Answer:
Step-by-step explanation:
Let x be the random variable representing the height of the students. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 68.5
σ = 2.7
the probability that a student's height is between 67.5 and 71.0 inches exclusive is expressed as
P(67.5 < x < 71.0)
For x > 67.5,
z = (67.5 - 68.5)/2.7 = - 0.37
Looking at the normal distribution table, the probability corresponding to the z score is 0.36
For x < 71.0
z = (71.0 - 68.5)/2.7 = 0.93
Looking at the normal distribution table, the probability corresponding to the z score is 0.82
Therefore,
P(67.5 < x < 71.0) = 0.82 - 0.36 = 0.46
The number of students whose height is between 67.5 and 71.0 inches is
0.46 × 1000 = 460 students
The probability that a student's height is greater than or equal to 74.0 inches is expressed as P(x ≥ 74)
P(x ≥ 74) = 1 - P(x < 74)
For x < 74,
z = (74 - 68.5)/2.7 = 2.04
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
P(x ≥ 74) = 1 - 0.98 = 0.02
The number of students whose height are greater than or equal to 74.0 inches is
0.02 × 1000 = 20 students
Nikita's Work
Area of Base = B = 3 bn=(718) = 28 cm?
Volume=Bh= (28)(13) = 364 cm
Where, if any, did Nikita first make a mistake in her work?
Nikita used the wrong formula for the area of the base.
Nikita used the wrong measurements when finding the area of the base.
Nikita used the wrong formula for the volume of the prism.
Nikita did not make a mistake.
Complete question:
Nikita calculated the volume of the right triangular prism. Her work is shown below.
Where, if any, did Nikita first make a mistake in her work?
Nikita used the wrong formula for the area of the base.
Nikita used the wrong measurements when finding the area of the base.
Nikita used the wrong formula for the volume of the prism.
Nikita did not make a mistake
Note the shape is a right triangular prism with base sides of 8 cm and height of 13 cm. The height of the prism is 7 cm.
Answer:
Nikita used the wrong measurements when finding the area of the base.
Step-by-step explanation:
The formula for the base area of the triangular prism should be the area of a triangle.
Area of a triangle = 1/2 bh
where
b = base
h = height of triangle
According to her expression she uses the wrong measurement when finding the area of the base.
She did = 1/2 × b × h = 1/2 × 7 × 8 = 56/2 = 28 cm²
But the height of the triangle is suppose to be 13 cm not 7 cm she used
The volume of the prism = Bh
where
B = base area
H = height of the prism
The volume should be
Volume = 13 × 8 × 7 = 728 cm³
Answer:
Nikita calculated the volume of the right triangular prism. Her work is shown below.
Where, if any, did Nikita first make a mistake in her work?
Nikita used the wrong formula for the area of the base.
Nikita used the wrong measurements when finding the area of the base.
Nikita used the wrong formula for the volume of the prism.
Nikita did not make a mistake
Note the shape is a right triangular prism with base sides of 8 cm and height of 13 cm. The height of the prism is 7 cm.
Answer:
Nikita used the wrong measurements when finding the area of the base.
Step-by-step explanation:
The formula for the base area of the triangular prism should be the area of a triangle.
Area of a triangle = 1/2 bh
where
b = base
h = height of triangle
According to her expression she uses the wrong measurement when finding the area of the base.
She did = 1/2 × b × h = 1/2 × 7 × 8 = 56/2 = 28 cm²
But the height of the triangle is suppose to be 13 cm not 7 cm she used
The volume of the prism = Bh
where
B = base area
H = height of the prism
The volume should be
Volume = 13 × 8 × 7 = 728 cm³
Step-by-step explanation:
Raphael graphed the function g(x)=x+2 and f(x)=x-1. How many units below the y intercept of g(x) is the y intercept of f(x)
Answer:
3
Step-by-step explanation:
If you take the y-intercept of x+2 and the y-intercept of x-1 and graph them, count the number of units in between them and you should see that your answer is 3
Answer:
D) 3 units
Step-by-step explanation:
How do problems with extraneous solutions differ from problems with no real solutions or no solution at all? How are they similar?
Answer:
No real solution implies that there could possibly be imaginary solutions.
Step-by-step explanation: Extraneous solutions are created be using certain methods to solve the problem. They are not, never were, or never will be solutions. They are created by the process that is used to solve. hope this helps you :)
In each figure below, find m∠1 and m∠2 if a||b. Show your work with statements.
Answer:
m < 1 = 80
m < 2 = 70
Step-by-step explanation:
As we can see in the figure that
[tex]a || b[/tex]
Plus line s and t are considered to be transversals
That results into
m < 1 and 80
i.e alternate angles
And as we know that alternative angles are equal to each other
So,
m < 1 = 80
Moreover,
m < 2 = 70
As corresponding angles are equal to each other
Therefore the m < 1 = 80 m < 2 = 70 could be computed easily by applying the above things
Given that a and b are positive. If the values of a and b are decreased proportionally, which explains how the value of the expression is changed? 1 2 1 a + 1 b Q: A: A) decreases B) increases C) turns negative D) remains constant
Answer:
A
Step-by-step explanation:
it decreases
405 increased by 8.3
Answer:
413.03
Step-by-step explanation:
405 increased by 8.3 is 405+8.3.
[tex]405+8.3=\\405+8.0+0.3=\\413+0.3=\\413.03[/tex]
Answer:
413.3 if ADD, 437.5215 if add by percent
Step-by-step explanation:
If it's increaced by 8.3%, then it is 405 + 32.5215 = 437.5215
If it's add 8.3, then it's 413.3.
please help me please :(
Answer:
18
Step-by-step explanation:
There is a string that is 3 yards long that is divided into pieces that are 1/6 of yard long. Divide the total length by the length it was divided into to find the number of pieces.
When dividing with fractions, the second number will be inverted and multiplied by the first number.
3 ÷ (1/6) = 3 × 6 = 18
You will have 18 pieces
For which equations is 8 a solution? Check all that apply.
Ox+6=2
X+2 - 10
ox-4-4
Ox-2-10
0 2x=4
3x - 24
OŠ - 16
Answer:
3x-24
Step-by-step explanation:
because 3x-24 divide both side by co efficient of x which is 3 so 24/3=8
3/7 of students at a school are boys. If there are 2282 students at the school, how many are girls?
Answer:
2282 divided by 3over7
Answer:
1304
Step-by-step explanation:
2282:7 =326
326 . 3 = 978
2282 - 978 = 1304
An appliance store reduced the price of a refrigerator by 20% and then raised the prices by 10% from the lower price. What was the original price of the refrigerator, if the price was $70.49 ?
Answer: $80
Step-by-step explanation:
Let the original price of the refrigerator be represented by y.
We are told that an appliance store reduced the price of a refrigerator by 20%. This will be:
= y - (20% of y)
= y - (20/100 × y)
= y - (0.2 × y)
= y - 0.2y
= 0.8y
We are then told that the store then raised the prices by 10% from the lower price. This will be:
= 0.8y + (10% of 0.8y)
= 0.8y + (0.1 × 0.8y)
= 0.8y + 0.08y
= 0.88y
Since we told that now the price was $70.49, this means that we have to find the value of y using the above expression. This will be:
0.88y = $70.49
y = $70.49/0.88
y = $80.10
y = $80 approximately
The original price of the refrigerator is $80.
. A woman fences a 3m by 4m rectangular plot to keep her chickens in. The fencing costs N200 per metre. How much does it cost to fence the plot?
1 point
Answer:
Cost: "N2800"
Step-by-step explanation:
I'm assuming "N200" is "$200"? But I'll just use it as "N200"
Finding the perimeter:
3+3+4+4=
6+8=
14 metres
Finding the cost:
N200×14=
N2800
David, Malachy and Paul share some sweets in the ratio 4:3:3. David gets 24 sweets. How many did Paul get?
If David, Malachy and Paul share some sweets in the ratio 4:3:3 then Paul get 7.2 number of sweets
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that David, Malachy and Paul share some sweets in the ratio 4:3:3
All three shared 24 sweets together.
Let x be the number of sweets
4x+3x+3x=24
Add the like terms
10x=24
Divide both sides by 10
x=2.4
Now paul has 3x sweets so 3×2.4=7.2
Hence, Paul get 7.2 number of sweets
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what is as a percentage and decimal
[tex] \frac{11}{20} [/tex]
Answer:
Percentage: 55%
Decimal: 0.55
Step-by-step explanation:
11÷20=
0.55
[tex]\frac{11}{20}=\frac{55}{100}[/tex]
or 55%
3(x - 2) + 2 = 5(x - 3) + 9 por fa
Answer:
x = 1
Step-by-step explanation:
Given
3(x - 2) + 2 = 5(x - 3) + 9 ← distribute and simplify both sides
3x - 6 + 2 = 5x - 15 + 9
3x - 4 = 5x - 6 ( subtract 5x from both sides )
- 2x - 4 = - 6 ( add 4 to both sides )
- 2x = - 2 ( divide both sides by - 2 )
x = 1
Find the equation of the line through point (3,−3) and parallel to y=3x−4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12). Y=
Answer:
y =3x - 12
Step-by-step explanation:
I'm fairly certain this is the answer.
Consider the point (3,-3). In terms of variables this is written (x,y).
Remember that the equation for slope is y = mx + b.
In that equation, "b" is your y-intercept, and "m" is your slope.
If 2 lines are parallel, they have the same slope but different y-intercepts. So you can use the slope from the equation y=3x-4 to find the parallel line. You can also plug in the values 3 and -3 to solve for b, our y-intercept.
If we set up the equation, we have -3 = 3(3) + b.
Now solve for b.
-3 = 9 + b
Combine like terms, so that -12 = b, and you have your y-intercept.
To create the equation, take out the coordinate pair that the line passes through, and only have the SLOPE and the Y-INTERCEPT showing in the equation.
Therefore, y = 3x - 12
What are the dimensions of the poster at 1/3 its current size?
Answer:2 in. by 3 in
Step-by-step explanation:
only my best guess
Kayden is a stunt driver. One time, during a gig where she escaped from a building about to explode(!), she drove at a constant speed to get to the safe zone that was 160 meters away. After 3 seconds of driving, she was 85 meters away from the safe zone. Let D represent the distance (in meters) from the safe zone after t seconds. Complete the equation for the relationship between the distance and number of seconds. D=
Answer:
The answer is D(t) = 160 - 25t
Step-by-step explanation:
well khan academy said it lol
Anne, Becky and Charlotte had sums of money in the ratio 7:6:5. One of them gave £9 to one of the others and this changed the ratio (in the same order of names) to 6:5:4. The total sum of money remained the same; what was it?
Answer:
The total sum of money is £810
Step-by-step explanation:
The parameters given are;
The ratio of the sum Anne, Becky and Charlotte had = 7:6:5
One of them gave one of the others £9 and the new ratio becomes 6:5:4
The total sum of money remains the same = M
The initial fraction amount of the total sum of money each had is given as follows;
Anne = 7/(7 + 6 + 5)×M = 7/18·M = 0.389·M
Becky = 6/18·m = 1/3·M
Charlotte = 5/18·M = 0.278·M
After one of them gave £9 to one of the others, the fraction amount of the total sum of money each had became;
Anne = 6/(6 + 5 + 4)×M = 6/15·M = 0.4·M
Becky = 5/15·m = 1/3·M
Charlotte = 4/15·M = 0.267·M
Therefore, given that Anne's fraction of the total sum of money increased while Charlotte's fraction of the total sum of money decreased, it was Charlotte that gave Anne £9
Therefore, the fraction of the total sum of money equivalent to £9 is found s follows;
5/18·M - 4/15·M = 1/90·M = £9
Therefore;
M = 90 × £9 = £810
The total sum of money = £810.
Edward has 30 sweets.
The ratio of red sweets to yellow sweets is 2:3
How many red sweets does Ed have? *
Answer:
20 red sweets
Step-by-step explanation:
do two thirds of 30 and the part that cane out is the red sweets
Answer:
12
Step-by-step explanation:
Sum the parts of the ratio, 2 + 3 = 5 parts
Divide the number of sweets by 5 to find the value of one part of the ratio
30 ÷ 5 = 6 sweets ← value of 1 part of the ratio, thus
2 × 6 = 12 ← number of red sweets
Who wants to help I really really need it ❤️
Answer:
4^8
Step-by-step explanation:
4^5 * 4^3
We know that a^b* a^c = a^(b+c)
4^(5+3)
4^8
in Germany, VAT is at 19 % Jeremy buys a calculator for 58.31 German money this price contains VAT find the amount of VAT paid by jeremy
Answer:
9.31?
Step-by-step explanation:
2 circles labeled Set A and Set B overlap. Set A contains 1, set B contains 3, and the overlap of the 2 circles contains 2. The number 4 is outside of the circles.
On the Venn diagram, which region(s) represent the union of Set A and Set B (A⋃B)?
II
I and III
I, II, and III
I, II, III, and IV
Answer:
(A⋃B) = I, II, and III (C)
Step-by-step explanation:
Venn diagram is used to demonstrate the relationship between two or three sets. It enables visual organisation of data in a set.
From the information:
Set A = {I}
Set B = {II}
Set A⋂B = {III}
Where ⋂ means intersection.
A⋂B = objects that belong to set A and set B
Objects not belonging to any set = 4
U = Universal set
(A⋃B) means objects that belong to set A or set B
The objects that belong to set A or set B = I, II, and III
(A⋃B) = I, II, and III (C)
Answer:
The answer is C
Step-by-step explanation:
I took the test
Triangle ABC has perimeter 20 cm.
AB = 7 cm.
BC = 4 cm.
By calculation, deduce whether triangle ABC is a right-angled triangle.
Answer:
You have an obtuse, scalene triangle, so no :)
Step-by-step explanation:
Side a = 4
Side b = 9
Side c = 7
Angle ∠A = 25.209° = 25°12'32" = 0.43998 rad
Angle ∠B = 106.602° = 106°36'6" = 1.86055 rad
Angle ∠C = 48.19° = 48°11'23" = 0.84107 rad
Answer:
Triangle ABC is not a right-angle triangle.
Step-by-step explanation:
perimeter of the triangle: 20cm
AB=7cm and BC=4cm.
We can do the third length (AC) by subtracting the known lengths from the perimeter: 20 - 7 - 4 = 9
Therefore, the length AC is 9.If
ABC were a right angle triangle, we'd be able to use Pythagoras's Theorem to work out the length AC.
AC is the hypotenuse of the triangle because it is the longest length.
a2 + b2 = c242 + 72 = 16 + 49 = 65
Where AC = c, c2 = 65 If c = 9, then c2 = 81, however when using Pythagoras, c2 = 65.
I hope this helps. I am sorry if you get this wrong.
WILL GIVE BRAINLIEST! 7th GRADE MATH
Answer:
Third option is the right choice.
Step-by-step explanation:
The intersection point of both lines is [tex](-2, 2)[/tex].
Area of triangle [tex]\Rightarrow 12.5 = \frac{5\times x}{2}[/tex]
[tex]\Rightarrow x=5[/tex]
This represents the height of the triangle.
So, the y-coordinate of C, will be y-coordinate of point of intersection plus height of triangle.
y = 5+2 = 7
Best Regards!
p inversely as( m + 1 ). when p = 4, m = 8 . (a)Find a equation connecting P and ( m + 1 ). (b)calculate the value of p when m = 11
Answer:
a. p= 36/(m + 1)
b. p = 3
Step-by-step explanation:
If p varies inversely as (m + 1)
then p = k × 1/(m + 1). {Where k is the constant}
when p = 4, m = 8, that means 4 = k/(8 + 1)
4 × 9 = k and k = 36
a. Therefore the equation is p= 36/(m + 1)
b. When m = 11,
p = 36/(11 + 1)
p = 36/12
p = 3
y = 4x – 6
can someone find me the slope for this thanks
Answer:
Slope = m = 4
Step-by-step explanation:
y = 4x-6
Comparing this with the standard slope-intercept equation:
[tex]y = mx+b[/tex]
Where m is the slope and b is the y-intercept.
So, we get:
Slope = m = 4
Answer:
4
Step-by-step explanation:
The equation of a line has a formula.
y = mx + b
Where m is the slope, and b is the y-intercept.
The equation for this line is given:
y = 4x + - 6
m = 4
b = -6
4 is the slope, and -6 is the y-intercept.
9,6,3,0,-3,-6 work out the nth term (it decrease by the same amount each time)
Answer:
-3n+11 or 3n+11 or 3n-11 one of those
Step-by-step explanation:
Answer:
The answer is -3n+12
Step-by-step explanation:
It is because you do 9+3 and it is positive so it will be positive 12 (+12).
We got -3n from taking away -3 all the way.
I hope you got help
What is the length of Line segment S R?
The length of line segment SR is 15.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Using Pythagorean theorem.
The sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
16² + (RT)² = 20²
256 + (RT)² = 400
Subtract 256 on both sides
(RT)² = 144
Take square root on both sides
RT = 12
By using altitude theorem we find ST:
16/12= 12/ST
Apply cross multiplication
16ST = 144
Divide both sides by 16
ST = 9
Using Pythagorean theorem again:
12² + 9² = SR²
144 + 81 = SR²
225 = SR²
Take square root on both sides
SR= 15
Hence, the length of line segment SR is 15.
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Frankie wants to build a path from one corner of his yard to the opposite corner. His yard measures 20 ft. x 32 ft. What will be the length of his path to the nearest tenth of a foot?
Answer:
≈37.7 feet
Step-by-step explanation:
I'm assuming he goes diagonally.
We can form a triangle with legs 20 feet and 32 feet.
Using the Pythagorean Theorem, we get:
[tex]20^2+32^2=c^2\\400+1024=c^2\\1424=c^2\\c^2=1424\\c=\sqrt{1424}\\[/tex]
c≈37.7
Answer: 37.7 ft
Step-by-step explanation:
20^2 + 32^2 = C^2 where c squared is the distance of the diagonal distance that he wants to walk.
20^2 +32^2 =c^2
400 +1024 =c^2
1424 = c^2
c= 37.7359 rounded to the nearest tenth of a foot is 37.7
A certain arithmetic sequence has this explicit formula for the nth term:
an = 11 + (n - 1)(4)
The same sequence has this recursive formula:
an = an-1 +__
What number belongs in the blank space in the recursive formula?
Answer:
4
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
[tex]a_{n}[/tex] = 11 +(n - 1)4 , then
d = 4
The recursive formula allows a term in the sequence to be found by adding d to the previous term, thus
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 4
Answer:
The answer is 4
Step-by-step explanation: