Let the commission sales = X
Salary Plan 1
salary per week = $400
commission sales = 2%
[tex]\text{Commision sales = 2\%}\times X=\text{ \$0.02X}[/tex]Salary Plan 2
salary per week = $300
commission sales = 18%
[tex]\text{ Commission sales = 18\%}\times X=\text{ \$0.18X}[/tex]Becky's salary for both plans (inclusive of commission sales) would be:
Plan 1:
[tex]\text{ \$400+0.02X}[/tex]Plan 2:
[tex]\text{ \$300+0.18X}[/tex]In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:
[tex]\begin{gathered} \text{ \$400+0.02X= \$300+0.18X} \\ \text{collect like terms} \\ 0.18X-0.02X=400-300 \\ 0.16X=100 \\ X=\frac{100}{0.16}=625 \end{gathered}[/tex]Therefore, the commission sales should be $625
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
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.
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.
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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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
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
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)
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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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.
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?
The length and width of a rectangular table have a ratio of 8 to 5. The width of the table is 40 in. Find the length of the table.
Solution:
Let the length and the width of the rectangular table be represented as L and W respectively.
Given that the length and the width have a ratio of 8 to 5, this implies that
[tex]\frac{L}{W}=\frac{8}{5}[/tex]If the width of the table is 40 in, the length of the table is evaluated as
[tex]\begin{gathered} \frac{L}{40}=\frac{8}{5} \\ \text{cross multiply} \\ 5\times L=8\times40 \\ \implies5L=320 \\ \text{divide both sides by the coefficient of L, which is 5} \\ \text{thus,} \\ \frac{5L}{5}=\frac{320}{5} \\ \therefore L=64\text{ in.} \end{gathered}[/tex]Hence, the length of the table is 64 in.
What is the largest volume a sphere can have if it is covered by 6m2 of fabric?
The formula for determining the surface area of a sphere is expressed as
Surface area = 4 * pi * radius^2
From the information given,
surface area = 6
pi = 3.14
thus,
6 = 4 * 3.14 * radius^2
6 = 12.56radius^2
[tex]\begin{gathered} radius^2\text{ = }\frac{6}{12.56}=0.478 \\ \text{radius = }\sqrt[]{0.478} \\ \text{radius = 0.69} \end{gathered}[/tex]The formula for determining the volume of a sphere is expressed as
Volume = 4/3 * pi * radius^3
Thus,
Volume of sphere = 4/3 * 3.14 * 0.69^3
Volume of sphere = 1.38m^3
A math student compared the values of 17 and 60 on a number line. Which statement about the two values is true? Select one: A. The values of 17 and 60 are the same. B. The value of 17 is about 8, and the value of 60 is about 30. C. The values of both 17 and 60 are between the same two integers on a number line. D. The value of 17 is less than 5, and the value of 60 is greater than 7.
Given the two numbers, let us simplify to find the value;
[tex]\begin{gathered} \sqrt[]{17}=4.12 \\ \sqrt[]{60}=7.75 \end{gathered}[/tex]From the derived value, we can find which of the statements is true.
From the options, we can see that the only option that is entirely true is;
- The value of root 17 is less than 5, and the value of root 60 is greater than 7.
[tex]\begin{gathered} \sqrt[]{17}=4.12<5 \\ \sqrt[]{60}=7.75>7 \end{gathered}[/tex]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.
(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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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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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
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.
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
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
tanja wants to establish an account that will supplement her retirement income beginning 10 years from now. find the lump sum she must deposit today so that $200,000 will be available at time of retirement, if the interest rate is 6%, compounded quarterly. (round to the nearest cent as needed)
Solution
For this case we can use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]And for this case
n= 4 compounded quarterly
t= 10 years
A= 200000
P=?
r=0.06
And we can solve for P and we got:
[tex]P=\frac{200000}{(1+\frac{0.06}{4})^{4\cdot10}}=110252.5[/tex]So then the final answer would be:
110252.5
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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Choose the best estimate for the quotient.
8.23 divide by 65.29
A) 7
B) 8
C) 9
D) 10
Answer:
8
Step-by-step explanation:
65.29/8.23≈7.933
7.933 rounds to 8
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.
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]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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11. The distance formula is d = rt, where d is the distance, r is the rate, and t is the time.a. Rewrite the equation to isolater.r = d/tb. Brad drove from Athens to Atlanta in 1.5 hours, 72 miles away, before he flew out forKansas City. What was his rate of speed in miles per hours
B. we just replace the vlues of t=1.5 and d=72
[tex]\begin{gathered} r=\frac{72}{1.5} \\ \\ r=48\frac{m}{h} \end{gathered}[/tex]the rate of speed is 48 miles per hour
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
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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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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