The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The sample-set S consists of all combinations of 6 distinct elements of the set of 50 elements, and;
[tex]\rm |S| =C(50, 6)=\dfrac{50!}{44!6!}[/tex]
The winning event E ⊆ S is just one winning combination, so that
|E| = 1.
Therefore, the probability of winning a lottery is;
[tex]\rm P(E)=\dfrac{|E|}{|S|}\\\\ P(E)=\dfrac{1}{\dfrac{50!}{44!6!}}\\\\\\ P(E)=\dfrac{44!6!}{50!}\\\\ P(E)= 6 \times 10 {-8}[/tex]
Hence, The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
Learn more about probability here;
https://brainly.com/question/18162805
#SPJ4
Last month, luke spent $1,300 on his mortgage (home loan payment), $320 for food, $280 on entertainment, $275 for his car payment, $60 on car insurance, and $75 on clothing. what was the difference for the month between his fixed expenses and variable expenses? brainly
pls help!! 15 points!
A trapezoidal prism undergoes a dilation. The surface area of the pre-image is 35 m2. The surface area of the image is 315 m². The height of the pre-image is 5.8 m. What is the height of the image? Enter your answer as a decimal in the box m
When trapezoidal prism undergoes a dilation, the size of the prism changes
The height of the image is 52.2 meters
How to determine the height of the image?The given parameters are:
A1 = 35 m²
A2 = 315 m²
H1 = 5.8 m
To calculate the height of the image, we make use of the following equivalent ratio
A1 : H1 = A2 : H2
So, we have:
35 : 5.8 = 315 : H
Express as fractions
35/5.8 = 315/H
Make H the subject
H = 315 * 5.8/35
Evaluate the product
H = 52.2
Hence, the height of the image is 52.2 meters
Read more about dilation at:
https://brainly.com/question/3457976
Answer:
17.4
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer: Statements 3, 4, 5
Step-by-step explanation:
Statement (3) is true because an interior angle and its exterior angle are supplementary.
Statement (4) is true by the exterior angle theorem.
Statement (5) because the sum of the angles of a triangle is 180 degrees.
Find the value of X
And tell whether the side lengths form a Pythagorean triple
Answer:
8 and yes
Step-by-step explanation:
c² - b² = a²
100 - 36 = a²
64 = a²
a = 8
the three sides form a sequence, 6, 8, 10, which is the pythagorean triple.
thankyou for all the help
Answer:
1. x + y = 180
2. x = 50 y= 130
Step-by-step explanation:
They're parallel.
We can label the unamed angle z.
So z = y
and 50 = x
There's 360 degrees in a circle, so x + y= 180 because it's half 360 and half a circle.
x=50
so 50 + 50 = 100.
360 - 100 = 260
so 260 ÷ 2 = 130
y = 130 because y and z are equal so they're the same number
Step-by-step explanation:
1. x+y=180
hope that helps
Find the value of each variable. 22, 30, x.
x=
y=
(Simplify your answers. Type exact answers, using radicals as needed.
please hurry for fifty points!
Answer:
11 and 11 root 3
This is because it is a 30 60 90 triangle, making it x, x root 3, and 2x.
Answer:
x = 11, y = 19.05
Step-by-step explanation:
sin 30 = x/22
22*sin 30 = x
22*0.5 = x
11 = x
tan 30 = 11/y
0.577350269 = 11/y
y = 11/0.577350269
y = 19.0525589
y= 19.05
Hope this helps :)
WHOEVER RESPONDS FIRST WILL GET MARKED BEST.
A circle has a diameter of 14.5 inches. Using 3.14 for 1, what is the circumference of the circles, rounded to the nearest hundredth of an inch?
22.77 inches
45.53 inches
91.06 inches 165.05 inches
[tex]c = 2 \pi \: r[/tex]
[tex]c = 2 \times 3.14 \times 14.5[/tex]
[tex]c = 91.06[/tex]
Answer:
2nd option - 45.53 inches
Step-by-step explanation:
Circumference of a circle when given the diameter is given by the formula :
[tex]\pi d[/tex]
Since we are given a certain value for pi we use that and multiply it by the diameter to given the cirumference:
3.14 × 14.5 in =
45.53 inches
Therefore our answer is 43.53 inches (the 2nd option)
solve pls brainliest
Answer:
No, no, no, yes, yes.
Step-by-step explanation:
A integer is a whole number, 1, 2, 3, etc.
Here is an expression 3/5 divided by 1/4 Which situation matches this expression?
Which situation matches this expression?
A: An athlete runs 3/5 kilometers in 4 minutes. At that rate, how many kilometers does the athlete run in 1 minute?
B: A teacher fills an empty white pitcher with 3/5 gallons of water and an empty blue pitcher with 1/4 gallon of water. How many more gallons of water are now in the white pitcher than in the blue pitcher?
C: Mr. Smith has 3/5 pounds of beans. He uses 1/4 pound of beans each week. At the rate, for how many weeks will beans last?
D: A worker cuts pieces of string that are each 3/5 yards in length. How many pieces of string can the worker cut from a piece of string that is 1/4 yard in length?
Answer:
C
Step-by-step explanation:
To find A you have to divide 3/5 by 4 so that would not work.
To find B you have to subtract 1/4 from 3/5 and that doesn't match the problem.
To find C you do divide 3/5 by 1/4 which matches the problem.
And lastly for D you would divide 1/4 by 3/5 which is the opposite of what the question is asking for.
Find the surface area of the prism shown below.
-4-(3) =
3+(-5) =
4+6=
-5-9=
-4+(-9) =
Step-by-step explanation:
-4-(3)=-7
step two
3+(-5)=-2
step three
4+6=10
step four
-5-9=-14
step five
-4+(-9)=-13
Answer:
a) -4 - ( 3) = - 7
b) 3 + ( -5) = 3 - 5 = -2
c) 4 + 6 = 10
d) -5 -9 = - 14
e) -4 + ( -9) = -4 -9 = - 13...
learn.flvs.net/educator/student/examform.cgi?eprice34 annсait*sit=bNTabyUk8FP9A*4870*0017
Lessons
W FLVS
Assessments
✓ Gradebook
Email 9
$ Tools -
Question 4(Multiple Choice Worth 1 points)
(03.01 MC)
Simplify 972-317 + V8 - 28
011/2-5/7
0 1184 – 5/14
065
be
C 6/9
Question 5 Multiple Choice Worth 1 points)
(03.01 LC
Answer:
The choice A.
Step-by-step explanation:
[tex]9 \sqrt{2} - 3 \sqrt{7} + \sqrt{8} - \sqrt{28} \\ \\ 9 \sqrt{2} - 3 \sqrt{7} + ( \sqrt{2} \sqrt{4} ) - ( \sqrt{4} \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + (2 \sqrt{2} ) - (2 \sqrt{7} ) \\ 9 \sqrt{2} - 3 \sqrt{7} + 2 \sqrt{2} - 2 \sqrt{7} \\ (9 \sqrt{2} + 2 \sqrt{2} ) + ( - 3 \sqrt{7} - 2 \sqrt{7} ) \\ 11 \sqrt{2} - 5 \sqrt{7} [/tex]
The simplified value of in radical form is 11√2 - 5√7.
What is Radical?In mathematics, a radical is the inverse of an exponent, which is represented by the symbol '√' , also known as root. It can be a square root or a cube root, and the number preceding the symbol or radical is known as an index number or degree. This is a whole integer with an exponent that cancels out the radical.
We have 9√2 - 3√7 + √8 - √28
First, solve the radical as possible
√8= 2√2
and, √28= 2√7
So, 9√2 - 3√7 + √8 - √28
= 9√2 - 3√7 + 2√2- 2√7
= 9√2 + 2√2- 3√7- 2√7
= 11√2 - 5√7
Learn more about Radical here:
https://brainly.com/question/1369233
#SPJ7
if 192 students are in 4 buses how many students are in each bus?
Answer:
48
Step-by-step explanation:
192/4=48
Hope this helps!!!
Answer:
48 students
Step-by-step explanation:
Given that:
192 student are in 4 buses
To Find:
How many students are in each bus
Solution:
To find how many students are in each bus we have to divide. 192 by 4.
192 ÷ 4 which given us 48.
Therefore, there are 48 students in each bus.
~lenvy~
The area of a square is (9a2 − 24a + 16) square units. determine the length of each side of the square by factoring the area expression completely. show your work.
can someone please help me
A bike rental company charges its customers p dollars per day to rent a bike, where 5≤p≤30. the number of bikes rented per day can be modeled by the linear function n(p)=300−10p. how much should the company charge each customer per day to maximize revenue? do not include units or a dollar sign in your answer.
Using the vertex of a quadratic equation, it is found that the company should charge each customer $15 per day to maximize revenue.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the number of bikes rented per day is given by:
n(p) = 300 - 10p.
Hence, the revenue function is given by:
R(n) = p x n(p)
R(n) = 300p - 10p².
Which is a quadratic function with coefficients a = -10, b = 300. Hence, the price in dollars that will maximize the revenue is given by:
[tex]x_v = -\frac{300}{-20} = 15[/tex]
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
PLS HELP ME FRENDS I NEED HELP HELP THIS IS MY LAST CHANCE What is the area of the real object that the scale drawing models?
Answer:
D. 16 square cm
Step-by-step explanation:
To solve this problem, we will have to look at the Scale factor.
1 : 8 = 1 cm (in the scale drawing) = 8cm (in the real object)
Since the area of the scale drawing is 2 cm, the equation will be 2 x 8 = 16.
Therefore, 16 will be the area of the real object.
-kiniwih426
Hello people ~
factorise↷
x^2 + 4x –21
Let's see
[tex]\\ \rm\rightarrowtail x^2+4x-21[/tex]
[tex]\\ \rm\rightarrowtail x^2+7x-3x-21[/tex]
[tex]\\ \rm\rightarrowtail x(x+7)-3(x+7)[/tex]
[tex]\\ \rm\rightarrowtail (x-3)(x+7)[/tex]
What is the value of x in the equation −5 + x = −2?
[tex]-5+x = -2\\\\\implies x = -2 +5 = 3[/tex]
Answer:
x=3
Step-by-step explanation:
−5 + x = −2
Add 5 to each side
−5+5 + x = −2+5
x = 3
Do number 17 please.
Answer:
667.2
Step-by-step explanation:
aP/2 apothem is 13.9, perimeter is 16(6)= 96
multiply apothem and perimeter then divide by 2.
Donna bought 5 bags of dog treats for 12.55. What is the cost per bag
Answer:
$2.51
Step-by-step explanation:
12.55/5= 2.51
a bag of dog treats is 2.51 per bag
Use the multiplier method to increase £56 by 14% you must show your working out
Answer:
Step-by-step explanation:
First, we have to find 14% of 56
14% of 56 is = 56 x 14/100
= 7.84
Now we have to increase the number 56 by 14%, which means we have to add 14% of 56 (7.84) to the given number (56)
56 + (14% of 56)
= 56 + 7.84
= £63.84
Fill in the table using this function rule
y=2x+2
Photo ⬇️
Answer:
Step-by-step explanation:
Put the values of x to the equation y = 2x + 2 and calculate the value of y:
x = 2
y = 2 · 2 + 2 = 4 + 2 = 6
x = 5
y = 2 · 5 + 2 = 10 + 2 = 12
x = 6
y = 2 · 6 + 2 = 12 + 2 = 14
x = 8
y = 2 · 8 + 2 = 16 + 2 = 18
Please help I'm extremely confused.
Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale. (picture of diagram included )
Answer:
8.4 is the correct answer on acellus
The graph of $y = f(x)$ is symmetric across the line $x = 5$. The graph also passes through the point $(8,-7).$ Find another point that must lie on the graph of $y = f(x).$
Because we know one point and an axis of symmetry, we know that the point (2, -7) must lie on the graph.
Which other point must lie on the graph?If a function has a line of symmetry at x = x₀, then we know that:
f(x₀ + x) = f(x₀ - x).
So we have symmetry around that line.
Then, if the line of symmetry is at x = 5 and we know that:
f(8) = f(5 + 3) = -7
We also must have:
f(2) = f(5 - 3) = -7
Then the point (2, - 7) must be on the graph.
If you want to learn more about symmetry you can read:
https://brainly.com/question/11408596
What is the angle of rotation for point G mapped to point H?
90° clockwise
72° clockwise
72° counterclockwise
90° counterclockwise
The rotation of point G to point H is an illustration of a circular movement
The rotation that maps point G to point H is 72 degrees clockwise
How to determine the rotation rule?From the figure, we have the following parameters:
Number of sections (n) = 5
Angle at the center = 360
The angle of rotation is then calculated as:
Rotation = 360/5
Evaluate
Rotation = 72
Point H is to the left of point G.
This represents a clockwise direction
Hence, the rotation that maps point G to point H is 72 degrees clockwise
Read more about rotation at:
https://brainly.com/question/4289712
Answer:
72° clockwise
Step-by-step explanation:
What is the area of triangle ABC?
Answer:
Step-by-step explanation:
The mayor of a city believes a large park in the city is becoming more popular and wants to expand nature programs at the park. A random sample of 30 summer days are selected and the number of park visitors is determined for each of those days. From this sample, the mean number of visitors was X(xbar) = 98.3 with a standard deviation of Sx = 11.2. Calculate a 99% confidence interval for the true mean number of visitors on summer days. Assume the conditions for inference are met.
a. 95.192 to 101.410 visitors
b. 34.123 to 162.480 visitors
c. 92.664 to 103.940 visitors
d. None of these is correct.
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 99% confidence interval for the true mean number of visitors on summer days is given by:
c. 92.664 to 103.940 visitors
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 30 - 1 = 29 df, is t = 2.756.
The other parameters are given as follows:
[tex]\overline{x} = 98.3, s = 11.2, n = 30[/tex].
Hence, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 98.3 - 2.756\frac{11.2}{\sqrt{30}} = 92.664[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 98.3 + 2.756\frac{11.2}{\sqrt{30}} = 103.94[/tex]
Hence option c is correct.
More can be learned about the t-distribution at https://brainly.com/question/16162795
If it is now two o'clock, how many hours later will be the first hour between the arrows of the clock is 90 degrees
Answer: 4 o clock
Step-by-step explanation:
Answer:
5 o' clock
Step-by-step explanation:
The angle between the hands of a clock on an hourly basis is 30°
thus for the hands to be 90° apart would be 3 hours
then 2 o' clock + 3 hours = 5 o' clock
The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4. 9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground
Using the given function, it is found that the projectile hits the ground after 20 seconds.
When does the projectile hits the ground?It hits the ground when it's height, given by h(t), is equals to zero.
In this problem, the function that models it's height is given by:
h(t) = -4.9t^2 + 98t.
Then:
h(t) = 0
-4.9t^2 + 98t = 0.
-4.9t(t - 20) = 0
t - 20 = 0 -> t = 20.
The projectile hits the ground after 20 seconds.
More can be learned about functions at https://brainly.com/question/25537936