Tt would take 15 minutes for there to be exactly 60 gallons in the hot tube.
What is proportion?Proportion can be defined as the mathematical comparison of two numbers.
It is also known as an equation defining that the two given ratios are equivalent to each other.
From the information given, we have the following deductions;
There are 150 gallons of waterThe water drains at a rate of 6 gallons per minuteTo determine the time taken for 60 gallons to be left in the hot tube, we have to subtract the number from the total number of gallons, we have;
= 150 - 60
Find the difference
= 90 gallons
Now,
If 6 gallons are drained in 1 minute
Then 90 gallons are drained in x minutes
cross multiply
x = 90/ 6
x = 15 minutes
Thus, it would take 15 minutes for there to be exactly 60 gallons in the hot tube.
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For each direct variation, find the constant of variation. Then find the value of y when x=-3 .
y=4 when x=3
After direct variation y = -4 when x = -3.
What exactly do we mean by "direct variation"?Direct variation equations use the same phrase, to give the reader a hint.Either "directly proportional" or "directly varies" is the phrase.The area of a square, for example, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = -3.
K constant will be y/x ⇒ 4/3That is y = kx ⇒ y = 4/3 × xWhen x = -3:
y = 4/3 × -3 ⇒ y = -4Therefore, y = -4 when x = -3.
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The table shows the starting and ending elevations of a hiking trail.
Point on Trail
Starting Point
180 ft below sea level
Ending Point 260 ft above sea level
Elevation
How much greater is the elevation of the ending point than the starting point for the trail?
_ft
Answer:
160 people in total
Step-by-step explanation:
The table shows the starting and ending elevations of a hiking trail. Point on Trail Elevation Starting Point 180 ft below sea level Ending Point 260 ft above sea level How much greater is the elevation of the ending point than the starting point for the trail
Which of the following are remote interior angles of 26? Check all that apply.
A. 6
B. 5
C. 1
D. 2
E. 4
F. 3
Answer:
The answer is 6 which is A .Suppose 3 < a < 4 and 4 < b < 5. find all possible values of each expression. 1/a+1/b
9/29 < 1/a + 1/b < 7/12
Here we have two expression
3 < a < 4 and 4 < b < 5
We have to find the value of the expression
1/a + 1/b
The lower bound of the expression is when we take the maximum value of both the expression a and b
a = 4 and b = 5
From this we get
= 1/ 4 + 1/5
= 5 + 4 / 20
9/ 20
In the same way, we get the higher bound of the expression taken by taking the minimum value of both the expression a and b
a = 3 and b = 4
By putting the value of a and in the expression we get:
1/ 3 + 1/4
= 4+3 / 12
= 7/12
Thus we get the possible value of the expression :
9/20 <1/a + 1/b < 7/12
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4. 1 / 3y + 9 = 12
Linear equations
Answer:
-2.886
Step-by-step explanation:
4.1/3y+9=12
41/10/3y+9=12
41/10=12(3y+9)
41/10=36y+108
41=10(36y+108)
41=360y+1080
41-1080=360y
-1039=360y
y= -1039/360
y= -2.886
Please help me please help me
Answer:
U'(-2 , -2)
Step-by-step explanation:
U(2 , -2)
Let R be the rotation of center the origin O(0 , 0) and angle 270
Let M(z = x + iy) a point of the plane and its image M'(z' = x' + iy') by the rotation R.
Then
[tex]z^{\prime }=e^{i\frac{3\pi }{2} }\times z[/tex]
Then
x' + iy' = (0 -i)×(x + iy)
Then
x' + iy' = (-i) × (x + iy)
= -ix + y
Then
x' = y and y' = -x
Then
R transform M(x , y) to the point M'(y , -x)
Conclusion :
The image of U(2 , -2) by R is :
U'(-2 , -2)
a) Select all of the fractions below that are smaller than 1/9 1/8 1/3 1/10 5/9 1/90
Rearrange the Fraction in the order of least to largest:
1/8 > 1/91/3 > 1/9 1/10 < 1/95/9 > 1/91/90 < 1/9What is Fraction?A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator.
What is the significance of fraction?Fractions are significant because they indicate what percentage of a whole you require, have, or desire. In baking, fractions are used to indicate how much of an ingredient to use.
Why is it necessary to study fractions?Fractions are a vital basis for studying more advanced math's. As a student's first introduction to abstraction in mathematics, fractions give the greatest foundation for algebra.
According to the given data:Rearrange the items in the order of least to largest.: 1/8 > 1/9
Rearrange the items in the order of least to largest.: 1/3 > 1/9
Rearrange the items in the order of least to largest.: 1/10 < 1/9
Rearrange the items in the order of least to largest : 5/9 > 1/9
Rearrange the items in the order of least to largest.:1/90 < 1/9
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Given f (x) = 10x and g (x) = 2x – 1, find (f /g) (x).
Then evaluate the division when x = 3
Answer:
6
Step-by-step explanation:
(f / g)(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{10x}{2x-1}[/tex] ← substitute x = 3
= [tex]\frac{10(3)}{2(3)-1}[/tex]
= [tex]\frac{30}{6-1}[/tex]
= [tex]\frac{30}{5}[/tex]
= 6
The measure of Angle b is 40 degrees and the measure of angle c is 66 degrees. What is the measure of angle a?
Answer:
74
Step-by-step explanation:
All the angles of a triangle add up to 180
66+40 = 106
To find the missing angle...
180-106 = 74
Answer:
ANGLE A=74
Step-by-step explanation:
LET ANGLE A BE X
ANGLE B=40°
ANGLE C=66°
SUM OF ADJACENT ANGLE IS 180°
SO, WHEN:
40+66+X=180
X=180-106
ANGLE A=74°
HAVE A NICE DAY!!
What is each product or quotient in simplest form?
b. √x³ / ³√x²
Converting the given radicals into their exponential forms, √x³ / ³√x² = ⁶√x⁵
When work with radical numbers, sometimes it is easier to express them in exponential form first.
[tex]\sqrt[n]{a^{b}}=a^{\frac{b}{n}[/tex]
Recall the rules of exponent operations:
Product. [tex]a^{b}.a^{c}=a^{b+c}[/tex]Quotient. [tex]a^{b}:a^{c}=a^{b-c}[/tex]Power. [tex](a^{b})^{c}=a^{b.c}[/tex]Power of a product. [tex](a.b)^{c}=a^{c}.b^{c}[/tex]Zero power. a⁰ = 1Negative exponent. [tex]a^{-b}=\frac{1}{a^{b}}[/tex]Note that the first 3 rules use the same base. If there are more than 1 base number, then group the exponent that have the same base first.
Example:
[tex](2^{3}.3^{-2}) : (2^{-3}.3^{2})=( 2^{3}:2^{-3}).(3^{-2}:.3^{2})[/tex]
Tips: To simplify exponent numbers, sometimes it is useful to modify the base whenever possible.
Example:
8².2⁻⁵ = (2³)². 2⁻⁵ = 2⁶. 2⁻⁵ = 2⁶⁻⁵ = 2¹ = 2
The given problem:
Simplify √x³ / ³√x²
[tex]\sqrt{x^{3}}=x^{\frac{3}{2}}[/tex]
[tex]\sqrt[3]{x^{2}} =x^{\frac{2}{3}[/tex]
Using quotient rule of exponent:
[tex]x^{\frac{3}{2}}:x^{\frac{2}{3}}=x^{(\frac{3}{2}-\frac{2}{3}) }=x^{\frac{5}{6} }=\sqrt[6]{x^{5}}[/tex]
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What is the quotient of 3 and 1 over 5 divided by 1 over 3? SHOW WORK
The quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
How to solve for the quotientWe we would start first by having the definition for the term quotient. This is defined as the value that is gotten when we divide on quantity by another quantity.
From the definition that we have gotten here, we would have to divide the values by themselves and get the final solution.
We have 3 and 1 over 5 divided by 1 over 3 to be represented as
[tex]3\frac{1}{5} / \frac{1}{3}[/tex]
This would be rewritten as
(16 /5) / (1/3)
= 16 / 5 x 3/1
= 48 / 5
= 9.6
Hence the quotient of 3 and 1 over 5 divided by 1 over 3 is 9.6
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Please help will give great points
The sample space is 0, 1, 2, 3, 4, 5, 6, 7.
Set A is {0, 1, 2, 3, 4}
Set B is {1, 2,3, 4, 5, 6, 7}
The probability of selecting a number less than 5 is 5 / 8.
The probability of spinning a natural numbers is 7/8
The probability of spinning natural numbers and numbers less than 5 is 1/2
A and B is {1, 2, 3, 4}
A' and B = {5, 6, 7}
The probability of spinning a number not less than 5 or a natural number is 1 3/8
What is the sample space?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. The relationship that is being illustrated with this Venn diagram is the relationship between natural numbers and numbers less than 5.
A natural number includes all positive numbers from 1 to infinity. Natural numbers does not include zero (0). The sample space represents all the possible sets of outcome. In mathematics, a set can be described as a collection of objects whose elements are fixed and cannot be changed.
The probability of selecting a number less than 5 = numbers less than 5/ total numbers
5 / 8
The probability of spinning a natural numbers = all natural numbers / total numbers
7/8
The probability of spinning natural numbers and numbers less than 5 = 4/8 = 1/2
A' = 5,6,7
B = 1, 2, 3, 4, 5, 6, 7
A' and B - 5, 6, 7
The probability of spinning a number not less than 5 or a natural number= ( 4/8) + (7/8) = 11/8 = 1 3/8
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A rectangle has a length 6 meters more than six times the
width. The area of the rectangle is less than 72 meters².
Using the variable x, write an expression that represents all
possible widths of the rectangle. Write your answer as an
inequality in the form a
The required expression or inequality for possible widths of the rectangle is -4 < x < 3.
Given:
A rectangle has a length 6 meters more than six times the width.
The area of the rectangle is less than 72 meters squared.
We have to find,
The expression or inequality that represents all possible widths of the rectangle.
Let x be the width of the rectangle.
Length of the rectangle is 6 meters more than six times the width.
length = 6x + 6
Area of rectangle is:
Area = length × width
Area = (6x + 6) × x
Area = 6x² + 6x
The area of the rectangle is less than 72 meters squared.
6x² + 6x < 72
6x² + 6x -72 < 0
Divide both sides by 6.
x² + x - 12 < 0
x² + 4x - 3x - 12 < 0
x(x + 4) - 3(x + 4) < 0
(x + 4) (x - 3) < 0
It is true if one factor is negative and other is positive. So,
x - 3 < 0 ⇒ x < 3 ...(i)
x + 4 > 0 ⇒ x > -4 ...(ii)
Using (i) and (ii), we get
-4 < x < 3
Therefore, the required expression or inequality for possible widths of the rectangle is -4 < x < 3.
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The bakery at Oaktown Grocery Store sells two types of bread, white and wheat. Last week, the store sold 4 loaves of white bread for every 5 loaves of wheat bread. If the store sold 117 loaves of bread in all last week, how many loaves of white bread did they sell?
The number of white bread sold is 65.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
We have,
Let the White bread be M
Let the Wheat bread be N
4 loaves of white bread for every 5 loaves of wheat bread can be written as:
4M = 5N _____(1)
Total number of bread sold = 117
M + N = 117 _______(2)
The number of white bread sold:
From (1)
N = 4M / 5 Putting in (2)
M + 4M/5 = 117
(5M + 4M) / 5 = 117
9M = 117 x 5
M = 13 x 5
M = 65
Thus the number of white bread sold is 65.
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Answer:
52 i just did the test
Step-by-step explanation:
Lamont has purchased 20 trading cards and wants to have at least 42 trading cards. write and solve an inequality to find the number of trading cards lamont needs. select all of the true statements.
The inequality which helps to find the number of trading cards Lamont needs, x as required in the task content is; x + 20 >= 42 and it's solution is; x >= 22.
What is the inequality which represents the number of cards needed by Lamont?It follows from the task content that the inequality which represents Lamont's situation as described by the word phrase is required.
First, the word phrase "at least" is represented by the inequality sign, greater or equal to.
Hence, since he has 20 trading cards already and needs at least 42, the number of cards needed x is such that;
x + 20 >= 42.
Hence, the required inequality is as represented above and it's solution is;
x >= 42 -20
x >= 22.
Ultimately, The inequality which helps to find the number of trading cards Lamont needs, x as required in the task content is; x + 20 >= 42 and it's solution is; x >= 22.
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Kayla and Shawna are selling fruit for a school fundraiser. Customers can buy small boxes of tangerines and large boxes of tangerines. Kayla sold 7 small boxes of tangerines and 4 large boxes of tangerines for a total of $166. Shawna sold 7 small boxes of tangerines and 3 large boxes of tangerines for a total of $ 149. Find the cost each of one small box of tangerines and one large box of tangerines.
The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
Let the price of small boxes be x and the price of large boxes be y
we need to form a linear equation in two variable
So, Kayla's equation is
7x + 4y = 166
and Shawna's equation is
7x+ 3y = 149
Subtracting equation 2 from equation 1
7x + 4y = 166
(-) 7x +3y = 149
we get y = 17
Now substituting the value of y in equation 1
7x + 4(17) = 169
7x +68 = 169
7x = 101
x= 14.428
Hence, The price of small box of tangerines is $14.43 approx. and price of large box of tangerines is $ 17
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Multiply. (√5+√11)(√5-√11)
The multiplication of the expression ( √5 + √11 )( √5 - √11 ) is - 6.
Multiplication in elementary algebra is the process of figuring out the outcome of multiplying a number by a number b. The product of a and b is the outcome of multiplication, and each of the integers a and b is referred to as a factor of the product ab.
Consider the expression,
y = ( √5 + √11 )( √5 - √11 )
Using the distributive property,
a( b + c ) = ab + ac
y = (√5 + √11 )( √5 - √11 )
y = √5( √5 - √11 ) + √11( √5 - √11 )
y = ( √5 )² - √5 × √11 + √11 × √5 - ( √11 )²
y = 5 - √55 - √55 - 11
y = 5 - 11
y = - 6
The value of the expression (√5 + √11 )( √5 - √11 ) when simplified is - 6.
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What is the area of the figure? step by step please
Answer:
*A = 60 sq units
Step-by-step explanation:
Area(*A) = Length(*l)×breath (*b)
split the shape in two such that you get two rectanglesrectangle(*rec) 1 dimensions being *l=2,*b=18*rec 2 dimensions being*l=2 *b=12*A of *rec1 = 2 × 18 = 36*A of *rec2 = 2× 12 =24*A of the total shape = *A of *rec1 + *A of *rec1*A of the total shape = 36 +24*A of the total shape = 60 sq units
Answer:
Area = 60
Step-by-step explanation:
First make the rectangle 12 and 4 and a square 6 and 2.
12*4=48
6*2=12
48+12=60
Determine the solution for 0.4(3y + -18) = 1.2y + 7.2.
No solution
Infinite solutions
y = 10
y=6
Answer:
i think its B
Step-by-step explanation:
3/
A and B are two similar solids.
15 cm
10 cm
A
B
The volume of A is 400 cm³.
Work out the volume of B.
+
12. DIG DEEPER The sum of a three-digit
number and a one-digit number is 731.
The product of the numbers is 2,908,
What are the numbers?
The three digit number is 727 while the one digit number is 4
Given data
The sum of a three-digit number and a one-digit number is 731.
The product of the numbers is 2,908
How to solve for the numberslet three digit number be x, y, and z
let the one digit be w
The sum
xyz + w =731
xyz * w = 2,908
making xyz the subject of formula
xyz = 731 - w
plugging in xyz into xyz * w = 2,908
( 731 - w ) * w = 2908
731w - w^2 = 2908
w^2 - 731w + 2908 = 0
solving the quadratic equation gives
w = 727 or 4
since w is a one digit number then w = 4
plugging in w = 4 into xyz + w =731 we have
xyz + w =731
xyz + 4 =731
xyz =731 - 4
xyz = 727
Hence the three digit number is 727 while the one digit number is 4
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What is the estimate of 827 times 4 ?
Answer:
3,308
Step-by-step explanation:
the internet said that 3,308 was the answer.
[tex]827 \times 4 \approx820 \times 4[/tex]
[tex]820 \times 4 = 800 \times 4 + 20 \times 4 \\ 820 \times 4 = 3200 + 80 \\ 820 \times 4 = 3280[/tex]
[tex]827 \times 4 \approx3280[/tex]
In reality it's just that additional 4 sevens,so
[tex]827 \times 4 = 820 \times 4 + 4 \times 7 \\ 827 \times 4 = 3280 + 28 \\ 827 \times 4 = 3308[/tex]
help i need help on this question
t-r divided by 21 and t= -6 and r= 12
Answer: (t-r) / 21 = -0.857 where, t= -6 and r= 12
Step-by-step explanation:
Given data,
t-r divided by 21
where, t= -6 and r= 12
So, we can write,
= (t-r) / 21
Let us assume,
(t-r) / 21 = x
So,
x = (t-r) / 21 { t = -6 and r = 12 (eq-1)
x = (t-r) / 21
We can substitute, t = -6 and r = 12 values in this equation 1
so, we can write,
x = (t-r) / 21
x = (-6-12) / 21
x = -18/21
x = -6/7
x = -0.857
Therefore,
(t-r) / 21 = -0.857 where, t= -6 and r= 12
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Leo knows that each time a dight moves one place to the left in a whole number, the value of the dight is 10 times as much
Describe an example you would show to Leo to
demonstrate that this is true for decimal numbers also.
Help me if you may
The example regarding the values of digits is also true for decimal numbers, as we showed with 0.52.
How do values of digits work?For the integer part of a number, the unit digit is worth 1, and for each subsequent digit, moving left, the value of the digit is multiplied by 10. For example 22, 22 = 2 x 10 + 2 x 1 = 22.For the fractional part of a number, the first decimal digit is worth 0.1, and for each subsequent digit, moving right, the values is divided by 10.For example, for the decimal 0.52.
.52 = 5 x 0.1 + 2 x 0.01 = 0.52.
Hence, moving a digit one place to the left, the value is 10 times as much, as we saw with digits 5 and 2 in the number 0.52.
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What are the slope of the two lines?
Answer:
- 3/4 for line passing through AB
- 2/3 for line passing through CD
Step-by-step explanation:
Slope = rise/run = (y2-y1)/(x2-x1) for any two points (x1, y1) and (x2, y2)
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing thru CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
The slope of the two lines - 3/4 for line passing through AB
- 2/3 for line passing through CD
What is a meaning of a slope?
A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises.two points (x1, y1) and (x2, y2)
Slope [tex]m = \frac{y_{2}- y_{1} }{x_{2} - x_{1} }[/tex]
Line Passing through AB
Take points (0, 6) and (8, 0)
Slope = (0-6)/(8-0) = - 6/8 = -3/4
For line passing through CD
take points (0, 2) and (3, 0)
Slope = (0 - 2)/(3 - 0) = -2/3
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Solve the equation t − 5 = 12 for t.
17
7
−7
−17
Step-by-step explanation:
t - 5 = 12 | add 5 to both sides
t = 17
and that is it. that's all we needed to do.
Please Help, If you could provide a step by step on how to solve these it'd be greatly appreciated as well <3
Answer:
animals vs. gender:
male dogs: 74.4%
marginal distribution for female animals: 49.4%
weight class vs gender:
marginal distribution for female: 62.0%
males who are underweight: 71.5
overweight individuals: 21.8%
Step-by-step explanation:
animals vs. gender:
male dogs:
there are 43 dogs
and there are 32 male dogs
32 divided by 43
say it like 32.000 ÷ 43 = .744186
move the decimal two times to the right to find your percentage
74.4%
marginal distribution for female animals:
there are 39 females
and 79 animals
39 divided by 79
.49367
move the decimal two times to the right to find your percentage
49.36%
which would approximate to
49.4%
weight class vs gender:
marginal distribution for female:
there are 620 girls
and 1000 people
so, 620 divided by 100
write it like this 620.0 ÷ 1,000
.62
move the decimal two times to the right to find your percentage
62%
males who are underweight:
there are 93 underweight males
and 130 underweight people in total
93 divided by 130
.7153846
move the decimal two times to the right to find your percentage
71.5%
overweight individuals:
there are 218 overweight people and 1000 people in total
218 divided by 1000
.218
move the decimal two times to the right to find your percentage
21.8%
0.0939 as a fraction
Answer:
0.0939 as a fraction is 939/10000
Step-by-step explanation:
939 all over 10,000
in 0.0939 the point move
trying to figure out how to put in a question so if it works say hi as an answer
Answer:
hello!!
i like ur pfp! :)
2 + (8 - 4) + 32 * 3
Answer: 102
Step-by-step explanation:
solved