Using the normal distribution, it is found that there is a 0.0125 = 1.25% probability that a randomly selected 10th grade boy exceeds 70 in.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, given by [tex]\mu = 63.5, \sigma = 2.9[/tex].
The probability that a randomly selected 10th grade boy exceeds 70 in is one subtracted by the p-value of Z when X = 70, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 63.5}{2.9}[/tex]
Z = 2.24
Z = 2.24 has a p-value of 0.9875.
1 - 0.9875 = 0.0125.
0.0125 = 1.25% probability that a randomly selected 10th grade boy exceeds 70 in.
More can be learned about the normal distribution at https://brainly.com/question/24663213
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Suppose a line, with a slope of -3 and a y-intercept of 4, is translated -4 units along the x-axis and 6 units along the y-axis. What is the equation of this new line?
pls hurry
Find equation of old line first
m=-3b=4Equation in slope intercept form
y=-3x+4Translated 4units left(x+4)
Translated 6 units up(y intercept +6)
Put it.
y=-3(x+4)+6+4y=-3x-12+10y=-3x-2Answer:
y = -3x -2
Step-by-step explanation:
The equation of the given line, with slope -3 and y-intercept 4, can be written in slope-intercept form as ...
y = -3x +4
When the line is translated by (h, k), it can be written as ...
(y -k) = -3(x -h) +4
__
Here, we want to translate the line -4 in the x-direction and 6 in the y-direction. That is, (h, k) = (-4, 6). Using these values in the above equation, we have ...
y -6 = -3(x -(-4)) +4
y = -3x -12 +4 +6 . . . . simplify, add 6
y = -3x -2
__
The attached graph shows the original line (red) with its y-intercept, and the translated line (green) with that y-intercept moved 4 units left and 6 units up.
There are 4 consecutive integers that have a sum of 54. What is the greatest of the 4 integers?
Answer:
x + x-1 + x-2 + x-3 =54.
x-1
Answer:
15
Step-by-step explanation:
Let the consecutive numbers be x, x + 1, x + 2, x + 3
==========
x + x + 1 + x + 2 + x + 3 = 544(x) + 6 = 544(x) = 54 - 64(x) = 48x = 12Greatest of the 4 integers:
x + 312 + 3153 and 3/4 - 2 and 1/5
Answer:
[tex]3 \frac{3}{4} - 2 \frac{1}{5} \\ \\ \frac{15}{4 } - \frac{11}{5} \\ \\ \frac{75}{20} - \frac{44}{20} \\ \\ = \frac{31}{20} = 1.55 = 1 \frac{11}{20} [/tex]
Answer the question below.
Answer:
Class B has much better scores than class A
Step-by-step explanation:
1. What is the of the combined rectangles below?
Answer:
please where's the diagram
There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
Colour
blue
red
yellow
Probability
0.4
The number of red cubes in the box is the same as the number
of yellow cubes in the box.
a) Complete the table.
(2)
There are 30 blue cubes in the box.
b) What is the total number of cubes in the box?
Answer:
a) 240 grams
b) 360 grams
c) 2 packs
Step-by-step explanation:
a) 1 biscuit = 4 grams of flour
60 biscuits = 240 grams of flour
Conclusion, 240 grams of flour is needed for 60 biscuits.
b) 240×3÷2 = 360 grams of butter
c) 360÷250
= 1.44
≈ 2 packs
Hope this helps =)
What is the slope of the line that passes through the points (1, -6) and (-2, –8)?
Write your answer in simplest form.
Answer:
Where the line is going
Step-by-step explanation:
Put attention next time
Ps. Just check if its on x or on the y
The slope of line that passes through the points (1, -6) and (-2, –8) is 2/3.
What is a linear equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
y = mx + b
In which the coefficients are described as follows:
• The coefficient m is the slope of the function, representing the rate of change of the function.
• The coefficient b is the y-intercept of the function, representing the value of y when the function crosses the y-axis(x = 0).
Here the points are(1, -6) and (-2, –8) :
and it is to find the equation of line passing through these points :
Now using slope formula to find the slope of line m :
m = (y₂-y₁)/ (x₂-x₁)
m = (-8+6)/(-2-1)
m = -2/-3
m = 2/3
Therefore, the slope of line that passes through the points (1, -6) and (-2, –8) is 2/3.
More can be learned about linear functions :
brainly.com/question/24808124
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i don’t understand this question
Answer:
3/2
Step-by-step explanation:
To find the slope, choose two points.
For example, choose (2, 5) and (4, 8).
Now find the difference between the y-coordinates.
8 - 5 = 3
Find the difference between the x-coordinates.
4 - 2 = 2
Divide the difference in y by the difference in x. That is the slope.
slope = 3/2
PLS HELP I'LL GIVE BRAINLIEST
Expand The Expression: -4(8+5t)
Answer:
[tex]\Longrightarrow:\boxed{\sf{-32-20t}}[/tex]
Step-by-step explanation:
Use the distributive property to expand the expression.
Distributive property:
→ A(B+C)=AB+AC
-4(8+5t)Multiply.
→ -4*8=-32
⇒ -4*5t=-20t
Rewrite the problem down.
→ = -32-20t
Therefore, the correct answer is -32-20t.I hope this helps you! Let me know if my answer is wrong or not.
Answer:-32-20t
Step-by-step explanation:
-4 times 8 is -32 and -4 times 5t is -20t
Hope this helps! :)
Estimate the value of 101.4^0.5 +6.43^0 x 7.99^(2/3)
I’m not really sure of the answer, if you know, please tell me.
Answer:
14
Step-by-step explanation:
101.4^0.5 = 10.0697 etc
it says estimate so I'm going to round that to 10
6.43^0 Anything with an exponent of 0 = 1
7.99^(2/3) = 3.9966 etc you can round that to 4
Put in the values:
10 + 1 × 4
Use PEMDAS
Parentheses
Exponents
Multiplication
Division
Addition
We have to multiply 1 × 4 which is 4
We're left with 10 + 4 which is 14
Answer:
14
Step-by-step explanation:
[tex]\sf 101.4^{0.5} +6.43^0 \times 7.99^{\frac23}[/tex]
[tex]\sf a^{0.5}=\sqrt{a}[/tex] so round 101.4 to 100 as the square root of 100 is easy to calculate mentally [tex]\sf a^0=1[/tex] so [tex]\sf 6.43^0=1[/tex]7.99 ≈ 8[tex]\sf a^{\frac23}=(a^{\frac13})^2[/tex][tex]\sf8^{\frac13}[/tex] = the number that you cube to get 8[tex]\begin{aligned}\sf 101.4^{0.5} +6.43^0 \times 7.99^{\frac23} & = \sf \sqrt{100} +1 \times8^{\frac23}\\\sf & = \sf 10 + (8^{\frac13})^2\\& = \sf 10 + (2)^2\\& = \sf 10 + 4\\& = \sf 14\end{aligned}[/tex]
Two customers took out car loans from a bank. marcus took out a 5-year loan for $10,000 and paid 4.7% annual simple interest. gianna took out a 6-year loan for $10,000 and paid 4.5% annual simple interest. what is the difference between the amounts of interest marcus and gianna paid for their car loans? question 2 options: $500 $400 $450 $350
Why would neighborhoods with more station wagons tend to have more
playgrounds?
A. Adoring crowds of children like to follow station wagons to the
nearest playground.
B. Playground equipment dealers tend to buy station wagons and
then have kids to fill them.
C. Families with children tend to own station wagons and move to
neighborhoods with playgrounds.
D. Playgrounds are made from former used car lots (which used to
sell station wagons).
O E. Station wagon owners like to build playgrounds.
Answer:
C
Step-by-step explanation:
Based on my knowledge, thast what i think it is, but im not sure
Amy fills an ice cream cone to the top edge. The diameter of the ice cream cone is 2 inches and its height is 6 inches. Don fills a bowl (V = 5 cubic inches) with ice cream. Amy has how much more ice cream than Don?
Answer:
1.28 in³
Step-by-step explanation:
Volume of Amy's cone
Cone = 1/3πr²hCone = 1/3 x 3.14 x 1² x 6Cone = 2 x 3.14 = 6.28 in³Volume of Don's bowl
It's given to be 5 in³Difference
Amy's cone - Don's bowl6.28 - 51.28 in³Answer:
So obviously in the context of this question you are meant to find the volume. Since Don's bowl already has a given value of 5 cubic inches we will use that same unit when calculating amy's ice cream cone volume.
Step-by-step explanation:
You are given that amy has a cone and need to find the volume. The formula for the volume of a cone is (V=πr^2*h/3).
π = pi or 3.14......
r = radius (in this case the opening/ diameter of the ice cream cone is given as 2 inches and the radius is half of diameter so d/2 = r (r=1)
h = height (in this case it is given that height is 6 inches)
Remember all variable units must be kept the same so in this case all units are inches.
Now Plug in and solve V = [tex]3.14*(1)^{2} *\frac{(6)}{3}[/tex]
Remember order of operations / PEMDAS (in this case, do exponent first then just multiply from left to right and at the end divide that number by 3.
V= 6.28 cubic inches (since all our units were inches and we are finding cubic volume of a cone)
Now Amy volume of cone - Don volume of bowl = your answer. 6.28-5 = 1.28 cubic inches
Find the value of each trigonometric ratio. Simplify
(look at screenshot) Best answer gets brainliest
Answer:
The second method is correct because in the first method she eliminates a solution by dividing through by x and assuming she graphed correctly, the solutions she gave are correct.
Step-by-step explanation:
Answer:
Yes she's correct
Step-by-step explanation:
Let's check
x²=7xCancel one x
x=7Another root is 0
So as a quadratic equation it's correct
Factor the polynomials completely, then solve. 4^2- 81 = 0
Answer:
[tex]x=\pm\frac{9}{2}[/tex]
Step-by-step explanation:
I assume you mean [tex]4x^2-81=0[/tex]:
[tex]4x^2-81=0\\(2x-9)(2x+9)=0\\x=\frac{9}{2},\:x=-\frac{9}{2}\\x=\pm\frac{9}{2}[/tex]
We were able to work quickly here since the original left-side expression was a difference of squares.
Answer:
Step-by-step explanation:
4x^2 - 81 = 0
(2x - 9)(2x + 9) = 0
x = -9/2, 9/2
tan x * csc x = sec x
Answer:
see explanation
Step-by-step explanation:
using the identities
tanx = [tex]\frac{sinx}{cosx}[/tex] , cscx = [tex]\frac{1}{sinx}[/tex] , secx = [tex]\frac{1}{cosx}[/tex]
consider left side
tanx × cscx
= [tex]\frac{sinx}{cosx}[/tex] × [tex]\frac{1}{sinx}[/tex] ( cancel sinx on numerator/ denominator )
= [tex]\frac{1}{cosx}[/tex] × 1
= secx = right side
An angle in standard position measures startfraction pi over 2 endfraction radians, and p(0, 1) is on the terminal side of the angle. what is the value of the cosine of this angle? –1 0 1 undefined
The value of the cosine of angle for π/2 radians is 0. Then the correct option is B.
What is trigonometry?Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.
An angle in standard position measures π/2 radians, and p(0, 1) is on the terminal side of the angle.
Then the value of the cosine of this angle will be
[tex]\cos \dfrac{\pi}{2} = 0[/tex]
More about the trigonometry link is given below.
https://brainly.com/question/22698523
Answer:
B. 0
Step-by-step explanation:
edge 2023
Mr. Potter's class will take a test for 1\dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction hours. They need to finish by half past 111111 to get to lunch on time. What is the latest time the class can start the test to get to lunch on time?
Answer:
is it half past one or another no?
HELP PLEASE!
15 POINTS
Answer:
Its 58
Step-by-step explanation:
2+2+2+2+2+4+4+4+6+10+10=58 but the closest number to it is 56
10) Write the equation of the line passing through the points (-1, 2) and (3, 4)
A) y = 2x - 2
B) y - 2x - 10
9-x
D) y x -
Step-by-step explanation:
(-1,2) = x1 , y1(3,4) = x2 , y2Using two points formula equation AB is :( y - y1 ) = y2 - y1 / x2 - x1 ( x - x1 )( y - 2 ) = 4 - 2 / 3 - ( -1 ) ( x - ( -1 ) y - 2 = 4 - 2 / 3 + 1 ( x + 1 )y - 2 = 2 / 4 ( x + 1 ) y - 2 = 1 / 2 ( x + 1 )y - 2 = ( x + 1 ) / 2 2( y- 2 )= ( x +1 ) 2y - 4 = x + 1 - 4 - 1 = x - 2y-5 = x - 2yx - 2y +5 = 0 , which is the required equation..
An event has a probability of 1/2. How would you best describe the likelihood of this event? (Hint: Change it to a decimal)
A. Impossible
B. Less likely
C. Equally likely
D. More likely
E. Certain
Answer:
C. Equally likely
Step-by-step explanation:
1/2=0.5=50% probability
Need Help!
Milk is on sale for 40% off when it is normally $3.75 per gallon. How much will a gallon of milk cost?
The discounted price for milk is $____ (Round to the nearest cent.)
Which of the following values of x does NOT satisfy the inequality: √x > ∛x *
A:) 1
B:) 2
C:) 3
D:) 4
Answer:
1
Step-by-step explanation:
1>1 NO FALSE 1==1
A designer is adding a pendant to a jewelry collection. the shape of the pendent can be defined by the equation y = startfraction 1 over 20 endfraction x squared endfraction. if the largest dimension of the pendant is 10 cm wide, what is the greatest length? 1.25 cm 2.50 cm 5 cm 10 cm
If the largest dimension of the pendant is 10 cm wide then the greatest length will be 5 cm. Then the correct option is C.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
A designer is adding a pendant to a jewelry collection.
The shape of the pendant can be defined by the equation
[tex]\rm y = \dfrac{1}{20}\ x^2[/tex]
If the largest dimension of the pendant is 10 cm wide then the greatest length will be
[tex]\rm y = \dfrac{1}{20}\ (10)^2\\\\\\\rm y = \dfrac{1}{20}\ 100\\\\\\\rm y = 5[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
Answer:
1.25 cm
Step-by-step explanation:
I need help with my math homework
VW = 6
hope it helps...!!!
The diameter of a circle is 88 centimeters. What is the area?
[tex]\Huge\color{pink}{{★ƛƝƧƜЄƦ ↦}}[/tex]
[tex] \large \purple { \sf{ Points \: →}}[/tex]
The diameter of a circle is 8 centimeters.✯ To find→
Area of circle......✯ we know that area of circle
[tex] \boxed{ \sf{A=\pi {r}^{2} }} \\ [/tex]
↬ 1st find the radius by
half of diameter[tex] \sf {r = \cancel \frac{8}{2} } \\ \\ \sf{r = 4}[/tex]
✯ Now solve according to formula →
[tex] \sf{↬A=3.14 \times {4}^{2}} \\ \sf{↬A =3.14 \times 16} \\ \sf {↬A = 50.24 {cm}^{2} }[/tex]
____________________☃️[tex]\pink{\sf{\:мѕнαcкεя\: ♪...}}[/tex]
The pre-image has coordinates D(-1,3),E(4,3),F(4,1),G(-1,1) What is the image of DEFG
Answer:
•SEE ABOVE ATTACHMENT•The image of DEFG forms QUADRILATERAL SHAPE
hope it helpsmark as brainliastWhat is the volume of the rectangular prism below in cubic inches?
Answer:
24
Step-by-step explanation:
The volume formula is all the dimensions multiplied together, or lengthxwidthxheight.
So, you do 1x1x2 which is 2 feet. HOWEVER, it is looking for CUBIC INCHES, not cubic FEET.
There are twelve inches in a foot so 2x12=24 inches.
Hexagon DEFGHI is translated 8 units down and 3 units to the right. If the coordinates of the pre-image of point F are (-9,2), what are the coordinates of F?