Consider the given expression,
[tex]56-21[/tex]The expression can be transformed as,
[tex](7\times8)-(7\times3)[/tex]Since 7 is a common factor, take it as common,
[tex]7(8-3)[/tex]Thus, the expression is obtained that,
[tex]56-21=7(8-3)[/tex]Therefore, option (B) is the correct choice.
A candy company has fixed costs (costs that it must pay regardless of how much candy they
make) of $500 per day, and it costs them an additional $3 to manufacture each box of candy.
They can sell their candy for $3 a box. If we jet x represent the boxes of candy sold, the number of
boxes they need to sell to break even can be found by solving the equation 3x + 500 = 3x. How
many boxes of candy to they need to sell to break even?
You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.
What is Break even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."
Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
Fixed cost (in manufacturing) = $500
Manufacturing cost of each candy = $3
and selling price of candy = $3
let x be a box of candy sold,
hence for no of box to be sold for a break even,
3x + 500 = 3x
but if you see above equation, that has no solution
Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.
hence there is no solution, and you will never be able to achieve break even.
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O GRAPHS AND FUNCTIONSDomain and range from the graph of a continuous function
According to the graph we have:
Domain are the values of x. We can see that the graph extends horizontally from -5 to 3, but -5 and 3 are not included. Then, the domain is
[tex](-5,3)[/tex]Range are the values of y. Therefore, we see that the graph extends vertically from 4 to -3, so the range is:
[tex](-3,4)[/tex]Answer:
a. domain = (-5, 3)
b. range = (-3, 4)
Element X is a radioactive isotope such that every 20 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 770 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answer:
[tex]t = 18.9[/tex]
Information given :
We know that:
- Element X is a radioactive isotope such that every 20 years, its mass decreases by half
- the initial mass of a sample of Element X is 770 grams
And we must find how long it would be until the mass of the sample reached 400 grams
Step-by-step explanation:
To find it, we need to use the following formula:-
[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]
- A(0) is the initial amount
From given information, A(0) = 770 grams
Now, replacing the value in t :
[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]
Then, we must solve for t :-
[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]
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What is the maturity value given the following:$10,800 at 8% for 8 months
The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as
I = PRT
where
I is the interest after time t
P is the principal or initial amount
R is the interest rate
T is the time in years
From the information given,
P = 10800
R = 8/100 = 0.08
T = 8 months
We would convert 8 months to years. Recall,
12 months = 1 yr
8 months = 8/12 = 0.67
Thus,
t = 0.67 yr
By substituting these values into the formula, we have
I = 10800 x 0.08 x 0.67
I = 578.88
Thus,
Maturity value = 10800 + 578.88
Maturity value = $11378.88
What is the next step in the construction?
An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. Make an arc by setting the compass's needle at A. Please indicate intersections B and C.
What is meant by arc?An arc is, in general, any straight curve that connects two points. The term "arc length" refers to an arc's length. A graph arc is an ordered pair of adjacent vertices in a graph. An arc is specifically any section of a circle's circumference (other than the full curve).
An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.
A circle's circumference forms an arc. An arc length is the length of the arc, whereas an arc measure is the measurement of the angle the arc makes at the center of a circle.
Therefore, the correct answer is option b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
The complete question is:
What is the next step in the construction?
a) Step 1: Select a point on line 1 and label it point A. Draw in PA.
b) Step 2. Put the point of the compass at A and make an arc. Label the intersections B and C
c) Step 3. Without changing the compass setting. put the compass at point P and make an identical arc. Label the intersection D
d) Step 4. Put the compass at point B and use it to measure the distance to C.
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Find the nth term of this quadratic sequence
2,8, 18, 32, 50,
Answer:
72
Step-by-step explanation:
8 = 2×2^2
18 = 2×3^2
32 = 2×4^2
50 = 2×5^2
72 = 2×6^2
Find the equation of the line graphed below. Write the equation in the form y = mx + b and identify m and b m = b =
ANSWER:
m = -3/4
b = -3
[tex]y=-\frac{3}{4}x-3[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation in its slope-intercept form is the following:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:
[tex]m=\frac{-3-0}{0-(-4)}=\frac{-3}{4}=-\frac{3}{4}[/tex]Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:
[tex]y=-\frac{3}{4}x-3[/tex]An election ballot asks voters to select six city commissioners from a group of twenty two candidates. In how many ways can this be done?
In this case, we have 6 places to fill from a pool of 22 candidates. There is no difference in the places: they are all commissioners, so if candidate A is selected, the order does not matter, but there is only one candidate, so there is no repetition.
Then, this is a combination (as the order does not matter) with no repetition of 22 elements in 6 places.
We can calculate this as:
[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ C(22,6)=\frac{22!}{6!(22-6)!}=\frac{22!}{6!\cdot14!}=\frac{22\cdot21\cdot20\cdot19\cdot18\cdot17\cdot16\cdot15}{6\cdot5\cdot4\cdot3\cdot2\cdot1}=17907120 \end{gathered}[/tex]Answer: there are 17,907,120 ways this can be done.
how do i do vertical analysis
To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.
What is a vertical analysis?Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.
The base figure is the revenue in the income statement or the total assets in the balance sheet.
The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.
Examples of vertical analysis can be shown with AT$T and Verizon below:
AT&T Percent
Revenue $132,447 100%
Cost of Services (Expenses) 60,611 45.8% ($60,611/$132,447 x 100)
Selling & Marketing Expense 39,697 30.0%
Depreciation & other expenses 20,393 15.4%
Operating Income $11,746 8.9%
Verizon Percent
Revenue $127,079 100%
Cost of Services (Expenses) 49,931 39.3% ($49,931/$127,079 x 100)
Selling & Marketing Expense 41,016 32.3%
Depreciation & other expenses 16,523 13.0%
Operating Income $19,599 15.4%
Thus, we have performed the vertical analysis of AT$T and Verizon above.
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Question Completion:Income Statements of AT&T and Verizon (in millions) are:
AT&T Verizon
Revenue $132,447 $127,079
Cost of Services (Expenses) 60,611 49,931
Selling & Marketing Expense 39,697 41,016
Depreciation & other expenses 20,393 16,523
Operating Income $11,746 $19,599
Solve the linear programming problems: (find the constraints, objective function, feasible region, and the minimumand maximum values)12. A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week.Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week formaterials. Each oak chair sells for $400 and each walnut chair sells for $500. What are the number of oak and walnutchairs that the small business should produce in order to maximize / minimize sales?
The firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
What are linear equations?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So,
Production of oak chairs: xProduction of walnut chairs: y(Refer to the graph attached below)
Then,
x + y ≤ 20100x + 150y ≤ 2400x ≥ 0y ≥ 0I = 400x + 500ySo, oak chair produced:
(0, 16) ⇒ $8000(20, 0) ⇒ $8000(12, 8) ⇒ $8800Therefore, the firm should produce 12 oak chairs and 8 walnut chairs to maximize its profit to $8,800.
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The correct question is given below:
Solve the linear programming problem: A small business produces oak chairs and walnut chairs. The business can make at most 20 chairs per week. Materials cost $100 per oak chair and $150 per walnut chair. The business has a budget of $2400 per week for materials. Each oak chair sells for $400 and each walnut chair sells for $500. How many each types of chairs should the business make each week to maximize income?
The surface area of the rectangular prism is given by formula S=2(ab+bh+ah). Find the value of h when a=6, b=5 and s=214
The value for the height of the rectangular prism is found as; h = 7.
What is defined as the rectangular prism?A rectangular prism is a three dimensional solid shape with six faces that have rectangles as their bases. Right rectangular prisms as well as non-right (oblique) rectangle prisms are the two types of rectangular prisms. The right rectangle prism does have two parallel end faces and 4 lateral faces, each of which is an rectangle; this same faces are perpendicular to the bases of the prism.The formula for the surface area of rectangular prism is;
S = 2(ab+bh+ah)
Where,
a=6, b=5 and s=214
Substitute the values in the formula.
214 = 2(6×5 + 5h + 6h)
Simplifying;
30 + 11h = 107
11h = 107 - 30
11h = 77
h = 7
Thus, the value for the height of the prism is found as; h = 7.
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Can you show me step by step how to get this answer please?
Answer: first six cannot go into three because three is too small so six is going to go into 31 Six can go into 31 five times because 6×5 = 30 then since you’re subtracting 31 and 30 you would be left with one you would have to bring the 1 from the 12 down and then it would be 11. 11 can go into six once so 6-11 =5 so then you have to bring the two from the 12 down so then that would equal 6-2=4 and your done! It was a little confusing so if it didn’t make sense I’m sorry
Select all the equations where x = 3 is a solution.X-3 = 01 + x = 209 - x= 3O 6 = 2xOf = 3x2 = 9
Let's begin by listing out the given information:
[tex]undefined[/tex]Calc Limits. Attatched question.
The correct option regarding the continuity of f(x) at x = 2 is given by:
B. lim x -> 2 f(x) exists, but f(2) exist.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For this problem, the denominator of the function is:
8cos(0.5πx) + 2x²
At x = 2, the denominator of the function is:
8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).
Then the function does not exist at x = 2, as the denominator is of 2.
From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:
lim x -> -2^- f(x) = -infinity.lim x -> -2^+ f(x) = -infinity.Since the lateral limits are equal, the limit exists, hence option B is correct.
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determine the inverse of the given function
f(x)= 2x-9/4
To find the inverse of a function:
Replace f(x) with ySwitch around x and yIsolate yReplace y with f⁻¹(x)Solving the Question[tex]f(x)= 2x-\dfrac{9}{4}[/tex]
⇒ Replace f(x) with y:
[tex]y= 2x-\dfrac{9}{4}[/tex]
⇒ Switch around y and x:
[tex]x= 2y-\dfrac{9}{4}[/tex]
⇒ Isolate y:
[tex]x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
⇒ Replace y with f⁻¹(x):
[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
Answer[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
Doris borrowed 7 dollars from Nikki. Doris then paid back 2 dollars. How much does Doris
still owe Nikki?
Answer:
He still owes Nikki $5.
Step-by-step explanation:
7 - 2 = 5
Answer:
5
Step-by-step explanation:
7-2=5
Represent a quadratic function
Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 1
Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 2
Using ratio
[tex]\frac{\frac{5}{6}pounds\text{ of oats}}{2\frac{1}{2}pounds\text{ of oats}}=\frac{1\text{ batch of granola}}{x}[/tex][tex]\begin{gathered} \frac{5}{6}x=\frac{5}{2} \\ 10x=30 \\ x=\frac{30}{10} \\ x=3 \end{gathered}[/tex]Answer;
[tex]3\text{ batches}[/tex]Answer:3
Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6
Which of the following is a true statement about a tangent and a radius?
A. A tangent and a radius of a hexagon are always equal lengths.
B. A tangent and a radius of a circle meet to form a 90 angle.
C. A tangent and a radius in a cylinder form two legs of a right triangle with the cylinders altitude serving as the hypotenuse.
D. A tangent and a radius intersect at the foci of an ellipse.
A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.
The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.
A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.
Hence the correct option is B
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Name the line of reflection used to map the preimage to its image.
Option A, Y- axis is the line of reflection used to map the preimage to its image.
The graph shows that if the graph is folded by a y-axis, Point G will cross Point G', which is two coordinates away from the y-axis.
Point F will cross point F', which is four coordinates away from the y-axis.
Points H will cross point H', which is in negative coordinates and 7 coordinates away from the y-axis.
Mirror images are symmetrical from any axis, which might be the x-axis or the y-axis. Flipping geometry refers to reflection. Mirror reflection is a type of reflection. When lines reflect an image, reflection lines form. A form is said to mirror another shape if each of its points is equidistant from each of the other shape's points.
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What is the value of x?
-6x + 6 > 12
Subtract 6 from both sides.
−6x > 12 - 6Subtract 6 from 12 to get 6.
−6x > 6Divide both sides by −6. Since −6 is <0, the inequality direction is changed.
x < 6/-6Divide 6 by −6 to get −1.
x<−1A population grows according to an exponential growth model. The initial population is 212 and the population after one year is 263.
Complete the formula where P is the population and n is the number of years.:
P=212*(___)n
Round your answer to three decimal places.
Answer: P=212*(1.240)n
Step-by-step explanation:
1) Find the % growth
263-212= 51
51/212 = 0.240566037735849
2) Add 1 to the decimal as the population isn't decreasing but increasing.
0.240566037735849 + 1 = 1.240
3) Fill in the equation
P=212*(1.240)n
Determine which of the following proportions are true.I 1mi2hr=12mi24hrII 7min9cents=36min24centsIII
1 and 3
1 * 12 = 12
2 * 12 = 24
so 1 is true
7 * 5.14 = 36
9 * 5.14 = 46.26
so 2 is not true
7 * 4 = 28
2 * 4 = 8
so 3 is true
What is the ratio of male teachers to male students?
Data:
Students: 180
Half male.
Male students: 180/2=90
Male teachers: 2
Ratio of male teachers to male students:
You can write the ratio in three different forms:
[tex]\begin{gathered} 2\colon90 \\ \\ 2\text{ to 90} \\ \\ \frac{2}{90} \end{gathered}[/tex]If f(x) = -3x-2, g(x) = - 4x² + 7x-2, and h(x) = 2x² + 4, find h(1).
Answer:
h(1) = 6
Step-by-step explanation:
h(1) will be
h(x) = 2x² + 4
h(1) = 2(1)² + 4 = 2 + 4
h(1) = 6
find the midpoint between. (-1,2) and (-7,-4).
The midpoint of two coordinates can be obtained using the formula:
[tex]\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2}[/tex]x1 = -1
y1= 2
x2= -7
y2= -4
[tex]\begin{gathered} \frac{-7\text{ +(-1)}}{2},\frac{2+(-4)}{2} \\ \\ \frac{-7-1}{2},\frac{2-4}{2} \\ \frac{-8}{2},\frac{-2}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{midpoint} \\ (-4,-1) \end{gathered}[/tex]In a paragraph of no less than 125 words, explain why you appreciate/love your chosen piece of music.
I adore BTS (the Korean boy band) because they encourage self-love. Their songs are artistically and romantically rich. They're well-known throughout the world and at the moment's top boy band in the US.
What is music about?In this sense, understanding the worth and excellence of various musical genres is referred to as appreciation. The word "appreciation" has philosophical roots; in that discipline, it is defined in relation to music as "a type of formal counterpart of emotional experience."
Someone's mood can be improved by listening to their music, which can also thrill or calm the listener. Importantly, music also enables us to experience almost all of the emotions we go through in life. There are countless options. Dopamine release in the mesolimbic reward system can be triggered by listening to extremely pleasurable music.
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The Faulk Corp. has a bond with a coupon rate of 4 percent outstanding. The Gonas Company has a bond with a coupon rate of 10 percent outstanding. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
If the interest rates suddenly rise by 2 percent, the percentage change in the price of these bonds are : 19.73%, 16.56%.
Percentage changeUsing this formula to find the current price of a bond
P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n
Where:
P =Current price of a bond
C = Coupon payment,
YTM = Yield to maturity
n = Time to maturity
F =Face value of a bond
The Faulk Corp. bond
C = Coupon rate / number of payments per year × face value = 4% / 2×$1,000 = $20
n = 13 years = 36 half-year periods
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
hence,
P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $405.81 + $289.83
P=$695.61
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.
Price of the Faulk Corp. bond:
P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $353.32 +$205.03
P=$558.38
Percentage change:
Percentage change = $558.38 - $695.61/$695.61×100%
Percentage change =19.73%
Gonas Company bond:
C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50
n = 18 years = 36 half-year periods,
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $1,014.52 + $289.83
P=$1,304.35
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :
P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $883.30 +$205.03
P=$1,088.33
Percentage change:
Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%
Percentage change =16.56%
Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 22 feet more than the length of the shortest side. Find the dimensions if the perimeter is 186 feet.
The three sides of the triangle will be 82, 63, and 41 feet.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.
That a flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side 22 feet more than the length of the shortest side.
Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.
Perimeter = A + B + C
A = 2B and C = 22 + B
Put the values in the equation as solve:-
Perimeter = A + B + C
186 = 2B + B + 22 + B
186 = 4B + 22
4B = 186 - 22
4B = 164
B = 164 / 4
B = 41 feet
Longest side = 2B = 2 x 41 = 82 feet
Shirtest side = B = 41 feet
Third side = 22 + B = 22 + 41 = 63 feet
Therefore, the three sides of the triangle will be 82, 63, and 41 feet.
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If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 7?
the probability that the card you select is a diamond or 7 is 4/13
WHAT IS PROBABILITY ?Mathematical representations of the likelihood of an event occurring or of a proposition being true are dealt with in the area of probability. A number between 0 and 1 represents the likelihood of an event, with 0 roughly denoting impossibility and 1 representing certainty.
CALCULATIONLets take diamond first total diamonds are 13 and total cards are 52 So prob is 13/52 which is 1/4
Lets take 7s
total 10s in the deck is 4 (one in each suite) (one in each suite)
Prob of 7s is 4/52 which is 1/13
Final answer =1/13+1/4=17/52 Total prob is addition of above two as it is "or."
Because the prob of the 7th diamond has been inserted twice, edit it as follows: 17/52-1/52=16/52=4/13
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