The ratio 120/150 represented in the simplest form is 4 : 5 .
The given ratio is 120 /150 .
Now if we write the expression in the form of the simplest ratio we have to divide the ratio by the highest common factor.
The HCF of the number is 30. Hence the ratio in simplest form will be
120÷30 : 150÷30 = 4 : 5 .
By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.
Ratio can be thought of as an ordered pair of integers, a fraction with the first number in the numerator and the second in the denominator, or as the value that this fraction represents.
Ratios of counts are rational numbers that can also be rational numbers and are occasionally expressed by (non-zero) natural numbers.
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one day is the amount of time it takes for a planet to make one complete rotation. The number of hours in one day is different for each planet. How many days are equal to 1,100 hours on Saturn? What do you need to do to solve the problem
A) 1,100 hours is equal to approximately 104days in Saturn.
B) You need to know how hours make 1day in Saturn. i.e 10 hours 34minutes or 10.567hours.
From the question note that the number of hours in one day is different for each planet.
Hence for Saturn;
1 day = 10hours.34minutes
X day =1,100 hours
Note; 34 minutes in hours will be:
60 minutes =1hour
34/60 =0.567hour
Thus;
10hours.34minutes = 10hours +0.567hour
=10.567hours
To find the number of days in 1,100 hours, we cross multiply;
X day * 10.567hours =1,100 hours * 1 day
X day = 1,100 hours * 1 day
10.567hours
X day =104.1 ≈ 104 days
Therefore, you need to know the number of hours that makes a day in Saturn.i.e 10 hours 34minutes or 10.567hours.
. Again, 1,100 hours is equal to approximately 104days in Saturn.
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Work out (3 x 10^199) + (2 × 10^201).
Give your answer in standard form.
The standard form of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201
The expression given is (3x10^199)+(2*10^201) we need to write it in the standard form
Take 10^199 from the equation
=10^199((3x1)+(2x10^2))
=10^199(3+(2x100))
=10^199(3+200)
=10^199(203)
=203x10^199
2.03 x 10^201
1. there are 201 zeros after 2 and 199 zeros after 3
2. difference between 201 and 199 is 2
3. on adding both of them the 3 will come 2 spaces to the right of 2
The value of (3 x 10^199) + (2 × 10^201). is 2.03 x 10^201
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Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
In a recent student government election the ratio of students who voted for the winner to all the students who was 0.70 to the number of students who wrote it was 75 how many votes did the winner get?
The winner received 53 of the 75 votes in the student gov. election according to provided ratio.
What is ratio?
In arithmetic, a magnitude relation shows range times one number contains another.
Main body:
Because the ratio of students who voted for the winner compared to all students who voted is 0.70
we can rewrite this as:
0.70 = 70/100
And, because we know the total number of students who voted is 75 and if we call the number of students who voted for the winner s , we can then write this relationship and solve for s :
[tex]\frac{70}{100} = \frac{s}{75}[/tex]
Multiplying both sides by 75.
75*[tex]\frac{70}{100} = \frac{s}{75}[/tex]*75
s= 75*70/100
s = 5250/100
s = 52.5
s ≈ 53.
Hence ,The winner received 53 of the 75 votes.
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the age of children in kindergarten on the first day of school is uniformly distributed between 4.74 and 5.85 years old. a first time kindergarten child is selected at random. round answers to 4 decimal places if possible. the mean of this distribution is the standard deviation is the probability that the the child will be older than 5 years old? the probability that the child will be between 4.84 and 5.34 years old is if such a child is at the 9th percentile, how old is that child? years old.
a) The mean distribution is 5.295.
b) The standard deviation is 0.1026
c) The probability that the child will be older than 5 years old is 0.7657
d) The probability that the child's age is between 4.84 and 5.34 is 0.4504
e) At the 9th percentile, the age of the child is 5.739 years old.
Given interval distribution is
4.74 - 5.85.
a) Firstly, we will find the mean distribution,
Mean distribution = Sum of intervals / Number of intervals
= 4.74+5.85 / 2
= 5.295.
Hence, the mean distribution is 5.295.
b) Now, we will find the standard deviation,
We use the formula:
SD = [tex]\sqrt{\frac{(b-a)^{2} }{12} }[/tex]
b = 5.85
a = 4.74
SD = [tex]\sqrt{\frac{(5.85-4.74)^{2} }{12} }[/tex]
SD = [tex]\sqrt{\frac{(1.11)^{2} }{12} }[/tex]
SD = 0.1026
Hence, the standard deviation is 0.1026
c) The probability that the child will be older than 5 years will be
p(older than 5) = 5.85 - 5 / 5.85 - 4.74
= 0.85 / 1.11
= 0.7657
Hence, the probability that the child will be older than 5 years old is 0.7657
d) The probability that the child will be between 4.84 and 5.34 years old will be
p(between 4.84 and 5.34) = 5.34 - 4.84 / 5.85 - 4.74
= 0.5 / 1.11
= 0.4504
Hence, the probability that the child's age is between 4.84 and 5.34 is 0.4504
e) If the child is at the 9th percentile, the age will be
At the 9th percentile = 4.74 + 9/100 ×(5.85 - 4.74)
= 4.74 +(0.9)(1.11)
= 4.74 + 0.999
= 5.739
Hence, at the 9th percentile, the age of the child is 5.739 years old.
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The tape diagram shows that there are 90 teeth on a comb.
Teeth
90
Complete the table to show different percentages of the teeth on the comb.
90
100%
Percentage
% of 90 teeth
% of 90 teeth
The asked percentages are given as
1. 90 is 100% of 90.
2. 9 is 10% of 90.
3. 27 is 30% of 90.
Explain percentage.A percentage is a particular number or fraction in every hundred. The denominator of the fraction is 100, and it is represented by the symbol "%."
The purpose of percentage calculations is to determine the percentage of a whole in terms of 100. A percentage can be determined using one of two methods:
Through the unitary approach.By making 100 the new denominator of the fraction.It should be noted that when the denominator is not a power of 100, the second technique of percentage computation is not used.
Given, a comb has 90 teeth.
1. Find out what percentage of 90 is 90 now.
Let the percentage be x,
(x/100) × 90 = 90
x = (90 × 100)/90
x = 100 %
2. Now, find what percent of 90 is 9.
Let the percentage be x,
(x/100) × 90 = 9
x= (9 × 100)/ 90
x = 10%
3. Now, find what percent of 90 is 27.
Let the percentage be x,
(x/100) × 90 = 27
x= (27 × 100)/ 90
x = 30%
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The table represents points on a line. What is the slope
X 1 4 7 10
Y 8 6 4 2
Answer:
slope = - [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 8) and (x₂, y₂ ) = (10, 2) ← 2 ordered pairs from the table
m = [tex]\frac{2-8}{10-1}[/tex] = [tex]\frac{-6}{9}[/tex] = - [tex]\frac{2}{3}[/tex]
Dario bakes a lasagna containing $\frac 23$ pound of parmesan cheese, $1\frac 34$ pounds of ricotta cheese, and $1\frac 13$ pounds of mozzarella cheese.
Dario cuts the lasagna into several equal slices, each containing exactly $\frac 14$ pound of cheese. How many slices are there?
Dario cuts the lasagna into 15 equal slices.
Given,
Quantity of Parmesan cheese = 2/3 pounds
Quantity of Ricotta cheese = 1 3/4 = 7/4 pounds
Quantity of Mozzarella cheese = 1 1/3 = 4/3 pounds
The quantity of cheese in each pieces when the lasagna is cut = 1/4 pounds
We have to find the number of slices of cheese.
Here,
Total quantity of cheese;
2/3 + 7/4 + 4/3 = 2 + 7/4 = 15/4 pounds
Number of slices = total cheese / quantity of cheese in pieces
= (15/4) / (1/4) = 15 slices
That is,
Dario cuts the lasagna into 15 equal slices.
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find the area of a rhombus whose diagonals are the lengths 36cm and 22.5 cm
Answer:
area of rhombus=1/2*36*22.5
=405cm^2
Step-by-step explanation:
Solve.
−46=21+3m
Enter your answer as a mixed number in simplest form in the box.
m =
Answer:
-22 1/3
Step-by-step explanation:
We should start by subtracting both sides of the equality by 21.
After doing this, we get that -67=3m.
Furthermore, we can divide both sides by 3 and get -67/3=m.
However, this is an improper fraction, not a mixed number.
If we divide -67 by 3, we get -22 1/3.
Therefore, m= -22 1/3
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
there is probably a way to do this w/o calculus, but I cheated and used that.
A = Length * Width
A = x * ( 650 -2x)
A = 650x -2[tex]x^{2}[/tex]
d/dx ( A = 650x -2[tex]x^{2}[/tex])
0=650 -4x
4x = 650
x = 135 m
A= 650*135 -2*[tex]135^{2}[/tex]
A = 51,300 [tex]m^{2}[/tex]
PLEASE HELP ITS DUE IN 20 MINUTES
Answer/Step-by-step explanation:
[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]
I hope this helps!
the length length of a species of plants is normally distributed with expected value 60 cm. it is known from past experience that seventy five percent of theses flowers have length between 50 and 70 cm. what can we say about the standard deviation of the length of this plant?
The standard deviation of the length of this plant be 25.
m = 60(mean)
Let the standard deviation be s,
As, the probability for 50<x<70 be 0.75
Z = (x−m)/s
for x=50,
Z=0
for x=70,
Z=(70−50)/s=20/s
Now, the probability for 50<x<70 be,
P(50<x<70) = 0.75
In the standard form 0<z<(20/s)
using Z-table, the area from 0 to 20/s,
= 0.75
s = 25
Hence, the standard deviation of the length of this plant be 25.
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Which equation represents a line which is perpendicular to the line y=2x-5y
A. 2x−y=−4
B. 2y−x=4
C. x+2y=-6
D.2x+y=-2
Answer:
c
Step-by-step explanation:
To find a perpendicular line, you must compare the slopes. With the equation y=2x-5, we're looking for the inverse/opposite slope of -1/2.
Option A still has a slope of 2. Option B, when everything is in the format of mx+b = y format is -x-4=-2y. which gives us 1/2 but not -1/2. C when everything is on the right side gives us -2y=x-6. Divide both sides by -2 to get the y by itself and you're left with y = -1/2x+3. Now we found the equation that gives us the -1/2 slope we were looking for.
-7 + 5x = 5x + 9 help me pls
Answer:
solve for x 7 (5x+9)=- (x-9) 7(5x + 9) = −(x − 9) 7 ( 5 x + 9) = - ( x - 9) Simplify 7(5x+9) 7 ( 5 x + 9). Tap for more steps... 35x+63 = −(x−9) 35 x + 63 = - ( x - 9) Simplify −(x−9) - ( x - 9).
Step-by-step explanation:
Rewrite 0+0+7(5x+9)= -(x----9)
Apply the distributive property. 7 (5x) + 7.9= - (x-9)
help me please please please
Answer:
SA = 148 cm²
Step-by-step explanation:
the opposite faces of the cuboid are congruent , then
SA = 2(6 × 5) + 2(4 × 5) + 2(6 × 4)
= 2(30) + 2(20) + 2(24)
= 60 + 40 + 48
= 148 cm²
3. Tina needs to build a fence. The fence
is 30 feet long and 20 feet wide. She
realizes she needs more so she increases
the length and width by x feet. Create an
expression that represents the perimeter
for the fence.
the area of a rectangle shown is 44m2
3 2/3 m
x?
work out the missing length x
Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin.
T=
U=
V=
W=
The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.
Thus,
The rule to rotate a point P(x, y) after a rotation 270° counterclockwise around the origin is:
P(x, y) → P'(y, -x)
From the Graph,
In our case, we have the points
T = (4, -8)
U = (6, -8)
V = (9, -3)
W = (7, -3)
Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
P(x, y) → P'(y, -x)
T (4, -8) → T'(-8, -4)
U (6, -8) → U'(-8, -6)
V (9, -3) → V'(-3, -9)
W (7, -3) → W'(-3, -7)
Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:
T'(-8, -4) , U'(-8, -6) , V'(-3, -9) , W'(-3, -7)
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How do you graph this?
Reflection at point y = -6 will have coordinates as
preimage image
Q(0, -9) Q' (0, -6)
R(4, -9) R' (4, -6)
S(6, -8) S' (6, -5)
T(2, -8) T' (2, -5)
How to find the coordinatesThe transformation involve is reflection and this is a type of transformation that produces the mirror image of the preimage
The transformation rule to get the mirror image is (x, y) → (x, y + 3)
The coordinates are applied as follows
Q(0, -9) → (0, -9 + 3) → Q' (0, -6)
R(4, -9) → (4, -9 + 3) → R' (4, 6)
S(6, -8) → (6, -8 + 3) → S' (6, -5)
T(2, -8) → (2, -8 + 3) → T' (2, -5)
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Are these parallel or perpendicular or neither? 3x+2y=10 and 2x+3y=-3
Answer:
These lines are neither parallel nor perpendicular.
Step-by-step explanation:
Parallel lines are lines that never intersect and perpendicular intersect at a ninety degree angle.
Using desmos, you can find your solution.
I hope this helps
-No one
Suav has a loyalty card good for a discount at his local grocery store. The item he wants to buy is priced at $21, before discount and tax. After the discount, and before tax, the price is $19.53. Find the percent discount.
The percent discount given to Suav in the local grocery store is
How to find the the percent discountinformation given in the problem
The item Suav wants to buy in the grocery store is priced at $21
After the discount, and before tax, the price is $19.53
The discount is found by subtraction as follows
discount = price at the store - price before tax
discount = $21 - $19.53
discount = 1.47
Discount in percent
the problem is discount of the price at the store
percentage deals with a fraction hundred and used as follows
= 1.47/21 * 100
= 7/100 * 100
= 7%
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Joanna saves $55 each month from her part-time job. She saves 1/5 of her earnings. Write and solve an equation determine Joanna’s earnings
If 1/5 of Joanna's monthly savings is $55 the equation of her savings is
x/5 = 55The solution to the equation is $275
How to determine the equation of Joanna's savingsinformation from the question include
Joanna saves $55 each month from her part-time job
She saves 1/5 of her earnings
let x represent the Joanna's earnings
The equation of Joanna savings is represented in the form
1/5 of x = 55
This equation deals with multiplication and the term 'of' as used in math represents multiplication
Hence 1/5 of x = 1 / 5 * x = x/5
x/5 = 55
multiplying both sides by 5
x = 275
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Find the area of a regular hexagon
with a side length of 5 cm. Round to
the nearest tenth.
5 cm
[? ]cm²
Answer: 64.95
Step-by-step explanation: The formula is (3√3 s2)/2 so using that we can find the answer which is, 64.95
There is a number written on the board.
One student increased the number by 12.
Another student multiplied the number written
on the board by 3. The first student’s result is 2
greater than the second student's result. What
number is written on the board?
The number written on the board is 2 2/5
What are linear equations?A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0. where, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. where, x and y are variables, A and B are coefficients and C is a constant.
represent the number on the board by x, the result of the second student by y , therefore the result of the first student is 2y
solving for the first student, 12+x= 2y
for the second student , 3x= y
substituting 3x for y in first equation
12+ x= 2(3x)
12+x= 6x
collecting like terms
5x= 12
divide both side by5
x= 12/5= 2 2/5.
Therefore the number on the board is 2 2/5
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write the missing number = 1/2 of 18
please help me !!!!
Answer:
a) 9b) 18Step-by-step explanation:
a) 1/2 of 18 = ?
→ 1/2 of 18
→ (1/2) × 18
→ 18/2 = 9
So, answer is 9.
b) 2/3 of 27 = ?
→ 2/3 of 27
→ (2/3) × 27
→ 54/3 = 18
So, answer is 18.
Use the diagram of AlL where k, S and are midpoints or the sides, RK = 3, KS = 4, and JK
Is perpendicular to KL.
Find the length of RS
Find the length of JK
Find the length of RT
Find the perimeter of JKL
1. The length of RS is 5.
2. The length of JK is 6.
3. The length of RT is 4.
4. The perimeter of triangle JKL is 24.
What do you mean by right angle triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
According to data in the diagram of the given question:
We have :
The ΔJKL, ΔRKS and ΔRTS are right-angle triangle.
The length of RK=3 and KS=4
We are using pythagoras theorem for determine the length of RS,
(RK)²+(KS)²=(RS)²
(3)²+(4)²=(RS)²
9+16=(RS)²
25=(RS)²
(5)²=(RS)²
RS=5
∴ The the length of RS is 5.
Now, we need to find the length of JK,
JK=2(RK)=2(3)=6
JK=6 [Because RK is midpoint of the side JK]
We have given value of KS=4 and the side KS is the opposite side of RT,
So, that's why the value of RT=4.
Now, we will find the perimeter of ΔJKL,
JK=6, KL=8 and we need to find the side JL,
(JK)²+(RL)²=(JL)²
(6)²+(8)²= (JL)²
36+64=(JL)²
100=(JL)²
(10)²=(JL)²
JL=10
The perimeter of the triangle ΔJKL,
Perimeter=6+8+10=24
Therefore, the perimeter of the triangle is 24.
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4) What type of slope does the following line have?
Answer: zero slope
Step-by-step explanation:
When the slope of a line is zero it creates a horizontal line.
A line passes through the points (–5, –4) and (0, 4). What is its equation in slope-intercept form?
Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.
Equation in slope-intercept form in this caseBeing (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:
m= (4 - (-4))÷ (0 - (-5))
m= (4 + 4)÷ (0 +5)
m= 8÷ 5
m= 8/5
Considering point 2 and the slope m, you obtain:
4= 8/5×0 + b
4= 0 +b
4= b
Finally, the equation of the line is y=8/5x + 4.
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if ratings on a measure of creativity contain nothing but random error, what would the reliability of that measure be?
50 would be the reliability of that measure by standard error.
What is the standard deviation?
The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is. If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.A measure that has no random error and no true score (i.e., is only random error) has zero reliability. A measure that has random error.
50 would be the reliability of that measure .
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