Answer:
Red paint = 12.5 gallons
Blue paint = 7.5 gallons
Step-by-step explanation:
The given ratio of red paint to blue paint is:
red : blue = 5 : 3Let x be the number of gallons of purple paint.
Therefore, the expression for each color of paint needed per x gallons of purple paint is:
[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8}x$}[/tex]
[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}x$}[/tex]
To calculate the number of gallons of red and blue paint needed to make 20 gallons of purple paint, substitute x = 20 into the found expressions:
[tex]\implies \textsf{Red\;paint $=\dfrac{5}{8} \times 20=\dfrac{100}{8}=12.5$}[/tex]
[tex]\implies \textsf{Blue\;paint $=\dfrac{3}{8}\times 20=\dfrac{60}{8}=7.5$}[/tex]
Therefore, the number of gallons of paint that should be used are:
Red paint = 12.5 gallonsBlue paint = 7.5 gallonsTable salt (sodium chloride, NaCl) is 40% sodium (Na) by weight. If a box of salt weighs 26 ounces, how much Na is in the box of salt?
The quantity of sodium in the salt is 10.4 ounces
How to find the quantity of sodium in the saltinformation from the problem
Table salt (sodium chloride, NaCl) is 40% sodium (Na) by weight
If a box of salt weighs 26 ounces, how much Na is in the box of salt
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
40%
= 40 percent
= 40 / 100
= 0.4
The factor 0.4 of the total weight of the salt is what we calculate
the total number is 26 ounces
= 0.4 * 26
= 10.4
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ab + bc + ac for a = 2, b = 5, and c = 3.
Answer:
31
Step-by-step explanation:
2⋅5+5⋅3+2⋅3
10+15+6
31
find three consecutive odd integers such that 4 times the largest is 17 more than 3 times the second
Answer:
3,4,5
Step-by-step explanation:
x+x+1+x+2
therefore ,
4(x+2)=17+3
4x+8=20
4x=20-8
4x=12
x=3
an oak tree can grow 24 inches a yea, for the first 75 years. if a newly planted oak tree is currently 90 inches, how tall, in inches, will the tree be in 8 years?
Answer:
282 inches
Step-by-step explanation:
24*8+
The last time it placed an order for ingredients, Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms. What is the percent of the decrease in the size of the sugar order?
hello anyone can help I would appreciate it
The percent of the decrease in the size of the sugar order is 40%.
According to the question,
We have the following information:
Sweet Treats Bakery ordered 1,090 kilograms of sugar. This time, the bakery is ordering 654 kilograms.
We know that following formula is used to find the percent decrease:
100*(original amount-final amount)/original amount
(More to know: the same formula is used to find the percent increase. It can used to find any percent increase or decrease given that the final and initial amount or price is given.)
100(1090-654)/1090
100*436/1090
40%
Hence, the percent of the decrease in the size of the sugar order is 40%.
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If Kelly has 12 pencils that are mechanical and 15 pencils that are not, what percent (to the nearest whole percent) of all of her pencils are mechanical?
Answer:
4/9
Step-by-step explanation:
Based on the given conditions, formulate: 12 division symbol(12 +15)
Calculate the sum or difference: 12/27
Cross out the common factor: 4/9
get the result:
Answer: 4/9
WHOEVER ANSWERS AND SHOW WORK GETS BRAINLIEST AWARD. Show that f(x)= 2x-3/2 and g(x)= 2x+3/2 are inverse functions. Must show fog=x and gof=x.
The functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.
The conditions for two functions f and g to be inverses: f(g(x)) = x or g(f(x)) = x.
where, f(g(x)) and g(f(x)) is the composite function.
We are given:
f(x) = (2x - 3) / 2
g(x) = (2x + 3) / 2
Let us find the value of f(g(x)) and g(f(x)):
Substitute the value of x with g(x) in f(x), we will get:
f(g(x)) = (2 * g(x) - 3) /2 = (2 * ((2x + 3) / 2) - 3) /2 = (2x + 3 - 3) / 2 = 2x / 2 = x
So, f(g(x)) = x.
Substitute the value of x with f(x) in g(x), we will get:
g(f(x)) = (2 * f(x) + 3) /2 = (2 * ((2x - 3) / 2) + 3) /2 = (2x - 3 + 3) / 2 = 2x / 2 = x
So, g(f(x)) = x.
Thus, the functions f(x) = (2x - 3) / 2 and g(x) = (2x + 3) / 2 are the inverse functions because the composite of the given functions equal to x that is fog = x and gof = x.
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How do i get the result for W in this equation -3 > 1/2w + 11
Answer:
w<-28
Step-by-step explanation:
multiply both sides by 2 : -6 > w +22
subtract 22 : w < -28
For the following right triangle find the side length X. Round your answer to the nearest hundredth.
The value of x in given triangle is 6.403
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angled triangle whose one angle is 90 degrees.
We find the value of x by using pythagoras theorem.
the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
4²+5²=x²
16+25=x²
41=x²
Take square root on both sides
x=√41=6.403
Hence the value of x in given triangle is 6.403
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Write an equation that has the given solutions. 0, 8, 2
∵∵∵∵∵∵∵∵∵∵∵∵.........................ω
What's is 100 x 100
(P.S don't cheat)
Answer:10,000
Step-by-step explanation:
North Conway Ski Shop ordered 300 pairs of skis. When the shop received the order, 60 pairs of skis were missing. What percent of the order did the shop receive?
Answer: 80% received, 20% lost.
Step-by-step explanation: [tex]\frac{60}{300}[/tex] × [tex]\frac{x}{100}[/tex] = [tex]\frac{6000}{300}[/tex] *Make sure to cross multiply!!*
——————————————6000 ÷ 300 = 20%
——————————————100 - 20 = 80% .
Therefore, the shop received 80% of the order because the other 20% are missing.
Solve for N. 5/3 = N/12
Answer:
N = 20
Step-by-step explanation:
5/3 = 1 2/3
20/12 = 1 8/20
They are equivalent
Describe and correct the error in finding m<1.
The error in this answer is that : The sum of angle of triangle is 180°
What is Triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Since, we know that Angle sum property of triangle is
∠A + ∠B + ∠C = 180°
Now, let ∠A = 115, ∠B = 39 and ∠C = m∠1
Substituting the value, we get
115° + 39° + m∠1 = 180°
154° + m∠1 = 180°
m∠1 = 180 - 154
m∠1 = 26°
Thus, m∠1 = 26°
Hence, The error for finding m∠1 is that angle sum of the triangle is equal to 180° and not 360°
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The graph of a quadratic function with vertex (4, 3)
Find the domain and the range.
Write the domain and range using interval notation.
Answer:
Domain: (neg infinity, pos infinity)
Range: (pos infinity, 3]
Step-by-step explanation:
To help out with her retirement savings, Lena invests in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money does she need to pay into the annuity each quarter for the annuity to have a total value of $96,000 after 18 years? Do not round intermediate computations, and round your final answer to the nearest cent
The amount of money that Lena needs to put each quarter for the annuity to have a total value of $96,000 is $953.45.
What amount should Lena deposit each quarter?An annuity is when a series of payment is made either at the beginning of a period or at the end of a period over a period of time.
An ordinary annuity is when the payment is made at the end of the period. When the interest is compounded quarterly, it means that four times in a year, the amount that is invested and the interest that has already being earned increase in value.
The formula that can be used to determine the quarterly payments is:
Payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = yearly interest / number of compounding = 3.6 / 4 = 0.9%n = total number of periods the payment is made = number of years x number of compounding = 18 x 4 = 72Payment = $96,000 / [{(1.009^72) - 1} / 0.009] = $953.45
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Evaluate the expression 2x square
+ 4y - z when x = 7, y = 9, and z = 11
Answer:
123
Step-by-step explanation:
2x square = 2.7 square = 98
98 + 4y = 98 + 4.9 = 98 + 36 = 134
134 - z = 134 - 11 = 123
Ur Wellcome ;)
What is the value of 3 + 5x when x
=
3?
Answer:
18
Step-by-step explanation:
What is the value of 3 + 5x when x=3?
3 + 5x =
replace the x with 33 + 5 × 3 =
Remember PEMDAS3 + 15 =
18
---------------
Which ordered pair is not a solution to the inequality y ≥ 2x2 − 4x + 2?
The ordered pair that is not a solution to the inequality y ≥ 2x² - 4x + 2 is:
(-1,6).
How to obtain which ordered pair is not a solution to the inequality?The inequality is given as follows:
y ≥ 2x² - 4x + 2.
Each ordered pair has the following format:
(x-coordinate, y-coordinate).
Then the numeric value of the inequality is going to be calculated for each ordered pair, as follows:
Replacing x on the inequality by the x-coordinate of the ordered pair.Replacing y on the inequality by the y-coordinate of the ordered pair.Then the numeric values of the inequality for each ordered pair are presented as follows:
(-1,6): 6 ≥ 2(-1)² - 4(-1) + 2 -> 6 ≥ 8.(1,0): 0 ≥ 2(1)² - 4(1) + 2 -> 0 ≥ 0.(0,3): 3 ≥ 2(0)² - 4(0) + 2 -> 3 ≥ 2.(2,5): 5 ≥ 2(2)² - 4(2) + 2 -> 5 ≥ 2.The contradiction, that is, the statement which is false, is given at the following ordered pair:
(-1,6).
Hence it is not a solution to the given inequality.
Missing InformationThe ordered pairs are given by the image shown at the end of the answer.
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What’s the answer to 5(2x + 1) = 50 ?
Answer:
x = 4.5
Step-by-step explanation:
5(2x + 1) = 50 Distribute the 5
5(2x) + (5) (1) = 50
10x +5 = 50 Subtract 5 from both sides
10x = 45 Divide both sdies by 10
x = 4.5
one serving contains 80 calories; how many calories are in 3 1/4 servings?
Answer: 260 calories
Step-by-step explanation:
If one serving has 80 calories, we will multiply 80 by 3 1/4 to find the total number of calories in 3 1/4 servings.
80 calories * (3 1/4) servings = 260 calories
Which statement is true about the solution of the system?
x − y = 4
-x + y = -4
There are no solutions.
There are an infinite number of solutions.
There is one solution.
Answer
Infinite solutions
Step-by-step explanation:
try any example you want it keeps going on and on.
-5x-13, For x<-7
H(x)={3, For -7<_ x< 3
x+2, For x_> 3
Solve for
H(-7)
H(-2)
H(3)
H(9)
Thank you
The values of H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 using the given equations by substituting the values.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. a formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.
Here,
H(x)= {-5x-13 for x<-7
3 for -7<=x< 3
x+2 for x=> 3}
when x=-7,
H(x)=3
when x=-2,
H(x)=3
when x=3,
H(x)=x+2
H(x)=5
when x=9,
H(x)=x+2
H(x)=11
H(-7)=3, H(-2)=3, H(3)=5, H(9)=11 when the values are substituted under the conditions stated for the given equation.
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in the spinner below what is the probability of landing on 1
Answer:
1/8Step-by-step explanation:
there are 6 numbers, but 3 and 6 take up double the space, so the probabilities are not 6 but 8
1/8 is your answer
What is the system of equations? Move the correct answer to each box. Not all answers will be used. 5x+3y=-6,3x+5y=-10,3x-5y=10,x-5y=-10,5x-y=2,x-5y=10 System of equations:
The correct system of equations is 5x-y=2,x-5y=10
How to find the system of equations?
In order to find the system of equations of the graph, we have to check the solution in the graph and then check for the system of equations that gives the same value.
Looking at the graph, the values of x and y at the point of intersection is the solution. Thus:
x = 0 and y = -2
Let's check the equations now:
5x+3y=-6, 3x+5y=-10
Solve for x and y using elimination
3 (5x+3y=-6)
5 (3x+5y=-10)
15x + 9y = -18
15x + 25y = -50
-6y = 32
y = -32/6 = -16/3 (This cannot be the system)
3x-5y=10, x-5y=-10
3x-5y = 10
x-5y = -10
2x = 20
x = 20/2 = 10 (This cannot be the system)
5x-y=2,x-5y=10
1(5x-y=2)
5(x-5y=10)
5x -y =2
5x-25y = 50
24y = -48
y = -48/24 = -2
put y = -2 into 5x -y =2:
5x -(-2) =2
5x + 2 = 2
5x = 0
x = 0
Therefore, 5x-y=2,x-5y=10 is the system of equations. The 3rd option is the answer. Move it to the box
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A board game uses the deck of 20 cards shown to the right. Two cards are selected at a random from this deck. Calculate the probability that first card selected has a yellow bird and second cared selected has a lion both with and without replacement
The probability with replacement is = 1/16
The probability without replacement is= 5/16
What do you mean by probability with replacement?
When the results must be put back into the sample space, the probability with replacement is utilized. This means that once an item is selected, it is replaced in the sample space, keeping the sample space's total number of elements constant.
Since cards should be replaced, 5 lions or 5 birds
so, the probability is
= 5/20 ÷ 5/20
=1/16
without replacement,
since cards should not be put back, for the second draw only 19 cards are left
so, the probability is
=5÷20 × 5÷19
=5/16
Hence ,
The probability with replacement is = 1/16
The probability without replacement is= 5/16
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for every 3 girls taking classes at a martial arts school there are 4 boys who are taking classes. suppose there are 236 boys taking classes at the school. write a proportion that could be used to predict the number of girls taking classes at the school. Use x to represent the number of girls, and find it
The mean of the data set is and the sample proportion of numbers less than the mean is
The mean of the data set is 22.1 , and the sample proportion of numbers less than the mean is 46.67 %
What are mean?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Mean of the data set is calculated by adding all numbers and dividing it with total number sample data.
Then Adding all the numbers;
25.5 + 26 +18.2 +15.3 + 28.5 + 27 + 20.7 +20.2 +26.1 +18.2 +21.4 +17.9 +24.3 +22.6+ 19.6 =331.5
Now Dividing by total,
331.5/15 =22.1
Mean =22.1
The sample proportion of numbers less than the mean will be;
= (7/15 ) 100
=46.67%
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The complete question is;
For this question, any non-integer answers should be entered as decimals, rounded to the hundredths place.
Consider this data set. The mean of the data set is ___ , and the sample proportion of numbers less than the mean is ___%
Consider the following equation:
X/4+3= 1/5
The value of a that will make the equation above valid lies between
which of the following numbers?
A) 10 and 15
B) -1 and -5
C) 1 and 5
D) -10 and -15
E) -5 and -10
For the given equation (x/4)+3= 1/5, the value of x which will make the given equation valid is lies between the numbers of ( -10 and -15).
As given in the question,
Given equation is equal to :
(x/4)+3= 1/5
Simplify the given equation (x/4)+3= 1/5 to get the value of x we have,
(x/4)+3= 1/5
Take least common multiple of 4 and 1 we get,
( x + 12) / 4 = 1/5
⇒5( x +12 ) = 4
⇒ 5x + 60 = 4
⇒ 5x = -56
⇒ x= -11.2
-11.2 lies between (-10 and -15).
Therefore, for the given equation (x/4)+3=1/5, the value of x which will make the given equation valid is lies between the numbers of
(-10 and -15).
The complete question is:
Consider the following equation:
(x/4)+3= 1/5
The value of x that will make the equation above valid lies between
which of the following numbers?
A) 10 and 15
B) -1 and -5
C) 1 and 5
D) -10 and -15
E) -5 and -10
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Need help with question
The first derivative by implicit differentiation of 2 · x⁶ + 5 · x⁴ · y - 7 · x · y⁶ = 8 is y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵).
How to find the derivative of a given function by implicit differentiation
Implicit differentiation is a differentiation method for implicit functions that combines chain rule and derivative rules. First, define the original function:
2 · x⁶ + 5 · x⁴ · y - 7 · x · y⁶ = 8
Second, use chain rule and derivative rules in the expression of the previous step:
12 · x⁵ + 20 · x³ · y + 5 · x⁴ · y' - 7 · y⁶ - 42 · x · y⁵ · y' = 0
Third, clear y' within the resulting equation:
12 · x⁵ + 20 · x³ · y - 7 · y⁶ + (5 · x⁴ - 42 · x · y⁵) · y' = 0
(5 · x⁴ - 42 · x · y⁵) · y' = 7 · y⁶ - 20 · x³ · y - 12 · x⁵
y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵)
The first derivative is y' = (7 · y⁶ - 20 · x³ · y - 12 · x⁵) / (5 · x⁴ - 42 · x · y⁵).
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