x
equate both equations
10x=7x+30,000
solve for x
10x-7x=30,000
3x=30,000
x=10,000 units
the answer Part 1 is 10,000 unitsPart 2
net profit of $ 21,000
so
R-C=21,000
10x-(7x+30,000)=21,000
10x-7x-30,000=21,000
3x=21,000+30,000
3x=51,000
x=17,000 unitsPart 3
net profit equal to $ 60,000
so
R-C=60,000
10x-(7x+30,000)=60,000
10x-7x-30,000=60,000
3x=60,000+30,000
3x=90,000
x=30,000 units
28. Find four consecutive integers with the sum of 54.
The four consecutive integers with the sum of 54 is 12, 13, 14, 15
Let the four consecutive integers be x, x+1 , x+2, x + 3
x + x + 1 + x + 2 + x + 3 = 54
4x + 6 = 54
4x = 48
x = 12
The consecutive integers are
x = 12
x + 1 = 12 + 1 = 13
x + 2 = 12 + 2 = 14
x + 3 = 12 + 3 = 15
Therefore, the four consecutive integers with the sum of 54 is 12, 13, 14, 15
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Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it. (10 points)
f(x) h(x)
f(x) = −4(x − 8)^2 + 3 graph of negative 1 times the quantity of x minus 3 squared, plus 2
I have attached a picture of the graph below.
Please do not answer if you don't know or are not sure. Thank you.
Answer:
x = 8 for f(x) and x = 3 for h(x)
Step-by-step explanation:
the axis of symmetry is a vertical line which passes through the vertex of the graph with equation
x = c ( c is the value of the x- coordinate of the vertex )
the equation of a parabola in vertex form is
f(x) = a(x - h )² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
f(x) = - 4(x - 8)² + 3 ← is in vertex form
with vertex (h, k ) = (8, 3 )
equation of axis of symmetry of f(x) is x = 8
given the graph of h(x) with vertex = (3, 2 ) , then
equation of axis of symmetry of h(x) is x = 3
Q
R
85°
6.7 cm
8.0 cm
38°
S
6.7 cm
38°
8.0 cm
What is the measure, in degrees, of
U
Answer:
VB.
Step-by-step explanation:
Mrs Nunez brought person receive? 2 1/2 cakes to school for her class. If there are 15 people in the class including Mrs. Nunez, how much cake will each person receive?
between which two numbers is = 1.5 located on a number line -4 and 3
EXPLANATION
Given the number 1.5, is located between 1 and 2.
If 0 ° < θ < 90 °, find θ to the nearest minute 1. Cos θ = 0.892. Cos θ = 0.729
1. Cos θ = 0.89
θ = 27.13 degrees
2. Cos θ = 0.729
θ = 43.20 degrees
Explanation:Given:
1. Cos θ = 0.89
θ = arccos(0.89)
= 27.13 degrees
2. Cos θ = 0.729
θ = arccos(0.729)
= 43.20 degrees
A city has a population of 260,000 people. Suppose that each year the population Grows by 6%. What will the population be after 5 years?
Answer:
3343621.39918 or rounding would be 3343621.40
Step-by-step explanation:
this is because taking 260,000 divided by .6 then dividing that answer by .6 so on till you done that five times
On Thursday, ShopRite sold 210 pounds of produce. On Friday they sold twice that amount. On Saturday they only sold 130 pounds. How much more produce did they sell on Friday than Saturday? Show your work
Write the sentence as an equation. 238 is 84 more than p Type a slash (/) if you want to use a division sign.
238 = 84 + p
definition of more than is to add.
definition of "is" is total
The map shows air travel distances from Minneapolis to four other cities. Use the triangle
inequality to find the range of possible distances between:
Minneapolis
1584
San Francisco
355
1056
1018
Chicago
Houston
New York
a.
b.
C.
d.
Chicago and Houston
San Francisco and Chicago
New York and San Francisco
Houston and New York
Answer:7
Step-by-step explanation:
Write it on the venn diagram:-School starts may include your expectations ; School ends include your experience. -The Center/middle area may include your experience from the start until this day.
It is a pictorial representation that shows a logical relations between sets.
The centre portion of the set is the intersection between the two sets. This will represent your experience from the start until this day.
The other portion of school starts will represent expectation while for school emds will represents your experience as shown
A longitudinal wave produced on a toy slinky travels at a speed of 30 m/s with a frequency of 20 Hz. Find the minimum separation between the consecutive compressions of the slinky.
Answer:
pagal
Step-by-step explanation:
pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagal pagalwhat is the meaning of a mad person
9. The graph shows a proportional relationship between the variables x and y. a. Write an equation to model the relationship. b. Reasoning Explain how you know if an equation or a graph represents a proportional relationship. у 96 72 48 24 X 2 4 6 8
Answer:12x
Step-by-step explanation:
Find the value of csc (13π/6) using the unit circle.
The meaning of 13*pi/6 is as if you made 13 complete revolutions around the point pi/6.
therefore, is the same calculate the sin of 13pi/6 than the sin of pi/6.
[tex]\begin{gathered} sin(\frac{\pi}{6})=\frac{1}{2} \\ sin(\frac{13\pi}{6})=\frac{1}{2} \end{gathered}[/tex]Substituing:
[tex]csc(\frac{13\pi}{6})=\frac{1}{sin(\frac{13\pi}{6})}=\frac{1}{\frac{1}{2}}=2[/tex]The answer is: csc(13pi/6)=2.
use the portion of the exponential graph below to answer questions 1. what is the domain 2. what is the range
Given:
Exponential graph.
Find-: 1) Domain
2) Range
Sol:
1)
Domain - The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
The input value is shown in the x-axis so in given graph possible value of x is:
[tex]\begin{gathered} \text{ Domain is:} \\ x\in[-1,3] \end{gathered}[/tex]2)
Range - The range of a function is the set of outputs the function achieves when it is applied to its whole set of outputs. In the function machine metaphor, the range is the set of objects that actually come out of the machine when you feed it all the inputs.
Output value for function is shown in y-axis
[tex]\begin{gathered} \text{ Range is:} \\ y\in[6,27] \end{gathered}[/tex]
Hello! I need some assistance with this homework question, pleaseQ2
Recall that:
[tex](f\cdot g)(x)=f(x)g(x)\text{.}[/tex]Then, if:
[tex]\begin{gathered} x\in\text{Dom(f)}\cap Dom(g) \\ \text{then} \\ x\in\text{Dom(f}\cdot g)\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\begin{gathered} x\in\text{Dom(f}\cdot g)\text{ if } \\ f(x)\text{ and g(x) exists,} \\ \text{then} \\ x\in\text{Dom(f)}\cap Dom(g). \end{gathered}[/tex]Therefore:
[tex]\text{Dom(f}\cdot g)=\text{Dom(f)}\cap Dom(g).[/tex]Answer: True.
whats the percentage of the object shaded?
Answer:
50%
Step-by-step explanation:
1/4 + 1/4 = 1/2 = 50%
:)
Nadia sells small boxes of chocolates and large boxes of chocolates.
The total number of chocolates in 3 small boxes and 1 large box is 66
The total number of chocolates in 1 small box and 2 large boxes is 72
Work out the number of chocolates in each small box and the number of chocolates in each large box.
Answer:
small box: 12large box: 30Step-by-step explanation:
You want the numbers of chocolates in a small box and a large box given these total numbers:
3 small, 1 large total 661 small, 2 large total 72EquationsIf x and y represent the numbers of chocolates in a small box and a large box, respectively, these relations can be written ...
3x +y = 66x +2y = 72SolutionSubstituting for y in the second equation, we have ...
x + 2(66 -3x) = 72
-5x +132 = 72 . . . . . . simplify
60 = 5x . . . . . . . . . add 5x-72 (keeps the numbers positive)
12 = x . . . . . . . . . . divide by 5
y = 66 -3(12) = 30 . . . . . use the expression for y to find y from x
The number in a small box is 12; the number in a large box is 30.
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If the length of EG is 22, find the length of EQ
Given that:
Diameter of the circle, EG = 22
To find EQ, take the half of the diameter.
[tex]\begin{gathered} EQ=\frac{EQ}{2} \\ =\frac{22}{2} \\ =11 \end{gathered}[/tex]The third option is correct.
If I drive 250 miles on Tuesday and 180 miles on Wednesday. How many miles did I drive in all? (Multiply)
The miles drive on Tuesday is , 250 miles.
The miles drive on Wednesday is , 180 miles.
The total miles drive on Tuesday and Wednesday is, the sum of drive on Tuesday and Wednesday.
[tex]S=250+180[/tex][tex]S=430.[/tex]Thus, the total miles drive on Tuesday and Wednesday is, 430 miles.