Two brothers, Michael and Alan, were in a bowling league that met once a
week. From past experiences, it is known that both brothers' scores are
approximately normally distributed where Michael has a mean score of 150
with a standard deviation of 30, and Alan has a mean score of 165 with a
standard deviation of 15. Assuming that their scores are independent, which
of the following values is closest to the probability that Michael will have a
greater core than Alan in a single game?
0.16
0.28
0.31
0.33
0.37
Answer:
The correct option is;
0.28
Step-by-step explanation:
The given parameters are;
The mean score for Michael, [tex]\bar x _1[/tex] = 150
The standard deviation, σ₁ = 30
The mean score for Alan, [tex]\bar x _2[/tex] = 165
The standard deviation, σ₂ = 15
Taking n₁ = n₂ = 1
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Taking μ₁ - μ₂ = 0
[tex]z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577[/tex]
The p-value for a z-score of -0.577 from the z-table is 0.28434
Therefore, the probability that Michael, with mean score, [tex]\bar x _1[/tex] = 150 will have a greater score than Alan, with a mean score of [tex]\bar x _2[/tex] = 165 is 0.28434 ≈ 0.28
Therefore, the correct option is 0.28
The three sides of a triangle are in different colors – blue, green and red. The ratio of the length of the blue side to the length of the green side to the length of the red side is 3 : 4 : 5. The perimeter of the triangle is 240 cm. a) Fill in the blank: ___ units = 240 cm b) Fill in the blank: 1 unit = ___ cm c) What is the length of the red side of the triangle?
Answer:
The perimeter is the distance around the triangle. Given the ratio, the perimeter using the ratio is;
= 3 + 4 + 5
= 12 units
a. 12 units = 240 cm
The perimeter in centimetres is 240cm and in ratio is 12 units so they are equivalent.
b. 1 unit = 20 cm
If 12 units are to 240 cm, 1 unit is;
= 240/12
= 20 cm
c. Length of red side;
Red side has length of 5 units. 1 unit is 20 cm.
Length in cm is;
= 5 * 20
= 100 cm
I really need help plz
Answer:
I think answer is A
Step-by-step explanation:
Cause you notice time is the x and distance (meters) is the y. So 1 minute = 200 meters.
A college student mows lawns to cover his weekly expenses. The student charges $10 for each hour he spends .mowing lawns Identify the related and unknown quantities.
Which two unknown quantities in this situation are related?
A.
The amount of money the student earns
B.
The number of college students mowing lawns
C.
The number of hours the student spends mowing lawns
D.
The number of lawns the student mows
Answer:
A. and C.
Step-by-step explanation:
If a population grows by 69%, what is the multiplier?
Find the distance between the two points in simplest radical form.
(-5,8) and (-3, 1)
Given:
The two points are (-5,8) and (-3,1).
To find:
The distance between the given two points in simplest radical form.
Solution:
Distance formula: The distance between two points is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, the distance between (-5,8) and (-3,1) is
[tex]d=\sqrt{(-3-(-5))^2+(1-8)^2}[/tex]
[tex]d=\sqrt{(-3+5)^2+(-7)^2}[/tex]
[tex]d=\sqrt{(2)^2+(-7)^2}[/tex]
[tex]d=\sqrt{4+49}[/tex]
[tex]d=\sqrt{53}[/tex]
Therefore, the distance between two points (-5,8) and (-3,1) is [tex]\sqrt{53}[/tex] units.
Help pls
im braindead still XD
Answer:
-2.5 , -1 , 15.03 , 15.32
-10 , -6 1/2 , -1 , 0
0.02 , 0.2 , 2.02 , 2.2
Step-by-step explanation:
Answer:
-2.5 , -1 , 15.03 , 15.32
-10 , -6 1/2 , -1 , 0
0.02 , 0.2 , 2.02 , 2.2
Step-by-step explanation:
For a crafts fair, Charlie made 25 necklaces with 96 beads in each necklace. Shaniqua made 28 necklaces with 84 beads in each necklace. Who used more beads? _____________________ How many more beads? ____________________
Answer:
A. Charlie
B. Charlie used 48 more beads than Shaniqua
Step-by-step explanation:
Charlie:
25 necklaces with 96 beads in each necklace.
Total beads used = number of beads per necklace × number of necklace
= 96 × 25
= 2,400 beads
Shaniqua:
28 necklaces with 84 beads in each necklace.
Total beads used = number of beads per necklace × number of necklace
= 84 × 28
= 2,352 beads
A. Charlie used more beads
B. 2,400 beads - 2,352 beads= 48 beads
Charlie used 48 more beads than
Shaniqua
Una empreza tiene contratadas 75 personas. En las oficinas trabaja el 16% de los hombres y 20% de mujeres, si el total de personas q trabaja en oficinas es de 13 personas ¿Cuantod hombres y cuantas mujeres hay en la empreza?
Answer:
50 hombres y 25 mujeres
Step-by-step explanation:
Sea m el número de hombres y w el número de mujeres.
El total es 75
Así; m + w = 75 •••••••• (i)
Además; 16% de m + 20% de w = 13
0,16 m + 0,2 w = 13
Multiplicar por 100
16m + 20w = 1300 ••••• (ii)
De i, m = 75-w 16 (75-w) + 20w = 1300
1200 - 16w + 20w = 1300
4w = 1300-1200
w = 100/4 w = 25
Recordar; w + m = 75
25 + m = 75
m = 75-25
m = 50
whats 2+2x (7/7)= to
Answer:
2+2x(7/7)= 0 (you do what's in the parenthesis first)
2+ 2x (1) =0 (then you multiply, and anything times 1 is itself)
2 + 2x= 0 (subtract 2 from both sides to get the x-term alone)
2x= -2 (divide both sides by 2 to get x isolated)
x= -1 (is your answer)
What's the ordered pair for R,S,T,U,V,W. Help plz
Answer:
R (1.5, 2.5)
S (2, 0.5)
T (0, 1.5)
U (2.5, 1.5)
V (1, 1)
W (0.5 2)
Step-by-step explanation:
The numbers in between are most like 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4
A family has a hybrid car that gets 40 miles per gallon (mpg) and a pickup truck that gets 17 mpg. They drive at least 500 miles per week using both vehicles but don't want to use more than 20 gallons of gas. Make a recommendation for using each vehicle. Part A Write an expression that represents the total amount of gasoline used. Then write an inequality to show the maximum amount of gasoline that the family wants to use. Define the variables and list any constraints on the variables.
Answer:
[tex]Z=x+y[/tex]
[tex]x+y<20[/tex]
Step-by-step explanation:
Let the gallons of fuel used in the hybrid per week car be [tex]x[/tex] and [tex]y[/tex] be the number of gallons used in the pickup truck per week.
Number of miles driven using both vehicles is at least 500 per week. The inequality that represents the number of miles driven is.
[tex]40x+17y\geq 500[/tex]
The expression of total amount of fuel used would be [tex]Z=x+y[/tex].
Now the sum of the fuels used in both the cars is more than 20 gallons per week. The inequality that represents the total amount of gasoline used is
[tex]x+y<20[/tex]
can someone help me don't show my math hw? ily and tysm.
Answer:
Step-by-step explanation:
16)
[tex]\frac{4}{10} , \frac{32}{72}\\\\\frac{4}{10} = \frac{32}{72}[/tex]
Cross multiply,
4 * 72 = 32 * 10
288 ≠ 320
So, these are not in proportion.
17)
[tex]\frac{40}{25} = \frac{32}{20}[/tex]
Cross multiply,
40 * 20 = 32 * 25
800 = 800
So, these are in proportion.
18)
[tex]\frac{15}{45}=\frac{9}{c}[/tex]
Cross multiply,
15 * c = 9*45
c = [tex]\frac{9*45}{15}[/tex]
c = 9*3
c = 27
19)
[tex]\frac{16}{120} = \frac{v}{15}[/tex]
Cross multiply
16 * 15 = v * 120
[tex]\frac{16*15}{120} =[/tex] v
v = 2
Problem - 6x - 3 (y+2)
What are you trying to find? we can't solve this without you telling us what you're trying to find first.
Which one is correct please help
A machine produces 42 parts in 7 minutes. How many parts will it produce in 1.5 hours?
You answer is going to be: 540
The volume of a cube is 125 cubic inches what is the length of 1 edge of the cube
Answer:
All the edges of a cube have the same length, and the volume of a cube is the length of an edge taken to the third power. So the length of the edge of a cube with a volume of 125 is 5.
Step-by-step explanation:
Mark me as brainliest!
Solve the system by substitution.
y = -7x + 6
y = -10x
Answer:
(-2, 20)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = -7x + 6
y = -10x
Step 2: Solve for x
Substitution
Substitute in y: -10x = -7x + 6Add 10x to both sides: 0 = 3x + 6Isolate x term: -6 = 3xIsolate x: -2 = xRewrite: x = -2Step 3: Solve for y
Define equation: y = -10xSubstitute in x: y = -10(-2)Multiply: y = 20Answer:
x = -2
y = 20
Step-by-step explanation:
y = -7x + 6
y = -10x
y = -10x
-7x + 6 = -10x
3x = -6
x = -2
y = -7x + 6
y = -7 ( -2 ) + 6
y = 14 + 6
y = 20
look at pic n answer plz, its math
Answer:
the answer is G because each grab the probability is 1/5 and 1/5*1/5= 1/25
2x – 3y = 15
-2x + y = -1
Answer: -y=7
Explanation:
Think of your problem as subtraction:
2x-3y+15
-2x+3y=-1
What is the range of the function f(x) =
-2x + 5 when the domain is {-5, 5}.
PLZ HELP
Answer:
i need points bro
Step-by-step explanation:
Two candidates ran for class president. The candidate that won received 60% of the 380 total votes. How many votes did the winning candidate receive?
this all my points pls dont troll;-;
Answer: 228
Step-by-step explanation:
10% of 380 is 38.
The winning candidate got 60% of the votes.
So, we will multiply 38 by 6.
38 x 6 = 228
The answer to the question is 228.
what is the solution to -6(3a+4)=3a-3
Answer:
a = -1
Step-by-step explanation:
-6(3a+4) = 3a-3
-18a-24 = 3a-3
-24+3 = 3a+18a
21a = -21
a = -21 ÷ 21
a = -1
16x – 20y
20y = 60
Slope intercept form
Answer:
16x=60
X=15/4
Step-by-step explanation:
Diana worked on her science project for 513 hours. Gabe worked on his science project 114 times as long as Diana. Paula worked on her science project 34 as long as Diana. How long did Gabe and Paula work on their projects?
Answer:
Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
Step-by-step explanation:
It is given that,
Diana worked on her science project for 5 1/3 hours.
Gabe worked on his science project 1 1/4 times as long as Diana.
Paula worked on her science project 3/4 as long as Diana.
Solution,
ATQ,
Gabe worked for :
[tex]5\dfrac{1}{3}\times 1\dfrac{1}{4}\\\\=\dfrac{16}{3}\times \dfrac{5}{4}\\\\=\dfrac{20}{3}\ h\\\\=6\dfrac{2}{3}\ h[/tex]
Pauls worked for :
[tex]\dfrac{3}{4}\times 5\dfrac{1}{3}\\\\=\dfrac{3}{4}\times \dfrac{16}{3}\\\\=4\ h[/tex]
Hence, Gabe worked for 6 2/3 hours and Paula worked for 4 hours.
Which is a unit rate?
1 Cookie/ 1/3 bag
1 Cookie/ 9 bags
2/3 cookies
3 cookies/bag
Answer:
3 cookies/bag
Step-by-step explanation:
First of all, let's define a unit rate. A unit rate is a ratio of the amount of one measurement to one unit of another measurement term. Unit rates can be expressed as fractions.
Now, here is something easier for you to remember: the second unit always have to be something with the quantity of 1.
In this case, "3 cookies/bag" shows how there are three cookies per, or in each bag--which means 1 bag. The second unit, which is bag, has the quantity of one.
i need this now ....... EXPLAIN YOUR ANSWER!!!
What is the solution to the equation? 5-3x = x - 7 1 O A. 2 OB. 1 OC. C. 2 D. 3
Answer:
D. x=3
Step-by-step explanation:
How do I solve and respond to this question?
Answer:
i think its 6 and 8
Step-by-step explanation:
sorry if i get it wrong
can you tell me if it is right or wrong
i rlly need this answer pls help
Answer:
d
Step-by-step explanation:
155$ after 3 months means 45$ less. 45$ divided by 3 (the number of months) =15
that means she spends 15$ per month