The equation representing the normal cost (x), for an individual, is 6(x - 3) = 54, so option A is correct.
What is 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.
Given:
Costs $54 for 6 people of the package, and $3 less per person than the normal cost for an individual.
The individual cost = 54 / 6 = $9, so the normal cost will be = 9 + 3 = $12
Apply the hit and trial method in the option,
(2)
3(x - 6) = 54
x - 6 = 54 / 6
x = 9 + 6 = 15
(1)
6(x - 3) = 54
x - 3 = 54 / 6
x = 9 + 3 = 12
Therefore, the equation representing the normal cost (x), for an individual is 6(x - 3) = 54.
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Suppose a designer has a palette of 15 colors to work with, and wants to design a flag with 5 vertical stripes, all of different colors.
How many possible flags can be created?
The number of flags that could possibly be created, given the palette of colors to work with, and the number of stripes, is 360, 360 flags.
How to find the number of flags?The designer has the choice to pick from 15 colors to work with. They will then pick another color, and then another, until they pick five colors to make stripes.
When they pick a single color, the number of choices drops to 14 colors. When they pick 5 colors, they will be left with 11 colors.
The number of possible flags is therefore:
= 15 x 14 x 13 x 12 x 11
= 360, 360 possible flags
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if 2x+5y=180 and 3x+3y=180
what are the x and y values?
Answer:
x=40,y=20
Step-by-step explanation:
a{2x+5y=180
b{3x+3y=180
b-a
x-2y=0
x=2y
substitute:
2×2y+5y=180
9y=180
y=20
substitute:
x=2y
x=2×20
=40
a photo has a width to length ratio of 2:3. if the width of the photo is 4.8 cm, the length of the photo is
The length of the photo having a width to length ratio of 2:3 is 6.9 cm.
What is length?Length is the distance between two points.
To calculate the length of the photo, use the formula below.
Formula:
L = W/R............ Equation 1Where:
L = Length of the photoR = Width to length ratio of the photoW = Width of the photo.From the question,
Given:
W = 4.6 mR = 2:3 = 2/3Substitute these values into equation 1
L = 4.6/(2/3)L = 4.6×3/2L = 6.9 cmHence, the length of the photo is 6.9 cm.
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An orange grower harvested oranges from 4 acres of land and collected 720 bushels of oranges. The next day, the farmer harvested oranges from 7 acres of land and collected 1,260 bushels of oranges.
Is there a proportional relationship between the number of bushels of oranges collected and the number of acres harvested over the two days? Explain.
Yes, there is a proportion relationship between the number of bushel and acres of land. The relationship is the number of busher is directly proportional to the number of acres of land.
What is direct proportion?Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.
direct proportion is given as y= kx
Where y and x are the variables and k is constant.
If the bushel of orange is given by x and the acres of land by y
then x= ky
for the expression to be correct the value of k should be thesame
when x= 720 and y = 4
k= x/y
k= 720/4= 180
when x= 1260 and y= 7
k= x/y
k= 1260/7
k= 180
therefore the x is directly proportional to y
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ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
Which of the following are essential elements of hypothesis testing?
-It uses probability theory to determine if a hypothesis is a reasonable statement.
-It makes use of sample data.
The following are crucial factors in hypothesis testing:
It employs probability theory to evaluate if a hypothesis is a valid claim.It employs sample data.Explain the term hypothesis testing?In statistics, the process of hypothesis testing involves putting an analyst's presumption about a population parameter to the test.
The type of data being used and purpose of the study will determine the methodology the analyst uses. A basic hypothesis can anticipate a causal relationship between variables, i.e., that one has an impact on the other. This is known as hypothesis testing, and it uses sample data to determine the plausibility of a hypothesis.It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an investigation are reliable.Thus, before conducting the hypothesis testing, a null hypothesis as well as an alternative hypothesis are established.
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Use the zero-product property to solve the equation.
(x + 3)^2 = 0
select all that are equal to 6^4(6^-5)
The options that are equal to 6⁴/(6⁻⁵) using laws of exponents are;
b. 1/6
c. 6^-1
d. 1/6^1
How to use laws of exponents?The laws of exponents are;
Product of powers rule.Quotient of powers rule.Power of a power rule.Power of a product rule.Power of a quotient rule.Zero power rule.Negative exponent rule.The exponent we are supposed to solve is;
6⁴/(6⁻⁵)
According to laws of exponents, we know that;
x³/x² = x^(3 - 2)
Thus;
6⁴(6⁻⁵) = 6^(4 + (-5)) = 6^(-1) = 1/6
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Complete question is;
Select all the are equal to 6^4(6^-5)
a. 1\6^-1
b. 1/6
c. 6^-1
d. 1/6^1
e. 1/-6
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a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Each week, Tasha saves 60% of the money she earns babysitting and spends the rest. This week she
earned $60.00
How much more money did she save than spend this week?
what is a x b when a=7 and b=9
Answer:
89
Step-by-step explanation:
if u divide and multiply theory is equivalent to its nominal answer thus your answer will be 89
Question
Solve for m.
m+1/3<−2 1/4
m>−2 7/12
m<−2 7/12
m<−1 11/12
m>−1 11/12
The expression m < - 2 7/12 solved for m is m < - 2 7/ 12. Option B
What are inequalities?Inequalities are described as a relation which making an unequal comparison between two numbers or expressions.
It is mostly used to compare two numbers on the number line on the basis of their size.
Given the expression;
m+1/3<−2 1/4
Covert to improper fraction
m + 1/ 3 < -9/4
Now, collect like terms
m < - 9/ 4 - 1/3
Find the lowest common multiple
m < -27 - 4 /12
m < -31/ 12
convert to mixed fraction
m < - 2 7/ 12
Hence, the value is m < - 2 7/ 12
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A drawing ha a cale of 1:30. An a drawing, a kitchen i a rectangle meauring 12cm by 27cm. A bedroom ha an actual area of 300000cm
which ha the bigger actual area, the kitchen or the bedroom?
you mut how your working
Actual area of bedroom is bigger than the kitchen as per the given measurements and scale.
As per the given question,
Given drawing scale is:
1 : 30
Shape of the kitchen is rectangle with measurements = 12cm by 27cm
Using scale :
Length = 12cm
Actual length = 12 × 30
= 360cm
Width = 27cm
Actual width = 27 × 30
= 810 cm
Actual area of kitchen = 360 × 810
= 291,600 cm²
Actual area of bedroom = 300,000cm²
300,000 > 291,600
Actual area of bedroom > Actual area of kitchen
Therefore, actual area of bedroom is bigger than the actual area pf kitchen.
The complete question is:
A drawing has a scale of 1:30 On the drawing, a kitchen is a rectangle measuring 12 cm by 27 cm A bedroom has an actual area of 300 000 cm² Which has the bigger actual area, the kitchen or the bedroom? You must show your working.
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Simplify the expression. negative 15 plus the quantity negative 3 and seven tenths plus 9 and 15 hundredths end quantity divided by 5 all times 3 squared minus 4 and 7 tenths
Using mathematical operators, the expression [15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100] is simplified as [5(20x + 409)] / 4500x - 407
ExpressionAn expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it. Let us understand how to write expressions. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
In this problem, we have to first of all write out the words and expression in mathematical form. To do this, we have to apply mathematical operators like addition, subtraction, multiplication and division.
This can be rewritten as:-
[15 + x - 3 7/10 + 9 15/100] ÷ [5x × 3² - 4 7/100]
Simplifying this, we have;
[5(20x + 409)] / 4500x - 407
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i need help quick!
this is my last attempt on this assignment and im stuck on this one question, thanks!
Answer:
41
Step-by-step explanation:
y = 4x + 21 plug in 5 for x
y = 4(5) + 21
y = 2-0 + 21
y = 41
a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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Find x and y values that make both y=−2/3x+3 and y=2x−5 true.
What is the ordered pair for your solution?
The ordered pair is (3, 1) which is the intersecting point of these two equations.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
Given, are two equations y = -(2/3)x + 3 and y = 2x - 5.
Now the solution to this system is the common intersecting point of these equations.
With the help of graphing we conclude that the intersecting point is (3, 1) and so is the solution.
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Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
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Helppppp, I don’t know what to do, I just really need the answer
The completed statement on the exponential model that fits the data in the question is presented as follows;
The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.
What is a correlation coefficient?The correlation coefficient is an indication of the level at which the variables are interdependent.
The table of values in the question can be entered into a spreadsheet application as follows;
In the spreadsheet application, enter Year since 1960 values in a column, and the Plastic Production in an adjacent columnSelect the all the data entered into the spreadsheet document such as MS Excel, then select the Insert tabIn the charts section select scatter plot to create a scatter plot of the dataIn the Design tab, that appears when the chart is selected, select the Add Chart Element button access the Trendline functionSelect the Exponential trendline from the menu for trendlinesThe exponential trendline is then created by the spreadsheet applicationThe equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)
The growth rate from the above exponential function is 7·88% per year
The production 15 years after 1960 is therefore;
f(15) = 9.2179·e^(0.0788 × 15) ≈30.06
The number of plastic produced 15 years after 1960 is about 30 million metric tons
The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model
The prediction is correct based on the strong correlation between the year and the number of plastic produced.
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what does it mean for two shapes to be proportional.
Answer:
It means that the quantities have the same relative size. In other words they have the same ratio.
Step-by-step explanation:
For example look at the attached files
What is the slope that passes through (1,2) and (2,6)
Answer:
4
Step-by-step explanation:
use slope formula y2-y1/x2-x1
6-2/2-1
4/1
4 is the slope
Hopes this helps please mark brainliest
I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Julian sells 4 pieces of artwork for $72, and each piece is sold at the same rate.
How much does one piece of Julian's artwork cost?
Enter your answer as a number, like this: 42
Answer: 18
Step-by-step explanation: 72 divided by 4= 18
What is the formula for simple interest
Answer: The formula for simple interest is P*R*T/100
Step-by-step explanation: Where P stands for Principal and R for Rate T for Time
i have lost, just help
The age of Jane is [tex]16\frac{5}{12}[/tex] years old.
How to find the age of Jane?Lydia is [tex]13\frac{5}{6}[/tex] years old . Morgan is [tex]1\frac{1}{3}[/tex] years older than Lydia.
Therefore,
age of Morgan = [tex]13\frac{5}{6} + 1\frac{1}{3} = \frac{83}{6}+\frac{4}{3}=\frac{83+8}{6} =\frac{91}{6}=15\frac{1}{6}[/tex] years
Jane is [tex]1\frac{1}{4}[/tex] years older than Morgan.
Therefore,
Age of Jane = [tex]15\frac{1}{6} + 1\frac{1}{4}[/tex]
Age of Jane = [tex]\frac{91}{6}+ \frac{5}{4}[/tex]
Age of Jane = [tex]\frac{364+30}{24}[/tex]
Age of Jane = [tex]\frac{394}{24}[/tex]
Age of Jane = [tex]16\frac{10}{24}[/tex]
Age of Jane = [tex]16\frac{5}{12}[/tex] years old
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Help me please, I don’t understand this question.
The average rate of change of the function:
f(x) = x^2 + 7x + 9
On the interval [-9, 0] is -2.
How to find the average rate of change?
For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is:
f(x) = x^2 + 7x + 9
And the interval is -9 ≤ x ≤ 0, it can also be written as [-9, 0]
Evaluating the function in the extremes of the interval we get:
f(0) = 0^2 + 7*0 + 9 = 9
f(-9) = (-9)^2 + 7*(-9) + 9 = 27
Then the average rate of change is:
r = ( f(0) - f(9))/( 0 - (-9)) = (9 - 27)/(9) = -18/9 = -2
The average rate of change is -2.
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What is 3x+6 I don’t know what this is
Answer:
it is a function.
Step-by-step explanation:
The answer is just 3x+6
Answer:
3x+6 can be be the result of 3(x+2) and then you distribute to get 3x+6
If you are asking how to solve you need an equal sign in the equation for example: 3x+6=27 you would have to solve to figure out wht x is. x is any unknown number we use x or any letter in the alphabet to fill in. You have to olve for the variable now.
A General Rule for Solving Equations
Simplify each side of the equation by removing parentheses and combining like terms.
Use addition or subtraction to isolate the variable term on one side of the equation.
Use multiplication or division to solve for the variable.
Step-by-step explanation:
the gram-schmidt process produces from a linearly independent set {x1, x2, . . . , xp} an orthogonal set {v1, v2, . . . , vp} with the property that span{v1, . . . , vk}
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
Answer:
A
Step-by-step explanation:
Eliminate B and C because they don't pass through (0,1).
Eliminate D because it doesn't decrease quickly enough.
If triangle xyz is translated using the rule (x, y) → (x − 3, y − 2) and then reflected across the y-axis to create triangle x″y″z″, what is the location of z″? (−7, 1) (−3, −1) (−1, −3) (3, 3)
The location of the y-axis to create a triangle is a(0,2).
So if the point X is (-3, -2) is translated using the rule
x,y ---> (x+3),(y+4)
then you simply plug-in the values of x and y which are x = -3 and y = -2
x,y ---> ((-3) +3), ((-2) + 4) which is (0, 2)
This is the new coordinate for X
so the answer is a(0,2).
What is a triangle?
A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is represented as triangle ABC.
In Euclidean geometry, any three points, if not collinear, define a unique triangle and, at the same time, a unique plane (that is, two-dimensional Euclidean space). That is, there is only one plane containing this triangle, and all triangles are contained in one plane. If all geometries were just Euclidean planes, there would be only one plane and all triangles would be in it. But this is not the case in high-dimensional Euclidean space.
Therefore, the location of the y-axis to create triangle is a(0,2).
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