The retailer would remit $4,900 to the vendor on July 13.
What is invoice date?
The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date is July 1.
Invoice receipt date?
This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.
2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.
From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available
discount=2%*$5000
discount=$100
The retailer would remit the invoice price of $5,000 minus the discount.
amount remitted=$5000-$100
amount remitted=$4,900
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If 1st and 4th term of G.P is 500 and 32 respectively ,its 2nd term is
The second term of sequence is 200
Geometric equationGeometric sequence are sequence that differs in their term by a common ratio. The nth term of a geometric sequence is expressed as:
Tn = ar^n-1
where
a is the first term
n is the number of term
If 1st and 4th term of G.P is 500 and 32 respectively, hence;
T1 = ar^0 = 500
T3 = ar^3 = 32
From both expressions, the first term a = 500
Substitute into equation 2
ar^3 = 32
500r^3 = 32
r^3 = 32/500
r = ∛32/500
r = 0.4
Determine the second term
T2 = 500(0.4)
T2 = 200
Hence the second term of sequence is 200
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What is the probability of flipping a coin once and getting heads if you have gotten 5 tails in a row before that?
a. 1/32
b. 1/5
c. 1/4
d. 1/2
Answer:
Answer is..... D
Step-by-step explanation:
every single flipping may two results, head or tail.So last one has equal chance.
lim f(x) 2^x-1/x. Find the limit of x as x approaches 0
The limit happens to be the derivative of [tex]2^x[/tex] at [tex]x=0[/tex]:
[tex]\displaystyle f'(c) = \lim_{x\to c}\frac{f(x)-f(c)}{x-c} \implies \lim_{x\to0} \frac{2^x - 1}x = (2^x)'\bigg|_{x=0} = \ln(2)\,2^x \bigg|_{x=0} = \boxed{\ln(2)}[/tex]
FInd the solution for the ordered pair
2x + y = 5 and x + y = 6
Answer:
(-1,7)
Step-by-step explanation:
Use elimination, x = -1, y = 7
Answer:
(-1, 7)
Step-by-step explanation:
Elimination Method:Elimination: Step 1
Write in standard form (you can have negatives)
(standard form= Ax+By=C)
Elimination: Step 2
Create(find) opposites
Elimination: Step 3
Add to cancel one variable
Elimination: Step 4
Solve for variable
Elimination: Step 5
Substitute into other equation to find other variable
Substitution (Method)
In a linear system of equations, substitution results in one equation with one variable. The solution to a linear system is an ordered pair, not just a single value.
Problem:
Solve 2x+y=5;x+y=6
Steps:
I will solve your system by substitution.
(You can also solve this system by elimination.)
2x+y=5;x+y=6
Step: Solve 2x+y=5 for y:
2x+y+−2x=5+−2x(Add -2x to both sides)
y=−2x+5
Step: Substitute −2x+5 for yin x+y=6:
x+y=6
x+−2x+5=6
−x+5=6(Simplify both sides of the equation)
−x+5+−5=6+−5(Add -5 to both sides)
−x=1
-x/-1 = 1/-1 (Divide both sides by -1)
x=−1
Step: Substitute −1 for x in y=−2x+5:
y=−2x+5
y=(−2)(−1)+5
y=7(Simplify both sides of the equation)
Answer:
x=−1 and y=7
Amanda makes $40,000 and gets an annual raise of $3,000. Marie makes $45,000 and gets an annual raise of $2,500. How many years will it take Amanda and Marie to make the same salary?
Answer:
Six years
Step-by-step explanation:
because it will divided the twoo digit and mutiple it self
A power company calculates a person's monthly bill from the number of kilowatt-hours (kWh), x, used.
The function b(x) = {
0.15x
0.10 (x – 400) + 60,
2 < 400
2 > 400
determines
the bill.
The function illustrates that the bill for someone who uses 600 kilowatt will be $80.
How to illustrate the function?It should be noted that a function simply means an expression that defines the relationship between a variable and another variable. In this case, one can infer that functions are essential in the formulation of relationship between the variables that are given.
Based on the information given, it should be noted that it was stated that the power company calculates a person's monthly bill from the number of kilowatt-hours.
The bill for someone who uses 600 kilowatt will be:
= 0.1(x - 400) + 60
= 0.1(600 - 400) + 60
= 0.1(200) + 60
= 20 + 60
= 80
In conclusion, the bill will be $80.
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find the maximum value of the function 7-2x-3x^2 and the equation of the axis of the curve
The maximum value of the function 7 - 2x - 3x² exists 22/3.
How to estimate the maximum value of the function 7 - 2x - 3x²?Given: 7 - 2x - 3x²
We must begin by estimating the first derivative:
Differentiating the equation above, we have:
dy/dx = 0 - 2 - 6x = - 2 - 6x
We know that dy/dx = 0 at maxima and minima
Therefore, we contain, - 2 - 6x = 0
6x = - 2
x = - 1/3
Substituting x = - 3 back into the equation of the curve yields the following result:
y = 7 - 2(-1/3) - 3(-1/3)² = 22/3
y = 22/3
Therefore, 22/3 exists the maximum value of y.
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Evaluate 2a x 3 + b, if a = 5 and b = 1.
Answer:
31
Step-by-step explanation:
replace the values of a and b in the given term
=2a x 3 + b
2(5) x 3 + (1)
2x5 x 3 + 1
10 x 3 + 1
30 + 1
31
a mother is 25 years older than her son.
Write down the son's age and the mother's age
Answer:
mother age 37
sons age 12
What is the length of the apothem of the regular pentagon shown below? Round to one decimal place
Answer:
A
Step-by-step explanation:
Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.
Let's see what we have so far:
The base of the triangle is 3.8
The angle at the bottom is 90
The angle at the top is 36
We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.
This gives you adjacent = opposite / tan(angle)
adjacent = 3.8 / tan(36)
adjacent = 5.2m
differentiate with respect to x (6-2x)^3
Answer:
- 6(6 - 2x)²
Step-by-step explanation:
using the chain rule
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{dy}{du}[/tex] × [tex]\frac{du}{dx}[/tex]
let y = (6 - 2x)³
let u = 6 - 2x , then y = u³
[tex]\frac{du}{dx}[/tex] = - 2 and [tex]\frac{dy}{du}[/tex] = 3u²
then
[tex]\frac{dy}{dx}[/tex] = 3u² × - 2 = - 6(6 - 2x)²
Find the indicated side of the
right triangle.
60°
30°
X
x = 3√√√/[?]
3
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
The given is a special right triangle with angle measures 30-60-90
The measure of side lengths for this special right triangle are represented with
a-a[tex]\sqrt{3}[/tex]-2a respectively
Now, since the side length that sees angle measure 30 is given as 3 (represented with a) then the measure of the side length that sees angle measure 60 would be [tex]3\sqrt{3}[/tex]
The figure shows two parallel lines PQ and ST cut by the transversals PT and QS:
Answer:
triangle PQR is similar to triangle TSR because the measure of angle 3 is congruent to the measure of angle 4 and the measure of angle one is congruent to the measure of angle 5
Step-by-step explanation:
angle 3 and angle 4 are congruent because they are vertical pairs.
Angles 1 and five are congruent because they are alternate interior angles
A couple deposits $20,000 into an account earning 5% annual interest for 30 years. Calculate the future value of the investment if the interest is compounded monthly. Round your answer to the nearest cent.
The future value of the investment if the interest is compounded monthly is $89,354.89.
What is the future value of the investment?Given that;
Principal P = $20,000Annual interest rate r = 5% = 5/100 = 0.05Time t = 30 yearsCompound monthly = 12Future value = A = ?Using the compound interest formula;
A = P( 1 + r/n )^(nt)
We plug in our values.
A = 20000( 1 + 0.05/12 )^(12 × 30)
A = 20000( 1 + 0.0041666666666667)^(360)
A = 20000( 1.0041666666666667)^(360)
A = 20000( 4.46774965 )
A = 89354.89
Therefore, the future value of the investment if the interest is compounded monthly is $89,354.89.
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Given the similar hexagon-based prisms pictured below, if prism 2 has a surface area of 256 cm, what is the surface area prism 1? Hint : the ratio of surface areas is the scale factor squared.
Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm
How to determine the surface area prism 1 using the hint that the ratio of surface areas is the scale factor squared?From the figure, we have the following parameters
Prism 1 = 3 cm
Prism 2 = 8 cm
Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation
Scale ratio = Prism 1/Prism 2
Substitute the known values in the above equation
Scale ratio = 3m/8m
This gives
Scale ratio = 0.375
The surface area of prism 1 is then calculated using the following equation
Area of prism 2 = Scale ratio^2 * Area of prism 1
Substitute the known values in the above equation
Area of prism 2 = 0.375^2 * 256 square cm
Evaluate the product
Area of prism 2 = 36 square cm
Hence, the surface area of prism 1 is 36 square cm
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Solve: ( − )( + ) = �
Answer:
+ and - is always equals to -
Hope it helps!
The sum of two numbers is 43 . The smaller number is 9 less than the larger number. What are the numbers?
Answer:
17 & 26
Step-by-step explanation:
The equation
[tex]x+(x+9)=43\\2x+9=43[/tex]
[tex]2x=43-9\\2x=34[/tex]
[tex]x=34/2=17[/tex]
One number is 17
The other number is:
[tex]x+9=17+9=26[/tex]
Hope this helps
Find the sum of the geometric series given a1 = 5, r = 3, n = 12.
The sum of the geometric series is 1328600
How to determine the sum?The given parameters are:
a1 = 5
r = 3
n = 12
The sum of the terms is:
[tex]S_n = \frac{a(1 - r^n)}{1 - r}[/tex]
This gives
[tex]S_n = \frac{5 * (1 - 3^{12})}{1 - 3}[/tex]
Evaluate the difference
[tex]S_n = \frac{5 * (1 - 531441)}{-2}[/tex]
This gives
[tex]S_n = \frac{5 * - 531440}{-2}[/tex]
Evaluate
[tex]S_n = 1328600[/tex]
Hence, the sum of the geometric series is 1328600
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The weight of each “Golden Dairy’s Probiotic Yogurt with Fruit” cup is normally distributed with a mean of 170 grams and a standard deviation of 12 grams. One package contains six random cups and any package with an average weight per cup lower than 158 grams will be rejected.
Part A: What fraction of packages will be rejected because the average weight is too low?
Part B: In addition to original rejection criteria, suppose any packages that have an average weight per cup higher than 179 grams must be rejected as well. What is the total fraction of packages that will be accepted?
Using the normal distribution, it is found that:
A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.
B. 0.96 = 96% of packages that will be accepted.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For this problem, the parameters are given as follows:
[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]
Item A:
The proportion is the p-value of Z when X = 158, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.0071 = 0.71% of packages will be rejected because the average weight is too low.
Item B:
The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:
X = 179:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{179 - 170}{4.9}[/tex]
Z = 1.84
Z = 1.84 has a p-value of 0.9671.
X = 158:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{158 - 170}{4.9}[/tex]
Z = -2.45
Z = -2.45 has a p-value of 0.0071.
0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.
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a local newspaper assigns a rating between 1 and 10 to every book and movie it reviews. Victor gathered data about five titles where the newspaper reviewed both the book and the movie version of the title. The ratings assigned by the newspaper are given in the table. Select the points that represent this data.
The points that represent this data are shown in the image attached below.
What is a scatter plot?A scatter plot is a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in table above, the points that represent this data are shown in the image attached below.
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Answer:
please look at the picture
Kristina wants to invest $6200 in a savings account that pays 7.6% simple interest. How long will it take for this investment to double in value? Round your answer to the nearest tenth.
The number of years it would take the investment to double in value is 13.2 years.
How long will it take for the investment to double?When the amount doubles, the interest earned would be $6200.
Time = interest earned / (amount invested x simple interest)
$6200 / (6200 x 0.076) = 13.2 years
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Solve the equation 5 (x + 1) = 5x
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
an equation = [tex]\sf{5(x+1)=5x}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]
x = ?✏[tex]\bigstar\textsf{Solution \quad steps:-}[/tex] ✏
first use the distributive property
[tex]\sf{\longmapsto{ 5x+5=5x}[/tex]
subtract both sides by 5x
[tex]\sf{\longmapsto{0x+5=0}[/tex] (strange expression right)
[tex]\sf{\longmapsto 0=-5}[/tex] (whattt ?!)
the above statement's false, so the equation has no solutions
`hope that was helpful to u ~
In 2003, Dullinger et al. examined patterns of shrub invasion into high mountain grasslands of the Northern Calcareous (Limestone) Alps in Austria. Dullinger and his colleagues wished to determine whether Pinus mugo, a species of invasive conifer, showed a preference for invading some grassland habitats over others. The data provided give the number of Pinus mugo observed in each of six grassland types studied by the investigators. Assume that the area covered by each of the six habitats studied are approximately equal. What is the Pvalue?
based on the given area for the six habitats, Dullinger and his colleagues can find the p-value to be 0.0018.
how can the p-value be found?a chi-squared test is the best test for to find the p-value and when the data given is put through a chi-square model, the observed values are:
= 7, 9, 2, 11, 2, 0
the expected values should be:
= 1/6, 1/6, 1/6, 1/6, 1/6, 1/6
the p-value will be 0.001819
df = 5
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Which transformations must be applied to object A to place it in the position of object B?
rotation and reflection
rotation and translation
reflection and translation
rotation, reflection, and translation
In order for object A to be placed in the position of object B, there needs to be a rotation and translation.
How would object A get to object B?The first step would be to rotate object A to the left to give it the same orientation as object B.
Then, translate object A to the coordinates of object B. This would lead to object A fitting into object B.
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In ΔABC, BC = 13, CA = 20 and AB = 19. Which statement about the angles of ΔABC must be true?
m∠B > m∠ A > m∠C
m∠C > m∠B > m∠A
m∠A > m∠B > m∠C
m∠C > m∠A > m∠B
m∠B > m∠C > m∠A
m∠A > m∠C > m∠B
Answer:
m∠B > m∠C > m∠A
Step-by-step explanation:
The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.
PLEASE IF ANYONE CAN HELP I HAVE 35 MINUTES LEFT 1-8 ANSWERS ONLY WILL DO THANK YOU
Answer:
1. x=2 2.
y=1
Step-by-step explanation:
Im sorry I TRIED :(
Find the equation of the line
Answer:
Step-by-step explanation:
hello :
Solut i on :
1) A line that passes through A(0, -6 ) andB (8 ,- -8)
Hello : let A(0,-6) B(8,-8)
the slope is : (YB - YA)/(XB -XA)
(-8+6)/(8-0) = -2/8=-1/4
an equation is : y=ax+b a is a slope
y = (-1/4)x +b
the line through point A (0;-6) : -6 = (-1/4)(0)+b
b = -6 the equation is : y =(-1/)4x-6
in triangle ABC, AC=13, BC=84, and AB=85. find the measure of angle C.
in triangle ABC, AC=13, BC=84, and AB=85. the measure of angle is C.5.1 degrees,
How can the angle be found?Using the The Law of Cosines in any triangle which can be expressed as;
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
Then if we expressed the given sides in the cosine formula we have
[tex]13^2 = 85^2 + 84^2 - 2 * 85 * 84 * cos(C)[/tex]
Then we have [tex]169 = 7225 + 7056 - 14280 * cos(C)[/tex]
[tex]14280 * cosC = (7225 + 7056 - 169)[/tex]
[tex]cosC = \frac{14212}{ 14280}[/tex]
cos 0.9947
[tex]C = cos^-1(0.9947)[/tex]
C = 5.1 degrees
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A company determines that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200), where x is the price of each lamp. At which of the following prices will the company’s revenue be $10,000?
The price that will maximize company’s revenue of $10,000 is $50.
How to calculate the price?From the information, the company determines 50that the revenue, in dollars, for selling a particular model of lamp is given by R(x)=x(−20x+1200),
Therefore, this will be:
R(x) = -20x² + 1200x
10000 = -20x² + 1200x
-20x² + 1200x - 10000 = 0
x² - 60x + 500
x² - 50x - 10x + 500
x(x - 50) - 10(x - 50)
(x - 50)(x - 10)
Therefore, x - 50 = 0
x = 0 + 50 = 50
The price is 50.
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Which of these is smaller? 1/3 or 35%
1/3 = 1/3 × 100%
= 33%
☆ 33 % < 35 %
Therefore
* 1/3 is the smaller one.
☆...hope this helps...☆
_♡_mashi_♡_
The comparison of 1/3 and 35% in decimals shows that 1/3 is smaller than 35%.
Given that:
The fraction is 1/3 and the number in percentage is 35%.
The conversion of a fraction to a percentage can be obtained by dividing the numerator by the denominator and multiply by 100.
The decimal form of the fraction 1/3 is 33.33...%
1/3 ≈ 0.3333...
0.3333... * 100 ≈ 33.33...%
The value 35% is already in percentage.
Since, both the values are in percentage form, it can be easily compared.
On comparing, the resultant would be
33.33...% < 35%
Since 35% is greater than 33.33...%
It can be concluded that 35% is larger than 1/3.
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