One needs to sell $6750 worth of goods to make the straight commission be at least good to the secondary offer
Straight offer = 6% commission on the sales
Second offer = $270 + 2% of the sales
For the straight offer to be competitive with the second offer it should be able to cover the fixed income of $270
Let x be the sales made in the week
Formulating the equation we get the following:
6% of x = 270 + 2% of x
6/100x = 270 + 2/100x
4/100x = 270
x = 6750
So, for sales up to $6750, the second job offer is good, while for sales more than $6750 the first job offer is good
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Which of the following scatterplots do not show a clear relationship and would not have a trend line?
Group of answer choices
The scatterplot that do not show a clear relationship and would not have a trend line is: graph B.
What is a trend line?A trend line is also referred to as a line of best fit and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between data points.
In Mathematics, there are different types of trend line and these include the following:
Linear trend line.Exponential trend line.Polynomial trend line.Logarithm or Natural logarithm trend line.Power trend line.Moving average trend line.By critically observing the scatter plot (see attachment) which models the data in the given table, we can reasonably and logically deduce that the data points in graph B are scattered around and as such, it does not illustrate a clear relationship (pattern).
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The half-life of silicon-32 is 710 years. If 50 grams is present now, how much will be present in 700 years?(Round your answer to three decimal places.)A) OB) 25.245C) 0.054D) 46.697
In this type of question, we will use the exponential equation
[tex]y=a(b)^x[/tex]Where:
a is the initial amount
b is the factor of growth or decay
Since it is a half-life, then
b = 1/2 = 0.5
Since it is now 50 grams, then
a = 50
Since x is the number of years, then
x = 700
Substitute them in the rule above
[tex]\begin{gathered} y=50(0.5)^{700} \\ y=0 \end{gathered}[/tex]It will be representing 0 grams after 700 years
The answer is A
Choose the point which shows the correct location for the polar coordinate (3, -45°)
The argument of the polar coordinate is -45 degrees, which can be converted as,
[tex]\begin{gathered} \theta=360^{\circ}-45^{\circ} \\ =315^{\circ} \end{gathered}[/tex]Thus, the required point is D.
An FICA tax of 7.51% and an SDI deduction of 1.2% are charged against
an employee's wages. If her total monthly wages were $1538.46, what
would her paycheck be after FICA and SDI deductions as well as
withholding tax deductions of $245.80?
The employee's paycheck after FICA and SDI deductions as well as
withholding tax deductions is $1158.65.
What is FICA?FICA is a federal payroll tax in the US. It is taken out of every paycheck and stands for the Federal Insurance Contributions Act. Your nine-digit number enables Social Security to precisely record your self-employment or insured wages. You accrue credits for Social Security benefits as you work and pay FICA taxes.
Employee monthly salary= $1538.46FICA calculation= 7.51% of $1538.46= $115.54SDI calculation= 1.2% of $1538.46= $18.47Employee final paycheck= Monthly wage - FICA - SDI - Tax deductions.$1538.46 - $115.54 - $18.47 - $245.80= $1158.65The final monthly paycheck of the employee after deducting all taxes is $1158.65.
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what is the lcm of the rational algebraic equation 6/x+x-3/4=2
The lcm of the rational algebraic equation 6/x+x-3/4=2 be (24 -3x - 4x²) / 4x = 0.
What is LCM?The least common multiple is defined as the set of numbers with the least common multiple. The lowest positive integer with more than one factor in the set is HCF.
The given equation below as:
⇒ 6/x + x - 3/4 = 2
We must find the lcm of the rational algebraic equation.
⇒ 6/x + x - 3/4 = 2
Rearrange the term of 2 in the equation,
⇒ 6/x + x - 3/4 - 2 = 0
Take LCM in the above equation,
⇒ [tex]\dfrac{6\times4+x\times4x-3\times x -2 \times 4x}{4\times x}[/tex]
⇒ (24 + 4x² -3x - 8x²) / 4x = 0
Combine the likewise terms in the numerator,
⇒ (24 -3x - 4x²) / 4x = 0
Therefore, the required answer would be (24 -3x - 4x²) / 4x = 0.
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30 locusts eats 420g of grass in a week ,how many days will 21locust take to eat 420g at the same rate .
420/30=14g
14g =2g why is 14g =2g
It will take 4.9 days for 21 locust to eat 420 grams of grass
How to determine the number of days?From the question, we have the following parameters:
Initial number of locust = 30Initial number of days = 7 days i.e. 1 weekNew number of locust = 21Given that the amount of grass is constant at 420 grams
The given parameters can be represented using the following ratio
Ratio = Locust : Days
So, we have
Locust : Days = 30 : 7
When there are a total number of 21 locust eating the grass, then we have
21 : Days = 30 : 7
Express as fraction
Days/21 = 7/30
This gives
Days = 21 * 7/30
Evaluate
Days = 4.9
Hence, the number of days is 4.9 days
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what is the best estimate for the product 9/10 x 5/11
The best estimate for the product 9/10 x 5/11 is 1/2.
What is product?Product in Mathematics simply means a number that you get when you multiply. It is used to illustrate tye concept of multiplication
In this case, the estimate for 9/10 is 1 and the estimate of 5/11 is 1/2. Therefore, the product will be:
= 1 × 1/2
= 1/2
This shows the estimation.
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Select the correct answer.Select how this number is read.3.7284A. three and seven thousand, two hundred eighty-four ten-thousandthsB. three and seven thousand, two hundred eighty-four hundredthsC. thirty-seven and two hundred eighty-four thousandthsD. three point seven two eight four
Given:
3.7284
The given number should be read as "three point seven two eight four.
Option D is the correct answer.
As the value of cosx approaches 1 and the value of sinx approaches 0, the value of cotx approaches infinity. True or false?
Recall that:
[tex]\cot \text{ x=}\frac{\cos x}{\sin x}[/tex]Therefore as sin x approaches 0 and cos x approaches 1, the value of cot x approaches infinity.
Answer: True.
Mal works at a photo gallery. He charges $50 for a large photo and $40 for a large frame. Sales tax is 5%. How much total tax will a customer pay on both?
Answer the questions to show how to write and simplify expressions that represent the problem.
1. One way to calculate the total tax is 0.05(50 + 40). Use the order of operations to evaluate this expression. Show your work. (2 points)
2. Use the distributive property to expand 0.05(50 + 40). (2 points)
3. Find the total tax using the expanded expression. Did you get the same answer as you did by evaluating the original expression? (3 points)
4. Which expression, the original expression or the expanded expression, involves finding the total cost first, then calculating the tax on that total? (3 points)
1. Using the order of mathematical operations, the values in brackets are added and multiplied to a product of $4.50 as the total tax.
2. Using the distributive property to expand the expression, 0.05(50 + 40) is 0.05 x 50 + 0.05 x40.
3. The total tax using the expanded expression is $4.50, the same product as when evaluating the original mathematical expression.
4. The original expression involves finding the total cost first before calculating the tax on the total.
What is the order of mathematical operations?The following is the order of mathematical operations:
ParenthesesExponentsMultiplicationDivision Addition Subtraction.1) The original expression, 0.05(50 + 40):
= 0.05 x 90
= 4.5
= $4.50
2) The expanded expression, 0.05(50 + 40)
= 0.05 x 50 + 0.05 x40
= 2.5 + 2.0
= 4.5
= $4.50
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which situation is most likely to show a constant rate of change
A. the shoe size of a young girl compared with her age in years
B. the amount spent on grapes compared with the weight of the purchase
C. the number of people on a city bus compared with the time of day
D. the number of slices in a pizza compared with the time it takes to deliver it
Answer:
B. the amount spent on grapes compared with the weight of the purchase
A ladder 10 ft long rests against vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.7 of ft/s, now fast (in rad/s) is
the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the
angle's rate of change when the bottom of the ladder 8 ft from the wall.)
Wall
Check the picture below.
[tex]cos(\theta )=\cfrac{x}{10}\implies \stackrel{chain~rule}{-sin(\theta )\cdot \cfrac{d\theta }{dt}}=\cfrac{1}{10}\cdot \cfrac{dx}{dt} -sin(\theta )\cdot \cfrac{d\theta }{dt}=\cfrac{1}{10}(0.7)[/tex]
[tex]\cfrac{d\theta }{dt}=\cfrac{0.07}{-sin(\theta )}~\hfill \stackrel{\textit{when the ladder's bottom is 8ft, x = 8}}{sin(\theta )=\cfrac{8}{10}\implies sin(\theta )=\cfrac{4}{5}} \\\\\\ \cfrac{d\theta }{dt}=-\cfrac{0.07}{~~ \frac{4 }{5 } ~~}\implies \implies \cfrac{d\theta }{dt}=-0.07\cdot \cfrac{5}{4}\implies {\Large \begin{array}{llll} \cfrac{d\theta }{dt}=-0.0875~\frac{rad}{s} \end{array}}[/tex]
the rate is negative because the angle is decreasing as the ladder slides outwards.
Write the equation of a circle given the center (2, 9) and raduis r = 3.
Answer:
[tex](x-1)^2+(y-9)^2=3^2[/tex]
Step-by-step explanation:
The standard form of the equation of a circle is:
[tex](x-a)^2+(y-b)^2=r^2[/tex]
Where a and b are the x and y, coordinates, and r is the radius.
So, you can just substitute the a and b values for the x and y values of the center to find the equation of the circle.
The formula V=4/3 pie r3 gives the volume with radius r. Find the volume of a sphere with radius x+9. Write your answer as standard form.
We will find it as follows:
[tex]V=\frac{4}{3}\pi(x+9)^3\Rightarrow V=\frac{4\pi}{3}(x^3+27x^2+243x+729)^{}[/tex][tex]\Rightarrow V=\frac{4}{3}\pi x^3+36\pi x^2+324x+972[/tex]The volume of such a sphere is given by the expression found.
***
When we have a binomial at the power of a number, of the form:
[tex](a+b)^n[/tex]We use Pascal's triangle to determine the expansion. Pascal's triangle is the following:
Each row can be used to calculate a specific power, in our case the binomial is at the power of three, and we will use the 4rth row to expand, that is:
[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]As you can see, the numbers that accompany a & b are the ones found in the 4th row of Pascal's triangle. We also see that the "degree" o the expansion always sums 3, that is a^3 has an overall degree of 3, a^2b has an overall degree of 3, ab^2 has an overall degree of 3 & b^3 has an overall degree of 3.
***
If we, for example, wanted to expand (a + b)^4, we then would have the following:
*We would use the 5th row and get:
[tex](a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex][Pascal's triangle expands to infinity. So, you in theory can manually expand any binomial at any power, but for big numbers, it will take a long time]
***
In our case, the binomial was:
[tex](x+9)^3[/tex]And, its respective expansion is:
[tex](x+9)^3=x^3+3x^2(9)+3x(9)^2+9^3[/tex][tex]=x^3+27x^2+243x+729[/tex]determine if the following sequence is Arithmetic if so what is the common difference -6 -2 2 6
We are given the following series
-6, -2, 2, 6
Common difference = last term - first term
For the first two terms
The common difference is calculated as
Last term - first term
Last term = -2
First term = -6
Common difference = -2 - (-6)
= -2 + 6
common difference = 4
Common difference = 2 - (-2)
common difference = 2 + 2
Common difference = 4
Last two terms
common difference = 6 - 2
Common difference = 4
The common difference for this sequence is 4
The sequence is arithmetic.
I dont understand the part "Would this be true if the numbers were-3, 5, -16, and -10?"
Yes, the numbers will be similar.
it will be true if the numbers were -3, 5, -16 and -10
Explanation:
The first list: -3, 5, 16 and -10
Arranging from least to greatest:
-10, -3, 5, 16
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-10, -3, 0, 5, 16
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-10, -3, 5, 16
The second list:
-3, 5, -16, -10
Arranging from least to greatest:
-16, -10, -3, 5
Arranging the same numbers from closest to zero to farthest to zero:
Let's use zero as our reference. Then start arranging towards the left and right side of it.
-16, -10, -3, 0, 5
Looking at the above: when we remove 0, we would have same answer as the arrangement from least to greatest:
-16, -10, -3, 5
Hence, fromt the above: if we arrange the same numbers from least to greatest and from closest to zero to farthest to zero, we would arrive at the same result.
Find the last term to make the trinomial into a perfect square:
x
2
+
6
x
+
When this is factored, it becomes:
The last term using factorization method to make the perfect square is 3 and the final expression is (x + 3)².
What is factorization method?
The factorization method is used for the quadratic based equation whose highest degree is either two or more than two. Depending upon the degree of the variable, the number of factors are calculated. And by substituting the calculated value to check whether the answer is correct or not.
According to the question, the given quadratic equation can be solved by performing factorization as well as by adding the half of the coefficient of the x-term to the given equation.
Therefore, the expression can be written as:
x² + 6x + 3² = 0
⇒(x + 3)² = 0
Hence, the last term by using factorization method to make the perfect square is 3 and the final expression is (x + 3)².
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Create a rational function that meets the following criteria.Vertical Asymptotes at x = 5 and x = -3Hole in the graph at x = -1Horizontal Asymptote at y = 7Leave your answer in factored form (do not multiply the factors out)
Choose the best estimate for the quotient. - See image inserted
Answer:
≈0.694 or rounded to 0.7
Step-by-step explanation:
4.06/5.85≈0.694
Find the result when 60 is increased by 40%.
Given:
The number is 60.
Aim is to find the result when 60 is increased by 40%.
First calculate 40% of 60,
[tex]\frac{40}{100}\times60=24[/tex]Now, add the amount 24 in 60.
[tex]24+60=84[/tex]Answer: 84 is a 40% increase of 60.
A line passes through the point (-4, 1) and has a slope of -2.
Write an equation in slope-intercept form for this line.
Answer:
y= -2x -7
Step-by-step explanation:
The equation of a line in slope-intercept form is given by y= mx +c.
m= slopec= y-intercept
Given that the slope is -2, we can substitute m= -2 into the equation.
y= -2x +c
The value of c can be found by substituting a point in which the line passes through into the equation. In this case, the point is (-4, 1).
y= -2x +c
When x= -4, y= 1,
1= -2(-4) +c
1= 8 +c
Subtract 8 on both sides:
c= 1 -8
c= -7
Substituting c= -7 into the equation:
y= -2x -7
Optional step:
To check our answer, we can substitute one coordinate and see if the other coordinate is the same as the given coordinate. For example, let's substitute the x-coordinate of -4 into the equation.
y= -2(-4) -7
y= 8 -7
y= 1
Since the y-coordinate is indeed 1, the equation above is correct.
Additional reading:
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When twenty is reduced by one-third of a number, the result is 19. Find the number.
Answer:
x = 3
Step-by-step explanation:
When twenty is reduced by one-third of a number, the result is 19. Find the number.
20 - 1/3x = 19
subtract 20 to both sides:
20 - 1/3x - 20 = 19 - 20
-1/3x = -1
multiply both sides by -3:
-3(-1/3x) = -1(-3)
x = 3
I need help with this practice problem solving in trigonometry
The secant function is the reciprocal of the cosine function.
We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. The procedure is the same:
Find the reference angle formed by the terminal side of the given angle with the horizontal axis. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x– and y-values in the original quadrant. (Figure) shows which functions are positive in which quadrant.
An even function is one in which f(-x) = f(x)
An even function is one in which f(-x) = - f(x)
Cosine and secant are even:
[tex]\begin{gathered} \cos (-t)=\cos (t) \\ \sec (-t)=\sec (t) \end{gathered}[/tex]Therefore from the drop down the correct answer : secant function is EVEN
Benny had 49 books. He sold
15 at a garage-sale. He used
the money he earned to buy 7
more books. How many books
does Benny have now?
Answer: 41
so he has 49 books and he sold 15 so its 49-15= 34 so he bought 7 more books so its 34+7=41
Step-by-step explanation:
Have great day
Great evening to you all, I need help with this math problem please
AA (or AAA) or Angle-Angle Similarity
If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.
We do not have 3 angles.
SAS or Side-Angle-Side Similarity
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then two triangles are said to be similar.
We have two sides and 1 angle. But, two sides of a triangle are not in the same proportion of the two sides of another triangle
SSS or Side-Side-Side Similarity
If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
Letter D
If f(x)=x²+5 and g(x)=3x, find (f . g)(x) and (g . f)(x).
(f . g)(x)= ____
(Simplify your answer.)
The value of the functions are;
(f. g)(x) = 9x² + 5
(g . f)(x) = 3x² + 15
What is a function?A function can be defined as a law, rule or expression showing the elaborate relationship between two variables in an expression or equation.
The variables are;
The dependent variableThe independent variableGiven the functions;
f(x)=x²+5g(x)=3xTo determine (f .g)(x), we substitute the value of g(x) as x in the function, we have;
(g)(x) = (3x)² + 5
expand the bracket
(g)(x) = 9x² + 5
To determine (g . f )(x), substitute the value of x as fx)
(g . f)(x) = 3(x² + 5)
expand the bracket
(g . f)(x)= 3x² + 15
Hence, the functions are 9x² + 5 and 3x² + 15
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Which equation could be represented by the number line?
An equation which could be represented by the number line is: D. -5 + (-1) = -6.
What is a number line?A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to compare or determine the difference between two numbers. Additionally, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
From the number line shown above, we have:
Distance = -5 + (-1)
Distance = -5 - 1
Distance = -6.
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On Sunday, Christina's savings account balance was $315.12.
On Monday,
she withdraws $78.95 and $143.80. She deposits
$63.29 on Tuesday. What is her balance after the deposit?
Justin has $7.50 more than Eva, and Emma has $12 less than Justin. Together, they have a total of $63.00. Write an equation to determine how much money each person has.
let j be justin, e for Eva and m for Emma. We get
[tex]\begin{gathered} j+e+m=63 \\ j=e+7.5 \\ m=j-12=e+7.5-12=e-4.5 \end{gathered}[/tex]so we get that, replacing all the variables
[tex]\begin{gathered} e+7.5+e+e-4.5=63 \\ 3e+3=63 \\ 3e=60 \\ e=20 \end{gathered}[/tex]so we get that Eva has $20. therefore Justin has $27.5 and Emma has $15.5
(2a) Multiple Choice: Place the letter of the correct answer on the answer line to the right:
For which of the following values of k will the equation have infinite solutions?
4(4x + 1) = k(8x + 2)
(a) 4
(b) 8
(c) 2
(d) 1
(2b) Using your answer from Part (2a) replace the value you selected in the equation below. Then solve the
equation and show that it will, in fact, yield infinite solutions.
4(4x+1)=k(8x + 2)
For k=2 for infinite solutions.
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. LHS = RHS is a common mathematical formula.
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:
4(4x + 1) = k(8x + 2)
Now, the equation should have infinite solutions
In consider the situation then we must put value of k such that LHS part become Equal to RHS.
Now, take k=2
4(4x + 1) = k(8x + 2)
LHS: 4(4x+1)= 16x+ 4
RHS: 2(8x+ 2)= 16x+ 4
Hence, k=2 for infinite solutions.
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