You have a budget of $300 to order shirts for a math club. The equation 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
a. Interpret the terms and coefficients in the equation.
b. Graph the equation. Interpret the intercepts.
c. Find three possible solutions in the context of the problem.
Answers
a) The coefficients are the costs of the respective shirts.
b) The graph can be seen on the image at the end, the intercepts are (0, 25) and (30, 0)
c) 3 solutions are:
(0, 25), (30, 0), (25, 4)
What does each coefficient means?
Here we know that:
x = number of short-sleeved shirtsy = number of long-sleeved shirts.And we have the linear equation:
10x + 12y = 300
The first coefficient is the one in the term "10x"
The coefficient 10 will mean the cost, in dollars, of each short-sleeved shirt.
The second coefficient is on the term "12y"
And 12 means the cost in dollars of each long-sleeved shirt.
b) The graph of the linear equation can be seen on the image at the end.
The y-intercept (when x = 0) is the number of long-sleeved shirts you can buy if you don't buy any short-sleeved one.
The x-intercept is the number of short-sleeved shirts you can buy if you don't buy any long-sleeved one.
c) 3 possible solutions can be seen on the graph, some examples are:
(0, 25), (30, 0), (25, 4)
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Related Questions
A house was valued at $254,000. Over several years, the value increased by 16%, giving the house a new value.
Answers
Answer:
289560
Step-by-step explanation:
Solve for j.
–3(j − 8) + –6 = –9
Answers
Answer:
j = 9
Step-by-step explanation:
Given equation,
→ -3(j - 8) + (-6) = -9
Let's solve for the value of j,
→ -3(j - 8) + (-6) = -9
→ -3j + 24 - 6 = -9
→ -3j + 18 = -9
→ -3j = -9 - 18
→ j = (-27)/(-3)
→ [ j = 9 ]
Hence, the value of j is 9.
Answer:
j = -9
Step-by-step explanation:
[tex] - 3(j - 8) + - 6 = - 9 \\ open \: brackets \\ - 3j + 24 + - 6 = - 9 \\ 3j + 24 = - 9 + 6 \\ 3j + 24 = - 3 \\ 3j = - 3 - 24 \\ 3j = - 27 \\ divide \: by \: 3 \\ j = - 9[/tex]
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $28, and the standard deviation is known to be $5.5. How large of a sample would be required in order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42? Round your answer up to the next integer.
Answers
In order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42. The sample size would be 85
How to find the size of sample when the error of at most $0.42Information form the question
the mean income is $28
the standard deviation is known to be $5.5
the mean per capita income at the 90% level of confidence
an error of at most $0.42
What is the formula for the sample size?This is given as from margin of error:
This is the term refers to the minimum error that is to be allowed
Margin of error, E = Zc * √(SD²/n)
n = sample size
n = SD x (Zc/E)²
SD = standard deviation
Zc = would be the critical value at 90 percent level of confidence = 1.65
plugging in the values
n = 5.5 x (1.65/0.42)²
n = 0.25 x 15.4337
n = 84.8854
n = 85
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When you flip a biased coin the probability of getting a tail is 0.4.
How many times would you expect to get tails if you flip the coin 160 times
Answers
Answer:
64 times
Step-by-step explanation:
Multiply 0.4, the chance of getting tails, which 160, the amount of times you flip the coin, and you get 64. This is reasonable, because the probability of getting heads is 0.6, and if you flip the coin 160 times, you will get heads 96 times. Hope this helped :)
A rectangular box is 12 in. x 14 in. x 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in
terms of pi.
Answers
The surface area of the largest sphere that could fit into the rectangular box of dimensions 12 in x 14 in x 18 in is 324π inches²
The surface area of sphere = 324π inches²
What is a Sphere?
A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the surface area of the Sphere be = S
Let the dimensions of the rectangular box be L x W x H
12 inches x 14 inches x 18 inches
Now , for the surface area of the sphere to have the largest surface area , the radius should be maximum
From the rectangular box , we can see that the height of the rectangle is best suited as the diameter of the sphere
So , Height of the Box = Diameter of the Sphere
And , Radius of the sphere = Height of the Box / 2
= 18 / 2
Radius of the sphere = 9 inches
Now ,
Surface Area of a Sphere = 4πr²
r = 9 inches
Substituting the values in the equation , we get
Surface Area of a Sphere S = 4 x π x ( 9 )²
= 4 x π x 81
= 324π inches²
Therefore , the value of S is 324π inches²
Hence , The surface area of sphere = 324π inches²
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
n=4;
i and 2i are zeros;
f(-1)=20
f(x) = ?
(Type an expression using x as the variable. Simplify your answer.)
Answers
The polynomial satisfying the given conditions is given as 2x⁴ + 10x² + 8.
What is a polynomial?The polynomial is an algebraic expression in which no any terms has the power other than a whole number.
The degree of a polynomial is the highest power of one of its terms.
Given that,
The degree of polynomial is n = 4.
The zeros of the polynomial are i and 2i.
And, f(-1) = 20
Since, a polynomial with real coefficients have either real zeros or complex conjugate zeros.
Here, the given zeros of the polynomial are imaginary which implies that the remaining two zeros are the conjugate of the given two zeros.
Thus, the zeros of the given polynomial are i, 2i, -i and -2i.
The general form of a 4th degree polynomial is given as,
ax⁴ + bx³ + cx² + dx + e
Use the factor theorem to get,
ax⁴ + bx³ + cx² + dx + e = K(x - i) (x - (-i)) (x - 2i) (x- (-2i)) (1)
⇒ ax⁴ + bx³ + cx² + dx + e = K(x² + 1) (x² + 4) (2)
Now, f(-1) = 20 which gives,
K((-1)² + 1) ((-1)² + 4) = 20
⇒ k = 2
Substitute K =2 in equation (2) to get,
ax⁴ + bx³ + cx² + dx + e = 2(x² + 1) (x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2(x⁴ + 5x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2x⁴ + 10x² + 8
Hence, the nth-degree polynomial function with real coefficients satisfying n = 4 and zeros i and 2i is 2x⁴ + 10x² + 8.
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What is the expression 9-z when z=8
Answers
9-(8)=1
Since z is equal to 8, it can be substituted in and solved
PLEASE HELP!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Number of Years at the Company Dianelys' Salary (Dollars)
00 40000\hspace{3px}\color{green}{\checkmark}40000
11 42500\hspace{3px}\color{green}{\checkmark}42500✓42500
22 45000\hspace{3px}\color{green}{\checkmark}45000✓45000
33 47500\hspace{3px}\color{green}{\checkmark}47500✓
Answers
1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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perpendicular bisector of the line segment whose endpoints are 7,4) and (−9,−4).
Answers
Answer:
y=-2x-2
Step-by-step explanation:
If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:
[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.
Now we find the equation!
y=mx+b. Plug in -[tex]2[/tex] as the "m", or slope:
y=-[tex]2[/tex]x+b
Now, plug in the point (-1, 0):
0=-[tex]2[/tex]*-1+b
0=[tex]2[/tex]+b
b=-[tex]2[/tex]
So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!
y=-[tex]2[/tex]x-[tex]2[/tex]
Hope this helps!! :D
bag has 5 red beads 3 Blue, 4 green random probability a single picked bead is blue
Answers
Answer:
1/4
Step-by-step explanation:
add all of them to get the sum which is 12. Since he asked for the blue which are 3. You put the 3/total which is 3/12. Then simplify. Which is equal to 1/4
1.25x10^-3/1.25x10^3
Answers
By solving the given fraction equation we get the answer is 1.
What is an exponent?
Exponent is the process of expressing large numbers in terms of powers. In other words, the exponent describes how many times a number has been multiplied by itself.
According to the zero exponent rule, any base with a zero exponent is equal to one. For instance, [tex]x^{0} = 1[/tex].
We have,
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\ * \\ 10^{-3}}[/tex]
[tex]= \frac{1.25\\ * \\ 10^{-3}}{1.25 \\} * 10^{3}[/tex]
Using the multiplication rule of fraction [tex]a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}[/tex]
[tex]= \frac{1.25 \ * \ 10^{-3} \ * \ 10^{3}}{1.25 \\}[/tex]
= [tex]= 10^{-3} * 10^{3}[/tex]
By applying the exponent rule [tex]\:a^b\cdot \:a^c=a^{b+c}[/tex] we get,
Add or subtract the numbers = 3 + 3 = 0
[tex]= 10^{0}[/tex]
By applying the rule [tex]a^{0} = 1[/tex], [tex]a \neq e^{0}[/tex]
= 1
Hence, by solving the above fraction equation we get the answer is 1.
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Solve for x.
Please help asap
Answers
Find the rate if a principal of $1,100 earned $1,089 interest in 12 years.
Answers
Answer:
8.25
Step-by-step explanation:
Parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n, what is true for the transformation that took place?
Line m was translated down 4 units.
Line m was translated up 4 units.
Line n was translated up 8 units.
Line l was translated down 8 units.
Answers
Line l was translated down 8 units, is true for the transformation that took place.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,
We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.
Hence, Line l was translated down 8 units, is true for the transformation that took place.
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Solve for d. 3 + d < 3 −d
d < −6
d < 6
d < 0
d < −3
Answers
Answer:
d is great than -3
Step-by-step explanation:
because negative numbers are less than whole numbers
5 pounds=______ounces
Answers
Answer:
Step-by-step explanation:
1. Basic systems in fluids: 1 pound equals 16 ounces.
2. Multiply 16 ounces by 5 to become equivalent!
16 ounces*5= 80 ounces!
3. Always double check
80 ounces/16=5 pounds
Answer: 80 ounces
HELP WILL GIVE BRAINLYEST!!!!!!! 30 POONTS Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−4, −25), (−4, −12), and (−7, −12)?
(−12, 7)
(−7, −25)
(−7, 12)
(−25, 7)
Answers
Answer: I believe the answer is (-7, 12)
Step-by-step explanation:
Answer:
-7,12
Step-by-step explanation:
The price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per
meter.
The table compares the total distance of a trip (in meters) and the price of the trip (in dollars).
Distance (meters)
80
110
140
How far can you climb for $131?
Answers
to be honest ion even know
Answer: 200 Meters
Step-by-step explanation:
ERROR ANALYSIS Describe and correct the error in finding m<1
Answers
Answer:
m∠1 = 26°
Step-by-step explanation:
Interior angles of a triangle sum to 180°, not 360°.
Therefore, the correct calculations to find the measure of angle 1 are:
[tex]\boxed{\begin{aligned}115^{\circ}+39^{\circ}+m \angle 1 &=180^{\circ}\\\\154^{\circ}+m \angle1 & = 180^{\circ}\\\\m \angle1 & = 26^{\circ}\end{aligned}}[/tex]
Please help ASAP
See Attached!!
Answers
When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.
When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.
The answers:
a) False, degrees not added,b) False, degrees added but not multiplied.Calculate the height (in m) of a cliff if it takes 2.41 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.14 m/s. (Enter a number.)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)
Answers
The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.
When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.
from equation of motion
H= ut-1/2gt^2( the object is moving upward)
where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity
(g=10ms^-2).
therefore h= 8.14×2.41-(1/2×10×2.41)
= 19.62-12.05
h= 7.57m
when the object is thrown Down,
V = u + gt
u will be 0 at top before coming down
V = gt
t= 8.14/10
= 0.814s
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Question 2b answer please
and working out
Answers
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
what is 2 +2
4+5
0+9
Answers
Answer:
Step-by-step explanation:
2+2=4
4+5=9
0+9=9
Answer:
4, 9 , 9 OR 4 + 9 + 9 = 22
Step-by-step explanation:
a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape
ice concentrate is 3 to 1.
a. Find two more ratios of cups of sparkling water to cups of juice concentrate that
would make a mixture that tastes the same as this recipe.
b. Describe another mixture of sparkling water and grape juice that would taste
different than this recipe.
Lesson 3 Practice Problem
Answers
Answer:
3:2
Step-by-step explanation:
You need to find two more equivalent ratio of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
ratio of cups of sparkling water : cups of grape juice concentrate = 3 : 1
Equivalent ratio to 3 : 1 are
6 : 2,
9 : 3,
12 : 4
15 : 5
21 : 7
Non equivalent ratio of 3 : 1 are
3 : 2
4 : 2
5 : 5
6 : 4
Therefore, another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
same as this recipe.
Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice
concentrate
Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
ratio of cups of sparkling water : cups of grape juice concentrate = 3: 1
Equivalent ratio to 3 : 1 are
6:2.
9:3.
Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 160 workers can produce 32 cars in 2 hours, find the number of workers that can produce 66 cars in 3 hours.
Answers
If 160 workers can produce 32 cars in 2 hours, The number of workers that can produce 66 cars in 3 hours is 220 .
How to find the number of workers?Using this formula
W = kC/H
160 = k(32 )/2= 17k
k = 160 /16
Hence,
W = (160 /16)C/H
W = (160 /16) (66/3)
W= 220 workers
Therefore we can conclude that 220 workers can produce the cars in 3 hours.
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Laura and Kirk are comparing how much they have been running. Laura has already
run 36 miles and Kirk has run 64. Laura begins running 21 miles per week and Kirk runs 17 miles
per week. How many additional weeks, w, will it take for their total distance run to be equal?
Answers
The additional weeks, w, will it take for their total distance run to be equal is 7 weeks.
How to calculate the number of weeks?From the information, Laura has already
run 36 miles and begins running 21 miles per week. This will be 36 + 21w.
Kirk has run 64 miles and runs 17 miles per week. This will be 64 + 17w
where w = number of weeks
This will be equated as:
36 + 21w = 64 + 17w
Collect like terms
21w - 17w = 64 - 36
4w = 28
Divide
w = 28/4
w = 7
It'll take 7 weeks.
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1. What is the result if you divide -12x8y8 by 3x4y ²?
O A. 4x4yê
O B. 4x²y
O C.-4x²yA
O D. -4x^y6
Please look at photo, it didn’t type correctly.
Answers
Divide -12/3 = -4
Then subtract the exponents for x and y
x^8-4 = x^4
y^8-2 = x^6
The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answers
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
what kind of transformation converts the graph of f(x)= -10(x-2)^2 into the graph of g(x)= -2(x-2)^2
Answers
The transformation that converts f(x) to g(x), f(x) is contraction by 5 units
What are transformations?Transformations are mathematical operations which change the shape and orientation of an object or function.
The types of transformations include
Dilation, Reflection, translationcontraction and rotationHow to find what kind of transformation converts f(x) to g(x)?Since we have the graph of f(x) = -10(x - 2)² into the graph of g(x)= -2(x - 2)².
We see that f(x) = -10(x - 2)²
= 5 × -2(x - 2)²
= 5g(x)
Since f(x) = 5g(x)
⇒g(x) = f(x)/5
So, we converts f(x) to g(x), f(x) is contraction by 5 units
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If f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55, then find the
value of f(-1), to the nearest hundredth.
Answers
The value of the exponential function (-1) will be equal to f(-1) = -0.02.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.
Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,
[tex]y=ax^b[/tex]
[tex]11=a(-3)^b\\55=a(4)^b[/tex]
Calculate the value of constants,
log5 = blog(4 / 3)
b = 0.7 / 0.125
b = 5.6
The value of 'a' will be,
11 = a(-3)⁵°⁶
a = -0.02
The exponential function f(-1) will be calculated as,
f(-1) = -0.02(-1)⁵°⁶
f(-1) = -0.02
Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.
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