Answer:
Jamie: His inequality would look like this: 25x >= 600
Stella: Her inequality would look like this: 15y >= 600
Her limitations would be listed as: y=40
Yep. Stella has plenty of money by baking 40 pies; $600.
We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.
Since the cost for washing one car is $25
Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.
Since the cost for making one pie is $15
Therefore, the cost of making y pies is 15y.
Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600
We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So.... y<=40
Bam.
In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40
The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.
Step-by-step explanation:
abraham lincoln declared thanksgiving a holiday in 1863 what is the prime factorization of 1863
3 x 3 x 3 x 3 x 23 = 1,863. It can also be written in exponential form as 3 to the power of four times 23.
Answer:
1863 = 3 · 3 · 3 · 3 · 23Step-by-step explanation:
[tex]\begin{array}{c|cc}1863&3\\621&3\\207&3\\69&3\\23&23\\1\end{array}[/tex]
For every part produced by a factory, there are 5 ounces of scrap aluminum that can be recycled. There are16 ounces in 1 pound and 2,000 pounds in 1 ton. How many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling
Answer:
The factory must produce 6,400 parts so that there is 1 ton of scrap aluminum for recycling.
Step-by-step explanation:
1 part produced ⇒ 5 ounces scrap aluminium recycled.
So, the ratio of parts produced : Scrap of aluminium = 1 : 5 .... (a)
Let us assume for m parts produced , 1 ton of scrap is recycled.
Also, 1 ton = 2, 000 pounds
and 1 pound = 16 ounces
⇒ 1 ton = 2000 x (16 ounces) = 32,000 ounces
So, for m parts made in the factory, 32,000 ounces scrap is recycled.
So, the ratio of parts produced : Scrap of aluminium = m : 32,000 .... (b)
From both the given ratio, we get
1 : 5 = m : 32,000
or, [tex]\frac{1}{5} = \frac{m}{32,000} \implies m = \frac{32,000}{5} = 6,400[/tex]
⇒ m = 6,400
Hence, the factory must produce 6,400 parts so that there is 1 ton of scrap aluminum for recycling.
Answer:
6,400
Step-by-step explanation
if im late then my bad, how ya'll day going? and Byeee, i'm at school ;)
A price that is regularly $81 was reduced by 55%.
Answer:
$36.45
Step-by-step explanation:
81 - 55%
Convert percentage to decimals
55% = 0.55
81 - 55%
= 81 - 0.55(81) <= 81 reduced by 55% of 81
= 81 - 44.55 <= simplify and solve
= 36.45
Lines r , s , and t are parallel. That means they have the same slope. Each of these lines has a slope of - 2 . Enter numbers to complete an equation for each line.
Answer:
(a) y = -2 x -2
(b) y = -2 x + 1
(c) y = -2 x + 3
Step-by-step explanation:
The given lines r , s and t are parallel.
⇒ Slope of line r = Slope of line s = Slope of line t = (-2)
The point slope equation for any line is given as
y = m x + C : m = slope pf line, C is y - intercept.
Y intercept is a point on line when x = 0.
Now for the line r, slope = (-2) and y intercept = (-2)
So, the equation is given as y = -2x -2
Now for the line s, slope = (-2) and y intercept = (1)
So, the equation is given as y = -2 x + 1
Now for the line t, slope = (-2) and y intercept = (3)
So, the equation is given as y = -2 x + 3
Please can someone help me answer this question attached.
Answer:
see the explanation
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal angles
step 1
Find the measure of angle BDA
we know that
Triangle ABD is an isosceles triangle
AB=AD ---> given problem
so
m∠ABD=m∠BDA
therefore
m∠BDA=72°
step 2
Find the measure of angle BAD
Remember that the sum of the interior angle in a triangle must be equal to 180 degrees
In the triangle BDA
m∠ABD+m∠BDA+m∠BAD=180°
substitute the given values
72°+72°+m∠BAD=180°
144°+m∠BAD=180°
m∠BAD=180°-144°=36°
step 3
Find the measure of angle BCA
In the triangle ABC
m∠BCA=m∠BAC
we have that
m∠BAC=m∠BAD=36°
therefore
m∠BCA=36°
step 4
Find the measure of angle ABC
In the triangle ABC
m∠BAC+m∠BCA+m∠ABC=180°
substitute the given values
36°+36°+m∠ABC=180°
72°+m∠ABC=180°
m∠ABC=180°-72°=108°
step 5
Find the measure of angle DBC
we know that
m∠DBC+m∠ABD=m∠ABC ----> by addition angle postulate
substitute the given values
m∠DBC+72°=108°
m∠DBC=108°-72°=36°
step 6
Find the measure of angle BDC
we know that
m∠BDC+m∠ADB=180° ----> by supplementary angles
substitute the given value
m∠BDC+72°=180°
m∠BDC=180°-72°=108°
step 7
In the triangle DBC we have
m∠DBC=36°
m∠BCD=m∠BCA=36°
so
The triangle BCD has two equal angles
therefore
Triangle BCD is an isosceles triangle
and
BD=BC
Andre wants to make an open box by cutting out corners of a 22 inch by 28 inch poster board and then folding up the sides. The volume V(x) in cubic inches of the open top box is a function of the side length x in inches of the square cutouts. Write and expression for v(x)
Answer:
v(x) = x(22 - 2x)(28 - 2x)
Step-by-step explanation:
The length of the box = 28 - 2x inches,
The width = 22 - 2x inches and the height = x inches.
v(x) = x * width * length.
The volume of the open top box is [tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches
The volume of the box is V = (length)(width)(height).
Let the cutout side length be [tex]x[/tex] inch,
We are to cut out [tex]x[/tex] by
So, the length of the box is [tex]28 - 2x[/tex] inch
the width of the box is [tex]22 - 2x[/tex] inch and
the height of the box is [tex]x[/tex] inch
Now, substituting the values in the volume formula, we get
[tex]V(x) = (28 - 2x)(22 - 2x)(x)[/tex] cubic inches
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A college has 9 more english instructors than math instructors. if the total number of English and math instructors is 57, find the number of english instructors and the number of math instructors.
Answer:
There are 24 math instructors and 33 english instructors.
Step-by-step explanation:
Let x be the number of math instructors and y be the english instructors. Since the college has 9 more English instructors than math instructors, set up the equation like this: x+(x+9)=57 where x+y=57, you can see that y=x+9.
Now, it's time to solve for x and y.
x+(x+9)=57
2x+9=57
2x=57-9
2x=48
x=48/2=24
y=24+9=33
x=24, y=33
Answer:
24 math instructors & 33 english instructors
Step-by-step explanation:
x+(x+9)=57
2x+9=57
2x=57-9
2x=48
x=48/2=24
y=24+9=33
x=24, y=33
Bill wants to make 22 small pizzas for a party. He has 16 cups of flour. Each pizza crust takes 3/4 cup of flour
he have enough flour?
The solution is 16.5 cups
The number of cups of flour for 22 small pizzas is 16.5 cups and Bill does not have enough flour for the party
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of cups of flour required be = A
Now , the equation will be
The number of pizza's Bill has for the party = 22 pizzas
The number of cups of flour Bill has = 16 cups
The number of cups of flour required for 1 pizza = 3/4 cups of flour
So , The total number of cups of flour for 22 pizzas = 22 x number of cups of flour required for 1 pizza
Substituting the values in the equation , we get
The total number of cups of flour for 22 pizzas = 22 x ( 3/4 )
The total number of cups of flour for 22 pizzas = 16.5 cups of flour
So , the number of cups of flour required > number of cups of flour Bill has
Therefore , the value of A is 16.5 cups
Hence , Bill does not have enough flour for the party
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644 divide by 32 pls help
The answer would be 20.125 or 161/8, because to divide numbers, it is like the fraction 644/32. For example, if you have 644 mcord.weebly.com sites or bananas and you need to equally divide them into 34 groups, their would be 20.125 mcord.weebly.com sites or bananas in each group.
3) The equation 41.44=k7 shows that buying 7 bags of apples
would cost 41.44 dollars. How much is it for one bag?
Answer:
k = $41.44/7 bags = $5.92/bag
The cost of one bag of apples is 5.92 dollars.
To find the cost of one bag of apples, we can divide the total cost by the number of bags.
Given the equation [tex]\(41.44 = 7k\)[/tex], where [tex]\(k\)[/tex] represents the cost of one bag, we can solve for [tex]\(k\)[/tex] by dividing both sides of the equation by 7:
[tex]\[ k = \frac{41.44}{7} \][/tex]
Calculating:
[tex]\[ k = \frac{41.44}{7} = 5.92 \][/tex]
What is another way to write the ratio 13:6
Answer:
13/6
Step-by-step explanation:
it can also be written as a fraction
33. Sarah has $200 in her bank account now. If she
deposits $10 weekly, which of the following formulas
will show her deposits (D) at the end of h weeks?
(1) D=200+ 10
in
(2) D = (200)(10n)
(3) D = 200 + 10
(4) D = 200 + 10
(5) D = 200n + 10
Answer:2
Step-by-step explanation:if she deposits 10 dollars every week she would be adding 10 dollars which means we have to multiply 10 by however many weeks she saves
Sarah's weekly deposits after h weeks can be calculated using the linear equation D = 200 + 10h. This equation includes her starting balance of $200 and adds $10 for each week.
Explanation:The subject of this question is Mathematics, specifically focusing on the concept of linear equations.
The correct formula to show Sarah's deposits at the end of h weeks would be (3) D = 200 + 10h. This formula works by establishing 200 as her starting amount (her current bank balance), and adding $10 for each week (h).
For instance, if h was 5 weeks, Sarah would have D = 200 + 10 * 5 = 200 + 50 = $250 in her bank account. This demonstrates how the formula allows you to calculate her weekly deposits effectively.
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Chang is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $86 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Answer:
35
Step-by-step explanation:
86-65=21$ (initial fee diffrence)
21/0.6= 35
for 35 m company B charge less than A unless if renter want to drive further 35m so company A present a better offer.
Rachel has 8/12 of a fun of frosting. If she used 1/4 of it, how much was left?
Answer:
6/12
Step-by-step explanation:
A fourth of 8 is 2, so there would be 6/12 of the tub of frosting left.
Answer:
5/12
Step-by-step explanation:
8/12=2/3
2/3-1/4=8/12-3/12=5/12
The square below represents one whole what percent is represented by the shaded area
Answer:
Step-by-step explanation:
The square has 100 smaller parts.
92 of them are shaded, that means 92% of the square is shaded.
what is 3.1n - 1.1n =
A digital clock displays military time in hh:mm format. Find the probability that the number made up of the first two digits is more than 25
Answer:
0
Step-by-step explanation:
In military time format, first two digits are in hours. We know that, on a digital clock, the first two digits always shows between 01 to 24.
So, there is no probability that the first two digits will show more than 25.
As there is no probability, the probability will be zero or 0. Because probability of any incident is whether 0 or 1; where 1 is for certain event.
Explain how you could convert 152 cups into gallons.
Answer: There are 16 cups in every gallon so we could divide 152 by 16 and get our number of gallons which would give us 9.63 or a little over 9 and a half gallons.
Step-by-step explanation:
A cookie recipe calls for 6 cups of flour
and 2 cups of sugar. What is the ratio of
the amount of sugar to the amount of
flour?
Answer:
1:3
Step-by-step explanation:
Sugar : Flour
2 : 6 (substitute the numbers of cups)
1 : 3 (simplify by reducing. divide both sides by 2)
The ratio is 1:3.
Answer:
1:3
Step-by-step explanation:
2:6[sugar is to flour]
1:3[to simplify divide both sides by two]
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week, 300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that visited the store in the second week?
Answer: C
Step-by-step explanation:
The answer is C because it says 360 and 300. If you do a problem solve for that one on a peace of paper I think it would be 16.7%
Answer:
Step-by-step explanation:
Change in number = number visited in 1st week - number visited in 2nd week
= 360-300 = 60
So percentage change in number= 60/360×100=16.67
Please help!!
The answers and question is in the picture!
conservation imporoper fraction to mixed number answer
solve the equation 5x-1=14
Answer:
x=3
Step-by-step explanation:
we move the 1 to the other side so
it goes from -1 to a positive 1 then add it to the 14 then you will have
5x=15
to remove the x divided 5 on both sides and you get x=3
The equivalent value of the equation is x = 3
Given data ,
Let the equation be represented as A
Now , the value of A is
5x - 1 = 14
So , the left hand side of the equation is equated to the right hand side by the value of ( 14 )
On simplifying the expression , we get
5x - 1 = 14
Combining the like terms in the expression , we get
Adding 1 on both sides , we get
5x = 15
Divide by 5 on both sides , we get
x = 15/5
x = 3
Therefore , the value of x = 3
Hence , the expression is x = 3
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How do I solve this? ( explanation with answer)
Answer:
a.) x= 11
d.) -7
g.) -5
Step-by-step explanation:
a.) x+1 = 4*3
x=12-1
d.)3x+1=-4*5
3x+1=-20
x=-7
g.)11x-1=-8*7
11x-1=-56
11x=-56+1
x=-5
Answer:
a) x = 11, d) x = -7, g) x = -5Step-by-step explanation:
[tex]a)\\\dfrac{x+1}{3}=4\\\\\dfrac{x+1}{3}=\dfrac{4}{1}\qquad\text{cross multiply}\\\\(x+1)(1)=(3)(4)\\\\x+1=12\qquad\text{subtract 1 from both sides}\\\\x+1-1=12-1\\\\\boxed{x=11}[/tex]
[tex]d)\\\\\dfrac{3x+1}{4}=-5\\\\\dfrac{3x+1}{4}=\dfrac{-5}{1}\qquad\text{cross multiply}\\\\(3x+1)(1)=(4)(-5)\\\\3x+1=-20\qquad\text{subtract 1 from both sides}\\\\3x+1-1=-20-1\\\\3x=-21\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}=\dfrac{-21}{3}\\\\\boxed{x=-7}[/tex]
[tex]g)\\\dfrac{11x-1}{8}=-7\\\\\dfrac{11x-1}{8}=\dfrac{-7}{1}\qquad\text{cross multiply}\\\\(11x-1)(1)=(8)(-7)\\\\11x-1=-56\qquad\text{add 1 to both sides}\\\\11x-1+1=-56+1\\\\11x=-55\qquad\text{divide both sides by 11}\\\\\dfrac{11x}{11}=\dfrac{-55}{11}\\\\\boxed{x=-5}[/tex]
Latisha has two pieces of ribbon she plans
to cut. One piece of ribbon is 48 inches and
the other is 80 inches. She plans to cut
all the ribbon into pieces of equal lengths.
What is the greatest possible length of each
piece?
The greatest possible length of each piece is 16 inches
Solution:Latisha has two pieces of ribbon. One piece of ribbon is 48 inches and the other is 80 inches
Ribbon is to be cut into pieces of equal length
To find the greatest possible length of each piece, we have to find greatest common divisor of 48 and 80
The greatest common factor, or GCF, is the greatest factor that divides two numbers
Steps to find G.C.F of 48 and 80
1) Find the prime factorization of 48
[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]
2) Find the prime factorization of 80
[tex]80 = 2 \times 2 \times 2 \times 2 \times 5[/tex]
3) To find the GCF, multiply all the prime factors common to both numbers:
Therefore, [tex]GCF = 2 \times 2 \times 2 \times 2 = 16[/tex]
So, 16 inches is the greatest possible length to cut so that every piece is of equal length.
I need serious help can anyone help me atleast with 3?
Answer:
z = 14
Step-by-step explanation:
Solve for z:
(4 z)/7 - 15 = -7
Put each term in (4 z)/7 - 15 over the common denominator 7: (4 z)/7 - 15 = (4 z)/7 - 105/7:
(4 z)/7 - 105/7 = -7
(4 z)/7 - 105/7 = (4 z - 105)/7:
1/7 (4 z - 105) = -7
Multiply both sides of (4 z - 105)/7 = -7 by 7:
(7 (4 z - 105))/7 = -7×7
(7 (4 z - 105))/7 = 7/7×(4 z - 105) = 4 z - 105:
4 z - 105 = -7×7
7 (-7) = -49:
4 z - 105 = -49
Add 105 to both sides:
4 z + (105 - 105) = 105 - 49
105 - 105 = 0:
4 z = 105 - 49
105 - 49 = 56:
4 z = 56
Divide both sides of 4 z = 56 by 4:
(4 z)/4 = 56/4
4/4 = 1:
z = 56/4
The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:
Answer: z = 14
Factor 3x2 - 18x + 27 completely.
Answer:
3(x - 3)²
Step-by-step explanation:
Given
3x² - 18x + 27 ← factor out 3 from each term
= 3(x² - 6x + 9)
= 3(x - 3)² ← in factored form
Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit and weighs slightly less than the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?
Answer:
Split the coins into three groups, A, B and C consisting of 3 coins in each group.
Weigh: A--B
1. If A=B, the the counterfeit is in group C
Weigh any two coins in group C and figure out the rest.
2. If A≠B, then the counterfeit is in the lighter group.
Weigh any two coins in the lighter group and figure out the rest.
Steven can find the counterfeit coin in just two weighings by dividing the 9 coins into 3 groups and using the balance scale.
Explanation:Steven can find the counterfeit coin in two weighing by following these steps:
Divide the 9 coins into 3 groups of 3 coins each. Weigh the two groups of 3 coins on the balance scale. If the two groups balance, the counterfeit coin is in the third group. Weigh two of the coins from this group on the scale.If one of the coins is lighter, it is a counterfeit coin. If the scale balances, the remaining coin is the counterfeit.By dividing the coins into three groups, Steven eliminates two-thirds of the coins after the first weighing and then narrows it down to just two coins in the second weighing.
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which graph represents a function?
Answer:
This graph does not represent a function.
Step-by-step explanation:
This graph does not pass the vertical line test. The vertical line test states that if a vertical line drawn intersects the graph of the relation more than once, then the relation is a NOT a function.
State under which condition the original and the simplified expressions are equivalent.
The expressions are equivalent if...
a) a≠0
b) a≠x
c) a≠-x
[tex]\frac{a^2}{ax-x^2} +\frac{x}{x-a}[/tex]
Answer:
a doesn't equal 0
Step-by-step explanation:
State under which condition the original and the simplified expressions are equivalent
25 + 11/12b =47 please answer
Answer:
The answer is b = 1/24.
Step-by-step explanation:
Given:
25+11/12b=47.
Now, to solve the equation to get the value of b:
[tex]25+\frac{11}{12b}=47[/tex]
Subtracting both sides with 25 we get:
[tex]\frac{11}{12b}=22[/tex]
Multiplying both sides by 12b we get:
[tex]11=264b[/tex]
Dividing both sides by 264 we get:
[tex]\frac{1}{24}=b[/tex]
Therefore, the answer is b = 1/24.