Answer:
Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves.
Step-by-step explanation:
Let in each large bookshelves Henry uses x nails and in each small bookshelves, Henry uses y nails.
Now, he built 10 small bookshelves and 1 large bookshelf, using a total of 412 nails.
So, 10x + y = 412 ......... (1)
Again, he built 10 small bookshelves and 8 large bookshelves, using a total of 776 nails.
So, 10x + 8y = 776 ........... (2)
Now, subtracting equation (1) from equation (2) we get, 7y = 364
⇒ y = 52
Again, from equation (1) we get, 10x = 412 - 52 = 360
⇒ x = 36
Therefore, Henry uses 36 nails in large bookshelves and 52 nails in small bookshelves. (Answer)
Final answer:
Henry uses 36 nails for a small bookshelf and 52 nails for a large bookshelf, according to the system of equations derived from the information given.
Explanation:
Calculating the Number of Nails Used by Henry
To solve this problem, we will use a system of equations.
Let's define x as the number of nails used for a small bookshelf and y as the number of nails used for a large bookshelf. From the question, we have the following equations based on the information given:
10x + 1y = 412 nails (first scenario with 10 small and 1 large bookshelf)
10x + 8y = 776 nails (later scenario with 10 small and 8 large bookshelves)
We can use these two equations to find out the values of x and y. Let's subtract the first equation from the second to eliminate x from our calculations:
10x + 8y − (10x + 1y) = 776 − 412
7y = 364
y = 52
Now we know that Henry uses 52 nails for a large bookshelf. Next, we will find the number of nails for a small bookshelf by substituting the value of y into the first equation:
10x + 1(52) = 412
10x = 412 − 52
10x = 360
x = 36
Hence, Henry uses 36 nails for a small bookshelf.
Solve for x.
X-8=-20
-12
12
-28
28
Answer:
-12
Step-by-step explanation:
x - 8 = -20 (add 8 to both sides)
x = -20 + 8
x = -12
Answer:
-12
Step-by-step explanation:
-12 + -8 is -20.
x= -12 because if you added 28 or 12, the answer would be positive. If you subtracted -28 from -8 your answer would be -36.
So the only answer is -12.
2) Jim get $200 for 50 sales, $350 for 70 sales, and $500 for
85 sales. This is called
Answer:
salary based on how many sales are made
Step-by-step explanation:
students at westbrook middle school hold green team meetings to plan ways to help protect the environment this week there are 144 at the meeting which is 90% of the total group
Answer:
160 member
Step-by-step explanation:
Here the question is, how many total member are there in the team?
Given: 144 member in the meeting is equal to 90% of the total group.
Let assume x be the total member in the green team.
Now, finding the number of member in the team, which is x.
[tex]\frac{90}{100} \times x = 144[/tex]
Next, cross multiply the number on both the side
⇒ [tex]x= \frac{144 \times 100}{90} = 16\times 10[/tex]
∴ x = 160
160 is the total number of member in green team.
Answer:
160 members
Step-by-step explanation:
How do I know this well 144/90 1.6 take away the decimal and it is 16 add a 0 from the 90 and 160
On a 95-degree day with 80% humidity, the amount of time it takes an air-conditioning unit to cool a 2000-square-foot home 1 degree follows a normal distribution with mean time of 24 minutes and standard deviation of 1 minute. What is the probability it takes an air-conditioning unit longer than 25 minutes to cool the house 1 degree? (Use the Empirical Rule.)
There's a 16% probability that the air-conditioning unit will take longer than 25 minutes to cool a 2000-square-foot home by 1 degree on a 95-degree day with 80% humidity, based on the empirical rule of normal distribution.
Explanation:To find the probability of the air-conditioning unit taking longer than 25 minutes to cool the house 1 degree, you first have to understand that the situation described follows a normal distribution with a mean (μ) of 24 minutes and a standard deviation (σ) of 1 minute.
Using the Empirical Rule, also known as the 68-95-99.7 rule, we can assess probabilities for normal distributions.
According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Since we are interested in the time more than 25 minutes, we are looking at the area to the right of the mean plus 1 standard deviation (24 + 1 = 25 minutes).
Approximately 68% of the data falls within one standard deviation (between 23 and 25 minutes), so about 34% is below 25 minutes, and another 34% is above. However, we're interested in the portion beyond 25 minutes, falling in the tail.
Because 50% of the distribution falls above the mean (by definition of a normal distribution), and we account for the 34% within one standard deviation above the mean, this leaves us with 50% - 34% = 16% of data points (times in this case) falling beyond 25 minutes on a 95-degree day with 80% humidity.
If triangle ABC = DEF AB = 8 , BC = 19 , AC = 14 , EF = 4x - 1 and DE=y-6, what are the values of x,y, and z
Answer:
x = 5 and y = 14
Step-by-step explanation:
Given [tex]\triangle[/tex]ABC[tex]\cong \triangle[/tex]DEF.
Congruent triangles have congruent corresponding parts, so
[tex]AB\cong DE\\ \\AC\cong DF\\ \\BC\cong EF[/tex]
Since
[tex]AB=8\\ \\BC=19\\ \\AC=14\\ \\EF=4x-1\\ \\DE=y-6,[/tex]
then
[tex]4x-1=19\\ \\4x=19+1\\ \\4x=20\\ \\x=5[/tex]
and
[tex]y-6=8\\ \\y=8+6\\ \\y=14[/tex]
a woman is walking at the rate of 90 yards per minute. How fast is she going in feet per second?
Answer:
She is going at the rate of 4.5 feet per second.
Step-by-step explanation:
Given:
The rate of walking is 90 yards per minute.
Now, to find the rate in feet per second.
1 yard = 3 foot.
1 minute = 60 seconds.
So, first we find the rate of walking per second in yard = [tex]90\div 60[/tex]
Therefore by dividing we get = [tex]1.5 yard[/tex]
Now, we find the rate of walking per second in feet = [tex]1.5\times 3[/tex]
So, by multiplying we get = [tex]4.5 feet[/tex]
Therefore, she is going at the rate of 4.5 feet per second.
what is the equation of a line parallel to y-2x=3 that passes through the point (3,1)
Answer:
y = 2x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange y - 2x = 3 into this form by adding 2x to both sides
y = 2x + 3 ← in slope- intercept form
with slope m = 2
Parallel lines have equal slopes, thus
y = 2x + c ← is the partial equation
To find c substitute (3, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 2x - 5 ← equation of line
Solve the inequality. Graph the solution.
7z< -28
Answer: The answer is -9
Step-by-step explanation:
7z<-28= -9
Because we take the -28 and add 19 because that's the common denominator and we come up with -9
There is a pile of nickles and dimes. The whole pile has 82 coins and is worth 6.75. How many nickles are in the pile?
There are 29 nickles in the pile.
Step-by-step explanation:
Let,
nickles = x
dimes = y
Total coins = 82
Total worth = $6.75 = 6.75*100 = 675 cents
1 nickle = 5 cents
1 dime = 10 cents
According to given statement;
x+y=82 Eqn 1
5x+10y=675 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=82)\\5x+5y=410\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](5x+10y)-(5x+5y)=675-410\\5x+10y-5x-5y=265\\5y=265[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{265}{5}\\y=53[/tex]
Putting y=53 in Eqn 1
[tex]x+53=82\\x=82-53\\x=29[/tex]
There are 29 nickles in the pile.
Keywords: linear equations, subtraction
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11. Any company plans to connect a total of 20 pF of capacitance to a 7200-V
dine. To make this connection, four capacitors will be connected in series, What is
the capacitance of each capacitori
1 W
oche minimum ac
Answer:
C = 80pF
Step-by-step explanation:
The total capacitance of 4 capacitors connected in series is given by:
[tex]Ct = \frac{1}{1/C1 + /C2 + 1/C3 + 1/C4}[/tex]
[tex]Ct = \frac{1}{1/C + /C + 1/C + 1/C}[/tex]
[tex]Ct = \frac{1}{4/C}[/tex]
[tex]Ct = \frac{C}{4}=20pF[/tex]
Solving for C:
C = 4*20pF
C = 80pF
There is a total of 2,512 people attending the fun fair. 5/8 of sttemdees are students and 1/4 of attendees are parents. the rest of the attendees are people living ioin the neigbourhood. How mnay o fthe attendees are people living in the neighbouhood?
Answer:
314 of the people attending the fun fair are people living in the neighborhood
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Number of people attending the fun fair = 2,512
Fraction of people attending the fun fair that are students = 5/8
Fraction of people attending the fun fair that are parents = 1/4
Rest of the people attending the fun fair lives in the neighborhood
2. Let's calculate the number of students, parents and people living in the neighborhood
Students:
Fraction of people attending the fun fair that are students = 5/8
5/8 * 2,512 = 1,570
1,570 of the people attending the fun fair are students
Parents:
Fraction of people attending the fun fair that are parents = 1/4
1/4 * 2,512 = 628
628 of the people attending the fun fair are parents
People living in the neighborhood
2,512 - 1,570 - 628 = 314
314 of the people attending the fun fair are people living in the neighborhood
What is (8x-30)+6x+(2x+10) simplified?
Answer:
16x-20
Step-by-step explanation:
(8x-30)+6x+(2x+10)
8x-30+6x+2x+10
8x+6x+2x-30+10
14x+2x-20
16x-20
Paul Hastings had a checkbook balance of $1345.00. His bank statement showed a deposit of $423.00 and he hadnt recorded a $15 service fee. What should his checkbook balance be?
Answer:
Paul Hastings checkbook balance be $1753
Explanation:
We are given Paul Hastings
current checkbook balance is equal to $1345.00
and a deposit of $423.00 is said to be made in the bank
so the new balance will be addition of this deposit in the current balance also there's a deduction of $15 as service fee.
So the total checkbook balance will be after subtracting $15 from sum of current balance and deposit.
So his checkbook balance = $1345 + $423 - $15
= $1753
which is the required value of checkbook.
Write an equation of the line that passes through the points
(0, 3) and (-5, 0).
Answer:
y-3=3/5x
Step-by-step explanation:
y-y1=m(x-x1)
Where m=slope and (x1, y1) is a point on the line.
m=(y2-y1)/(x2-x1)
m=(0-3)/(-5-0)
m=-3/-5
m=3/5
y-3=3/5(x-0)
y-3=3/5(x)
y-3=3/5x
(0, 3) is the y-intercept as it passes through y = 3 at x = 0, or the y-axis.
Slope:
[tex] \frac{y1 - y0}{x1 - x0} = \frac{3 - 0}{0 - ( - 5)} = \frac{3}{5} [/tex]
Equation of a straight line:
y = mx + c
m = slope (3/5)
c = y value of y-intercept (3)
Equation:
[tex]y = \frac{3}{5} x + 3[/tex]
If Carrie and Cory add on 18% tip to the bill after tax what does their lunch cost in total
Answer:
The cost of total lunch is 1.18 y ( 1+ 0.0 x )
Step-by-step explanation:
Given as :
The percentage of tip added tot he bill after tax = 18 %
Let the tax added to the bill = x % of total the lunch price
Let The total lunch cost = y
So, The cost of the lunch after tax = y + x % × y
I.e The cost of lunch after tax = y × ( 1 +x % )
Or. The bill of lunch after tax = y × ( 1 + 0.0 x )
Now the cost of lunch after tax and tip =18 % of y × ( 1 + 0.0 x ) + y × ( 1 + 0.0 x )
Or, the cost of lunch after tax and tip = y × ( 1 + 0.0 x ) (0.18 + 1 )
∴ The cost of lunch after tax and tip = y × ( 1 + 0.0 x ) × 1.18
Hence The cost of total lunch is 1.18 y ( 1+ 0.0 x ) Answer
This month Jan saved $80 from her babysitting job. Last month she saved $20. How many times more did she save this month than last month?
Answer:
4 times more
Step-by-step explanation:
80/20=4
Andrew draws a scale drawing of his office.If each 5 cm in the scale drawing equals 10ft, what are the actual dimensions of Andre’s office?
Answer:
well if it is a square then 10ft by 10ft. Otherwise, since you haven't given me the scale drawing, just find the area through 5cm. Then multiply your answer by 2 and instead of cm have ft.
Step-by-step explanation:
Write the equation of the line that passes through the point (4,3) and is perpendicular to the line y=2x-4
Answer:
y-3=-1/2(x-4)
Step-by-step explanation:
y-y1=m(x-x1)
perpendicular means negative reciprocal of the current slope,
and the negative reciprocal of 2 is -1/2.
y-3=-1/2(x-4)
A recipe for ice cream calls for 1.656 liters of milk.How many millimeters are in the recipe?
Answer:
In the recipe are 1,656 milliliters of milk
Step-by-step explanation:
The correct question is
A recipe for ice cream calls for 1.656 liters of milk.How many millimeters of milk are in the recipe?
Remember that
[tex]1\ liter=1,000\ milliliters[/tex]
To convert liters to milliliters multiply by 1,000
so
[tex]1.656\ L=1.656(1.000)=1,656\ mL[/tex]
therefore
In the recipe are 1,656 milliliters of milk
On a certain hot summer's day, 196 people used the public swimming pool. The daily prices are $ 1.50 for children and $ 2.00 for adults. The receipts for admission totaled $ 314.00 . How many children and how many adults swam at the public pool that day?
Number of adults = 40
Number of children = 156
Step-by-step explanation:
Let x be the number of adults and
y be the number of children
Then according to given statements
[tex]x+y=196\ \ \ Eqn\ 1\\2.0x+1.50y = 314\ \ \ Eqn\ 2\\[/tex]
From equation 1:
[tex]x+y = 196\\x = 196-y[/tex]
Putting in equation 2
[tex]2(196-y) + 1.50y = 314\\392-2y+1.50y = 314\\392-0.5y = 314\\-0.5y=314-392\\-0.5y=-78[/tex]
Dividing both sides by -0.5
[tex]\frac{-0.5y}{-0.5} = \frac{-78}{-0.5}\\y = 156[/tex]
Putting y = 156 in equation 1
[tex]x+156 = 196\\x = 196 - 156\\x = 40[/tex]
Hence,
Number of adults = 40
Number of children = 156
Keywords: Linear equations, Variables
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Which expression has a value of 35 when p = 7?
49/p
5p
45-p
25+ p
Answer: the answer is B. 5p
Step-by-step explanation:
just did it so i know its right:)
comment if so!
The rule which allows us to change the sign of an exponent is called the ____ rule.
Answer:
The rule which allows us to change the sign of an exponent is called the negative exponent rule.
Step-by-step explanation:
Consider the provided information.
The negative exponent rule is the rule which allows to change the sign of an exponent.
[tex]x^{-1}=\frac{1}{x}[/tex]
According to negative exponent rule: A negative exponents in the numerator moved to the denominator and become positive exponents.
If A negative exponents in the denominator moved to the numerator and become positive exponents.
Hence, the required statement is: The rule which allows us to change the sign of an exponent is called the negative exponent rule.
A 2 1/2 pound bag of grass seed cover 1/8 of an acre. How much grass seed is needed for 1 acre?
Answer:
8 times more 8*2 1/2 = 20 pounds.
Step-by-step explanation:
Answer:
20 pounds of grass seed is needed for one acre.
Step-by-step explanation:
You can set up a proportion to solve:
[tex]\frac{2.5 pounds}{1/8 acre}[/tex] = [tex]\frac{x pounds}{1 acre}[/tex]
Cross multiply:
[tex]\frac{1}{8}[/tex]x = 2.5
Divide both sides by [tex]\frac{1}{8}[/tex] or multiply both sides by 8.
x = 20
Which expression is equivalent to 8-4(x-6)/4?n is equivalent to 8-4(x-6)/4?
Answer:
B) -x+8
Step-by-step explanation:
8-4(x-6)=8-4x+24=-4x+32
(-4x+32)/4=-x+8
Answer:
the answer is B did it on edge
Step-by-step explanation:
please give brainlist
it takes one fourth of a gallon of paint covers one fifth of a car how much paint covers the whole car
Answer:
The volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
Step-by-step explanation:
Let the volume of paint required to cover whole car be 'x'.
Given:
Volume of paint to cover one-fifth of a car = one-fourth of a gallon.
We use unitary method to determine the volume of paint required.
∵ One-fifth of a car requires paint = [tex]\frac{1}{4}\ gal[/tex]
∴ Whole volume of car requires paint = [tex]\frac{\frac{1}{4}}{\frac{1}{5}}[/tex]
[tex]=\frac{1}{4}\times \frac{5}{1}\\=\frac{5}{4}\\=1\frac{1}{4}\ gal[/tex]
Therefore, the volume of paint that covers the whole car is [tex]1\frac{1}{4}[/tex] gallons or one and a quarter gallons.
What is the surface area of the right prism?
Answer:
The surface area of right prism is 12 feet² , option D
Step-by-step explanation:
Given as :
The measure of base = 4 ft
The height of base = 0.5 ft
The surface area of right prism = perimeter of base × height + 2 × base
Now ,
Perimeter of base = 4 + 4 = 8 ft
So, The surface area of right prism = 8 × 0.5 + 2 × 4
Or, The surface area of right prism = 4 + 8
∴ , The surface area of right prism = 12 feet²
Hence The surface area of right prism is 12 feet² . Answer
Answer:
17.5 ft2
Step-by-step explanation:
Rectangle PQRS is rotated 90 clockwise about the origin what are the coordinates of R
Since rectangle PQRS is rotated 90 clockwise about the origin what are the coordinates of R' are: A. R' (4, -1).
In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;
(x, y) → (y, -x)
Coordinate P (-3, -1) → Coordinate P' (-1, 3)
Coordinate Q (-1, -1) → Coordinate Q' (-1, 1)
Coordinate R (-1, -4) → Coordinate R' (-4, 1)
Coordinate S (-3, -4) → Coordinate S' (-4, 3)
Complete Question:
Rectangle PQRS is rotated 90 clockwise about the origin. What are the coordinates of R'?
The sum of three integers is 12
12
. The sum of the first and second integers exceeds the third by 32
32
. The third integer is 15
15
less than the first. Find the three integers.
The three integers are 5,17 and -10
Step-by-step explanation:
Let x, y and z be three integers then
[tex]x+y+z=12 \ \ \Eqn\ 1[/tex]
'The sum of the first and second integers exceeds the third by 32'
[tex]x+y=z+32\ \ \ \ Eqn\ 2[/tex]
The third integer is 15 less than the first.
[tex]z=x-15\ \ \ \ Eqn\ 3[/tex]
From Eqn 2:
[tex]x+y=z + 32\\x+y-z=32[/tex]
Subtracting Eqn 1 from eqn 2
[tex]x+y-z-(x+y+z)=32-12\\x+y-z-x-y-z=20\\-2z=20[/tex]
Dividing both sides by -2
[tex]\frac{-2z}{-2}=\frac{20}{-2}\\z=-10[/tex]
Putting z=-10 in Eqn 3
[tex]z=x-15\\-10=x-15\\x=15-10\\x=5[/tex]
Putting x=5 and z=-10 in Eqn 1
[tex]x+y+z=12\\5+y-10=12\\y-5=12\\y=12+5\\y=17\\[/tex]
Hence,
The three integers are 5,17 and -10
Keywords: Linear Equations, Variables
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Answer:
First = 5, second = 17, third = -10
Step-by-step explanation:
First integer = x
The third integer is 15 less than the first, so
Third integer = x - 15
The second integer = y
The sum of the first and second integers exceeds the third by 32, so
The sum of the first and second integers = x + y
The third integer = x - 15
x + y is 32 more than x - 15, hence
x + y - 32 = x - 15
y - 32 = -15
y = 32 - 15
y = 17
The second integer = 17
The sum of three integers is 12, so
x + 17 + x - 15 = 12
2x + 2 = 12
2x = 12 - 2
2x = 10
x = 5
x - 15 = 5 - 15 = -10
What is the name of a 21 sided polygon?
Answer:
We call a 21-sided polygon a Henacosagon.
Explanation:
See chart above
* 9 − nona-
I am joyous to assist you anytime.
The name of a 21 sided polygon is Henicosagon.
What is a polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. The interior of a solid polygon is its body.
Given that, what is the name of a 21 sided polygon,
Polygons have very simple names for the first twenty names.
They use a basic prefix naming system. Di, tri, tetra, penta, and so on.
But polygons with 21 to 99 sides have a different naming system.
First, we use a prefix for the tens (such as triaconta—30). Then we use a prefix for the ones (such as di—20).
At last, we put them together with a ‘kai’ between them. This would be formatted to look like (tens)kai(ones)gon.
In simpler words, a 32-sided polygon. We can normally refer to it as a 32-gon.
Hence, the name of a 21 sided polygon is Henicosagon.
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Write the number 9.359 × 105 in standard form.
Answer:
982.695
Step-by-step explanation:
9.359 x 105 = 982.695