Answer:
The speed is 74.0 miles per hour and the angle is 65.1° north-east
Step-by-step explanation:
We resolve the distance moved by the wind and plane into horizontal and vertical components. The direction moved horizontally by the plane is 178sin7.1 = 22 miles.
Since the wind is moving south east, it is at 45 south of east or a bearing of 135.
Since the wind speed is 30 mph and it takes 2 hours to complete the trip, the horizontal distance moved by the wind is vtcos135 = 30 × 2cos45 = 42.43 miles
Also, the vertical displacement moved by the wind is vtsin135 = -30 × 2 sin45 = -42.43 miles
The displacement moved vertically by the plane is 178cos7.1 = 176.64 miles
The total horizontal displacement of the plane is 22 miles + 42.43 miles = 62.43 miles
The total vertical displacement of the plane is 176.64 miles - 42.43 miles = 134.21 miles
The resultant displacement is thus d = √(62.43² + 134.21²) = 148.02 miles
The direction of this displacement is thus
Ф = tan⁻¹(total vertical displacement/total horizontal displacement)
= tan⁻¹(134.21/62.43)
= tan⁻¹(2.1498)
= 65.05°
= 65.1° to the nearest tenth degree.
The speed is thus v = distance/ time = 148.02 miles/ 2 hours = 74.01 mph ≅ 74 mph. Since the direction of the displacement is the direction of the velocity, the velocity is thus 74 miles per hour at 65.1° north-east.
So the speed is 74.0 miles per hour and the angle is 65.1° north-east
Help me plz? Plllzzzz?
find the area of triangle whose vertices are (- 8,4 )(- 6,6) and (- 3,9)
Answer:
Area of the triangle = 0
Step-by-step explanation:
We are given the vertices of a triangle as: (- 8,4 ), (- 6,6), (- 3,9)
The formula to find the Area of the triangle =
1/2[ x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
Where :
(x₁, y₁) = (- 8,4 )
(x₂, y₂) = (- 6,6)
(x₃, y₃) = (- 3,9)
Area of the triangle = 1/2[-8(6 - 9) + -6(9 - 4) + -3(4 - 6)]
= 1/2[ (-8 × -3) +( -6 × 5) +( -3× -2)]
= 1/2[ 24 - 30 + 6)
= 1/2[ 24 + 6 - 30]
= 1/2 [30 - 30]
=1/2[ 0 ]
= 0
Therefore, the area of triangle whose vertices are (- 8,4 ), (- 6,6) and (- 3,9) is ZERO( = 0 )
A basket is filled with 8 white eggs and 10 brown eggs. Half of the white eggs are cracked.
An egg is randomly selected from the basket. What is the probability that it is a cracked, white egg?
Write your answer as a fraction in simplest form.
Answer:
4 by 9 should be the answer
Step-by-step explanation:
N/A
Answer:
I think it is 2/9. I'm not sure.
Step-by-step explanation:
10/18 are brown eggs.
8/18 are white eggs.
4/18 are cracked.
Simplified answer is 2/9 chance.
Maddy and her cousin work during the summer for a landscaping company. Maddy's cousin has been working for the company longer, so her pay is 30% more than Maddy's. Last week, Maddy's cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy's hourly pay?
What is the simplified form of the equation fraction 4 over 5 n minus fraction 1 over 5 equals fraction 2 over 5 n?
n = −2
n = 4
n = fraction 1 over 2
n = fraction 2 over 3
Answer:
n=2
Step-by-step explanation:
⁴/5n-¹/5=²/5n
first we remove the denominators by multiplying all the numbers with their lcm
Lcm of 5n and 5 is 5n thus:
(5n×⁴/5n)-(¹/5×5n)=²/5n×5n
4-n=2
4-2=n
n=2
confirmationinsert 2 insted of n
⁴/5(2)-¹/5=²/5(2)
⁴/10-¹/5=²/10. simplify
²/5-¹/5=¹/5
¹/5=¹/5
so the correct value of n is 2
Please solve this question for me
x = 65° and y = 77.5°.
Step-by-step explanation:The triangle with the 50 degree angle and x, is an isosceles triangle. That means that the other unlabeled angle is also equal to x degrees.
x + x + 50 = 180
2x + 50 = 180
2x = 130
x = 65°.
Since x = 65 degrees, and the two angles make a 90 degree angle, the other unlabeled angle will be 90 - 65 = 25 degrees.
Since the other triangle is also isosceles, that triangle has two angles that measure y degrees and one angle measuring 25 degrees.
y + y + 25 = 180
2y + 25 = 180
2y = 155
y = 77.5°.
Hope this helps!
If the family decreases the clothing budget by 3 percent, what amount will it have to spend on clothing?
nearest dollar
$266
$466
$645
$665
Answer: $466
Step-by-step explanation:
Answer:
b.$466
Step-by-step explanation:
Ellen thinks if it has no slope it never touches the y axis , what can prove that her Statement is correct
Answer:
y+0
As y=0 represent x-axis whose slope is 0 and intersects y-axis at the origin.
Each new triangle shown below has one more dot per side than the previous triangle. What is the total number of dots on the 200th triangle of this sequence? Answer:
Answer:
The total number of dots on the 200th triangle is 603
Step-by-step explanation:
Please check the attachment for the diagram of the triangular dots that completes the question
From the diagram, we can see that the first triangle has 6 total dots, second has 9 total dots, third has 12 total dots;
This shows a arithmetic progression pattern of the triangles where we have our first term being 6, with our common difference being the number of dots increment on all sides as we progress which is 3
Now we want to calculate for the 200th triangle
Mathematically, the nth term of an arithmetic sequence is given as;
Tn = a + (n-1)d
where a = 6 , d = 3 and n = 200
Substituting these values in the equation above, we have
Tn = 6 + (200-1)3
Tn = 6 + 199(3)
Tn = 6 + 597
Tn = 603
Three alleles (alternative versions of a gene) A, B, and O determine the four blood types A (AA or AO), B (BB or BO), O (OO), and AB. The Hardy-Weinberg Law states that the proportion of individuals in a population who carry two different
alleles is P=2pq+2pr+2rq where p, q, and r are the proportions of A, B, and O in the
population. Use the fact that to show that p+q+r=1 is at most 2/3.
Answer:
The fact that shows that p+q+r=1 is at most 2/3 is well explained from what we have below.
Step-by-step explanation:
Given that:
The maximum of function P = 2pq+2pr+2rq is at most 2/3.
where ;
p+q+r=1
From p+q+r=1
Let make r the subject ; then r = 1 - p - q
If we replace the value for r into the given function; we have:
P = 2pq+2pr+2rq
P = 2pq+2p(1 - p - q)+2(1 - p - q)q
P = 2pq + 2p - 2p² - 2pq + 2q -2pq -2q²
P = 2p - 2p² + 2q -2pq -2q²
By applying the standard method for determining critical points we obtain:
[tex]P_p[/tex] = -4p - 2q + 2 = 0
[tex]P_q[/tex] = -4q - 2p + 2 = 0
Divide all through by 2
[tex]P_p[/tex] = -2p - q + 1 = 0
[tex]P_q[/tex] = -2q - p + 1 = 0
[tex]P_p[/tex] = -2p - q = - 1
[tex]P_q[/tex] = -2q - p = - 1
Multiplying both sides by - ; we have:
[tex]P_p[/tex] = 2p + q = 1 ----- (1)
[tex]P_q[/tex] = 2q + p = 1 ------(2)
From equation (1) ; let make q the subject ; then
2p + q = 1
q = 1 - 2p
Now; let us replace the value of q = 1-2p into equation (2) , we have:
2q + p = 1
2(1-2p)+ p = 1
2 - 4p+p = 1
2 - 3p = 1
3p = 2-1
p = 1/3
Replacing the value of p = 1/3 into equation (1) ; we have :
2p + q = 1
2(1/3) + q = 1
2/3 + q = 1
q = 1 -2/3
q = 1/3
Taking the second derivative D; we have
[tex]D = P_{pp}P_{qq}-p^2_{pq}[/tex]
D = -4 × -4 - (2²)
D = 16 - 4
D = 12
This implies that the given function has a minimum or maximum at its critical point for which 12 > 0
Therefore , the value for function p = q = r since p, q, and r are the proportions of A, B, and O in the population.
Hence r = 1/3
P=2pq+2pr+2rq
P = 2(1/3)(1/3) + 2(1/3)(1/3) + 2(1/3)(1/3)
P = 6/9
P = 2/3
determine (a) the area and (b) the circumference of the circle.
a. the area of the circle is ___
b. the circumference of the circle is ____
Step-by-step explanation:
a).To find the area of the circle we must first find the radius using the formula
radius = diameter / 2
From the question
diameter = 21 ft
The radius is
21/2 = 10.5 ft
Area of a circle = πr²
where r is the radius
Area = π(10.5)²
= 110.25π
= 346.36 cm²b).Circumference of a circle = πd
where d is the diameter
Circumference = π(21)
= 65.97cmHope this helps you
Answer:
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
Given,
Diameter of the ⭕ (d) = 21 ft
So, radius of the ⭕ (r) = ?
[tex]r = \frac{d}{2} \\ r = \frac{21}{2} \\ r = 10.5 \: \: ft[/tex]
[tex]\boxed{Radius \ = \ 10.5 \ ft}[/tex]
____________________
a) Find the area of the ⭕.
[tex]\boxed{Area \ (a) \ = \ πr^{2}}[/tex]
[tex]a = \pi \: r ^{2} \\ a = \pi(10.5) {}^{2} \\ a = 110.25 \: \pi \\ a = 110.25 × 3.14 \\ a = 346.18 \ ft^{2}[/tex]
[tex]\boxed{Area \ = \ 346.18 \ ft^{2}}[/tex]
____________________
b) Find the circumference of the ⭕.
[tex]\boxed{Circumference \ (c) \ = \ \pi \:d}[/tex]
[tex]c = \pi \: d \\ c = \pi(21) \\ c = 21\pi \\ c = 21 × 3.14 \\ c = 65.94 \ ft[/tex]
[tex]\boxed{Circumference \ = \ 65.94 \ ft}[/tex]
____________________
Value of [tex]\pi [/tex]is taken as 3.14
____________________
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
╭═══════ღ❦ღ══╮
[tex] ღRainbowSalt2^{2}2^{2} [/tex]
╰══ღ❦ღ═══════╯
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
x = 64Step-by-step explanation:
To find x we use tan
tan∅ = opposite / adjacent
From the question
The adjacent is x
The opposite is 30
So we have
tan 25° = 30/x
x tan 25 = 30
Divide both sides by tan 25
x = 30/tan 25
x = 64.34
x = 64 to the nearest tenth
Hope this helps you
Mrs. Watson wants to buy some dresses for her trip to Houston. There are three boutiques, each offering a different deal.
Table
Lara's Boutique 4 dresses for $64
The Dress Shop 5 dresses for $75
Marge's Dresses 8 dresses for $160
Which boutique has the best deal for dresses?
A. Both Marge's Dresses and Lara Boutique
B. The Dress Shop
C. Lara's Boutique
D. Marge's Dresses
Answer:
B. The Dress Shop.
Step-by-step explanation:
To find the best deal, we want to find the cost for one dress.
Lara's Boutique: $64 for 4 dresses.
x / 1 = 64 / 4
x = 64 / 4
x = $16 per dress.
The Dress Shop: $75 for 5 dresses.
x / 1 = 75 / 5
x = 75 / 5
x = $15 per dress.
Marge's Dresses: $160 for 8 dresses.
x / 1 = 160 / 8
x = 160 / 8
x = $20 per dress.
The boutique with the best deal will have the cheapest dresses. So, the best deal would be at B. The Dress Shop.
Hope this helps!
Where will her cut be located? Round to the nearest tenth. x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 A number line goes from 0 to 60. A line is drawn from 2 to 60. Genevieve is cutting a 60-inch piece of ribbon into a ratio of 2:3. Since 2 inches are frayed at one end of the ribbon, she will need to start 2 inches in. This is indicated as 2 on the number line
25.2 in.
29.4 in.
35.1 in.
40.7 in.
Answer:
The correct answer is 25.2 in.
Step-by-step explanation:
It is given that number line goes from 0 to 60 which can be used to represent a ribbon of length = 60 inches.
2 inches of the ribbon are frayed so actual length = 58 inches
Please refer to the attached image for the ribbon.
A is at 0
C is at 60
B is at 2
P is the point to divide the remaining ribbon in the ratio 2:3.
Part AB of the ribbon is frayed.
BP: PC = 2:3
Let BP = 2[tex]x[/tex] and PC = 3[tex]x[/tex]
Now, BP + PC = BC = 58 = 2[tex]x[/tex] + 3[tex]x[/tex] = 5[tex]x[/tex]
So,
[tex]5x =58\\\Rightarrow x =11.6[/tex]
BP = [tex]2\times x = 2 \times 11.6 = 23.2\ inches[/tex]
Location of the Cut = 2 + 23.2 = 25.2 inches
Alternatively, we can use the formula directly:
[tex]x = \dfrac{m} {m + n } (x_2 - x_1) + x_1[/tex]
[tex]x_1 = 2\\x_2 = 60[/tex]
m: n is the ratio 2:3
[tex]x = \dfrac{2} {2 +3 } (60- 2) + 2\\\Rightarrow 0.4 (58 )+2\\\Rightarrow 23.2+2 \\\Rightarrow \bold{25.2\ inches}[/tex]
Answer:
Yes i confirm the answer above is correct. A.) 25.2
Step-by-step explanation:
I took the test duhh
Answer choice
D) A worker with 15 years of service gets 5 weeks of vacation and each year.
Answer: it seems to be D, but the equation makes practically no sense!
The value of the factor changes for the different amounts of service years and vacation weeks.
Step-by-step explanation: The equation means that the employee is trying to figure out the value of the "v-factor" for how vacation time is earned.
If you substitute the number of service years into the left side of the "formula" and vacation weeks on the right side, then solve for "v", v(15)=5 you get v= 1/3 or 0.33
If you substitute other numbers, like v(2)=2, so v= 1 then v(30) = 8, v = 4/15 or 0.2667. You see the factor's value decreases. The company is much more generous to to employees with one or two years of service than with the older ones.
A librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections.
What is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book?
0.114
0.131
0.686
0.784
Answer:
For this case we have a total of 10 nonfiction books and 8 fiction books, we are going to assume that the selection is without replacement so then for the first case the probability of select a fiction book is:
[tex] \frac{8}{18}[/tex]
For the second selection we have 17 books remaining and the probability of select a nonfiction book is:
[tex] \frac{10}{17}[/tex]
For the last selection we have 16 books remaining and the probability of select a fiction book would be:
[tex]\frac{7}{16}[/tex]
Sinally since the events are independent the total probability would be:
[tex] \frac{8}{18} *\frac{10}{17}*\frac{7}{16}= 0.114[/tex]
Step-by-step explanation:
For this case we have a total of 10 nonfiction books and 8 fiction books, we are going to assume that the selection is without replacement so then for the first case the probability of select a fiction book is:
[tex] \frac{8}{18}[/tex]
For the second selection we have 17 books remaining and the probability of select a nonfiction book is:
[tex] \frac{10}{17}[/tex]
For the last selection we have 16 books remaining and the probability of select a fiction book would be:
[tex]\frac{7}{16}[/tex]
Sinally since the events are independent the total probability would be:
[tex] \frac{8}{18} *\frac{10}{17}*\frac{7}{16}= 0.114[/tex]
Answer:it’s A
Step-by-step explanation:
did the test
elp me BROS! its GEOMETRY 10 points REWarded, best answer gets BRAILIEST!
Answer:
Arc BD is 6.1 degrees
Step-by-step explanation:
So if 5.7 is in miles, the observer is 30096 feet above sea level, cruising height.
Solution.
Segment BC and DC are tangent to the circle,
so angles CBA and CDA are 90 degrees, hence
Triangles CBA and CDA are right triangles,
with
AC = 4005.7 miles
cos CAB = AB/AC = 4000/4005.7 = 0.9985770
angle BCA = arc cos(0.9985770) = 3.057 degrees
Arc BD = central angle BAD = 2*angle BCA = 6.114 degrees
Answer:
Step-by-step explanation:
i really just need points on my thingy so eh bye
The slope of the line is -5/7. Write a point-slope equation of the line using the coordinates of the labeled point
Answer:
The answer is C.
Step-by-step explanation:
The formula to find equation is y - y1 = m(x - x1).
Let (x1,y1) be (6,2) and m is -5/7.
So the equation is,
y - 2 = -5/7(x - 6)
Elsa's magic wand can cast 53 spells. Her wand can cast 17fewer spells than her sister Anna's wand, which is a little bigger and has more glitter. How many spells can Anna's wand cast?
Answer:
Anna's wand can cast 70 spells
Step-by-step explanation:
Elsa's wand can cast 53 spells
her wand casts 17 fewer cells than her sister Anna's
Amount of spells cast by Anna's wand = ?
We write the question down in the form of an equation
[tex]x - 17 = 53[/tex]
where [tex]x[/tex] is the amount of spells Anna's wand can cast.
we then proceed to solve by collecting like terms to different sides of the equation. We'll have
[tex]x = 53 + 17[/tex]
which leaves us with
[tex]x = 70[/tex]
This means that Anna's wand can cast 70 spells.
the sum of a two digit number and the number obtained by interchanging the digits is 154.If the tens digit number is 2 more than units digit number find the original number.
Please help me i want answer full process.I will mark the answer as brainliest plz plz plz helpe
Answer:
86
Step-by-step explanation:
We can set the first digit as (10x+y)
We can interchange it to be (10y+x)
X is the second digit and Y is the first.
1) (10x+y) +(10y+x) =154
2) 11x+11y=154
3) 11(x+y) =154
4) x+y=14
5) x+x+2=14
6) 2x=12
7) x=6
8) y=6+2=8 , so y =8
Find the value of x. Round the length to the nearest tenth.
Answer:
x=6 and x=5.1
Step-by-step explanation:
Susan bought a calculator for $120 . She had to pay a sales tax of 10% on the price. How much change would she receive from $140 ?
Answer: $8
Step-by-step explanation: $120+10%=$132. $140-$132=$8.
Find the interquartile range for a data set having the five-number summary: 4.9, 12.4, 20.5, 28.8, 34.3
Answer:
16.4
Step-by-step explanation:
The interquartile range is the difference between the upper and lower quartiles.
Given the five figure summary, then
upper quartile = 28.8
lower quartile = 12.4
interquartile range = 28.8 - 12.4 = 16.4
The Interquartile range is 16.4.
What is an Interquartile range?When values are ranked from lowest to highest, the Interquartile range designates the middle 50% of those values.
Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3).
The interquartile range represents the variation between Q3 and Q1.
The interquartile range is calculated as follows:
The upper quartile is 28.8
The lower quartile is 12.4
The interquartile range is,
= 28.8 - 12.4
= 16.4
The value of the interquartile range is 16.4.
To know more about the Interquartile range
https://brainly.com/question/4135956
#SPJ1
Please hel- I really need this it’s not a test I’m not cheating please help
Answer:
x = 45
Step-by-step explanation:
Since ray IK║EH and IG is a transverse,
∠GIK ≅ ∠IGF [Corresponding angles]
Therefore, m∠IGF = x
Since, m∠JIF + m∠GIF = 180° [Supplementary angles]
2x + m∠GIF = 180°
m∠GIF = (180 - 2x)
Similarly, m∠IFE + m∠IFG = 180°
3x + m∠IFG = 180°
m∠IFG = (180 - 3x)
By the property of a triangle,
"Sum of all interior angles of a triangle is 180°"
m∠IGF + m∠GFI + m∠FIG = 180°
x° + (180 - 2x)° + (180 - 3x)° = 180°
(x - 2x - 3x) + 360 = 180
-4x + 360 = 180
4x = 360 - 180
4x = 180
x = 45
Plot the image of point C under a dilation about the origin (0,0) with a scale factor of 1/2
Answer:
See Attachment for graph
Step-by-step explanation:
Given
Point C
Required
Plot C when dilated by 1/2
First, we have to determine the coordinates of point C
From the attached graph;
[tex]C = (0,6)[/tex]
Next, is to determine the new point when dilated;
This is calculated as thus;
[tex]New\ Point = Old\ Point * Scale\ Factor[/tex]
[tex]C' = (0,6) * \frac{1}{2}[/tex]
Expand the bracket
[tex]C' = (0 * \frac{1}{2}, 6* \frac{1}{2})[/tex]
[tex]C' = (0, \frac{6}{2})[/tex]
[tex]C' = (0, 3)[/tex]
This implies that C' will be plotted at x =0 and y = 3
(See attached for point C')
Answer:
(0,3)
Step-by-step explanation:
Using the linear combination method, what is the solution to the system of linear equations 5 x + 3 y = negative 10 and Negative 20 x minus 7 y = 15? (–5, 1) (–1, 5) (1, –5) (5, –1)
Answer:
work is shown and pictured
Answer:
The answer is C
Step-by-step explanation:
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x)=x-2
g(x) = 2x+2
Write the expressions for (f-g)(x) and (f.g)(x) and evaluate (f+g)(-1).
Answer:
(f-g)(x)= -x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(-1) = 3(-1) = -3
Step-by-step explanation:
Hi, to answer this question we have to solve the expressions:
(f-g)(x) = x-2 -(2x+2)
(f-g)(x)= x-2 -2x-2
(f-g)(x) = -2x+x-2-2
(f-g)(x)= -x-4
(f.g)(x) = x-2 (2x+2)
(f.g)(x)= 2x^2 +2x-4x-4
(f.g)(x)= 2x^2 -2x-4
(f+g)(x)= x-2 +2x+2
(f+g)(x) = x+2x-2+2
(f+g)(x)= 3x
(f+g)(-1) = 3(-1) = -3
Feel free to ask for more if needed or if you did not understand something.
Please answer this question now
Answer:
f =7.5Step-by-step explanation:
[tex]Opposite =f\\Hypotenuse = 9\\Adjacent = 5\\\alpha = 50\\Using \: Pythagoras \:Theorem \\Hypotenuse^2 = Opposite^2 +Adjacent^2\\9^2 = f^2+5^2\\81=f^2+25\\81-25=f^2\\56=f^2\\\sqrt{56} = \sqrt{f^2} \\f = 2\sqrt{14} \\f = 7.483\\\\f = 7.5[/tex]
A 10-sided die numbered 1 to 10 is rolled once. Find these probabilities.
A. Pr(8)
B. Pr(odd)
C. Pr(even)
D. Pr(less than 6)
E. Pr(prime) (remember that 1 is not prime)
F. Pr(3 or 8)
G. Pr(8, 9 or 10)
H. Pr(greater than 9)
^please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
^and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
Answer:
A. Pr(8) = 1/10
B. Pr(odd) = 1/2
C. Pr(even) = 1/2
D. Pr(less than 6) = 1/2
E. Pr(prime) = 2/5
F. Pr(3 or 8) = 1 / 5
G. Pr(8, 9 or 10) = 3/10
H. Pr(greater than 9) = P(10) = 1/10
Step-by-step explanation:
We assume a FAIR 10-faced die, meaning there is an equal probability of throwing any one of the ten numbers.
With 10 possible outcomes each with equal probability, the probability of throwing any number is 1/10.
(It is preferable to work with fractions in probability because fractions are exact numbers, while decimals can often be rounded, or truncated).
A. Pr(8) means probability of throwing an 8, therefore Pr(8) = 1/10
B. Pr(odd) there are 5 odd number from 1 to 10, so Pr(odd) = 5/10 = 1/2
C. Pr(even) there are 5 even number from 1 to 10, so Pr(even) = 5/10 = 1/2
D. Pr(less than 6) there are 5 numbers less than 6 (between1 to 10),
so Pr(less than 6) = 5/10 = 1/2
E. Pr(prime) (remember that 1 is not prime)
A prime number is an integer not divisible by any number except one and itself.
Between 1 to 10, the four prime numbers are 2,3,5,7
therefore Pr(prime) = 4/10 = 2/5
F. Pr(3 or 8)
(3 or 8) make 2 successful outcomes out of 10, so Pr(3 or 8) = 2/10 = 1 / 5
G. Pr(8, 9 or 10)
similarly, (8,9 or 10) make three successful possible outcomes out of 10, so
P(8,9 or 10) = 3/10
H. Pr(greater than 9)
there is only one successful outcome, namely "10" out of 10 possible outcomes. So
P(greater than 9) = P(10) = 1/10
1. please explain what’s a “die” all I know was “dice” but dice is 6 sided yea?
A die is singular for dice, which can take up any number of faces. With a 10-faced solid, we can make a 10-faced die numbered 1 to 10.
2. and please explain the answer... I’m international student so I still need some explanation for the questions and answers thank you
See solutions above.
Answer:
Remember that standard probabilities are defined as the ratio between the number of favorable cases, and the total number of possible events.
In this case, we have a 10-sided die, which means its faces are numbered from 1 to 10, which gives us 10 total number of possible events. In other words, the denominator of the ratio is going to be 10.
Now we're able to find each probability.
(A) Probability of getting an 8:[tex]P_{8} =\frac{1}{10}=0.10[/tex]
The numerator is 1 because there's only one number 8 in the die, that means the number of favorable cases is 1, and, as we said before, the total number of possible events is 10.
(B) Probability of getting an odd number:[tex]P_{odd} =\frac{5}{10}=0.5[/tex]
The numerator is 5 because there are 5 odd numbers from 1 to 10. In other words, there are 5 favorable cases to this probability.
(C) Probability of getting an even number:[tex]P_{even}=\frac{5}{10}=0.5[/tex]
There are 5 even numbers from 1 to 10, that's why we had the same probability.
(D) Probability of getting a number less than 6:We know that there are only 5 numbers less than 6 for this die.
[tex]P_{<6}=\frac{5}{10}=0.5[/tex]
(E) Probability of getting a prime number:A prime number is such that it can be divided only by itself and the unit. So, there are four prime numbers from 1 to 10, which are 2, 3, 5, 7.
[tex]P_{prime}=\frac{4}{10}=0.4[/tex]
(F) Probability of getting 3 or 8:When we are going to find the probability of an event "or" another, we must sum those favorable cases.
[tex]P_{3 \ or \ 8} =\frac{1+1}{10}=\frac{2}{10}=0.2[/tex]
(G) Probability of getting 8, 9, or 10:In this case, we need to some all three favorable cases. The die has only one 8, one 9 and one 10. So, the probability is
[tex]P_{8,9,10}=\frac{1+1+1}{10}=\frac{3}{10} =0.3[/tex]
(H) Probability of getting a number greater than 9:We know that there's only one number greater than 10 on such die.
[tex]P_{>10}=\frac{1}{10}=0.1[/tex]
Lastly, "die" refers to this special 10-sided dice. In other problems, you can find "a die" with more faces even. But, in general, "die" refers to a dice.
PLEASE HELP BRAINLY - which option is correct?
Answer:
[tex]y > \frac{2x}{3} + 1[/tex]
Step-by-step explanation:
Given:
The graph in the attachment where the coordinates are (3,3) and (-3,-1)
Required:
Which inequality represent the graph
The first step is to determine the slope of the graph
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where m represents the slope, [tex](x_1, y_1) = (3,3)[/tex] and [tex](x_2, y_2) = (-3,-1)[/tex]
[tex]m = \frac{-1 - 3}{-3 - 3}[/tex]
[tex]m = \frac{-4}{-6}[/tex]
Simplify to lowest term
[tex]m = \frac{2}{3}[/tex]
Next is to determine the equation of the line using the slope formula
[tex]m = \frac{y - y_1}{x - x_1}[/tex], [tex](x_1, y_1) = (3,3)[/tex] and [tex]m = \frac{2}{3}[/tex]
[tex]\frac{2}{3} = \frac{y - 3}{x - 3}[/tex]
Cross multiply
[tex]2 * (x - 3) = 3 * (y - 3)[/tex]
Open both brackets
[tex]2 x - 6 = 3y -9[/tex]
Collect like terms
[tex]2 x - 6 +9= 3y[/tex]
[tex]2 x+3= 3y[/tex]
Divide through by 3
[tex]\frac{2x}{3} + \frac{3}{3} = \frac{3y}{3}[/tex]
[tex]\frac{2x}{3} + 1 = y[/tex]
Reorder
[tex]y = \frac{2x}{3} + 1[/tex]
Next is to determine the inequality sign
The dotted lines on the graph shows that the inequality sign is either > or <Since the shaded region is the upper part of the graph, then the > inequality sign will be considered,The inequality becomes
[tex]y > \frac{2x}{3} + 1[/tex]