as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?
well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that
with an initial investment of £800 yielding £78 per year, what's the interest rate?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)(\frac{r}{100})(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r[/tex]
You are contracted to fabricate a gate with specifications shown below. As you start, you realize making a jig for the bottom spacing would make life easier. What is the spacing between bars?
5.85"
6"
5.95"
5.7"
Answer:
Let x be the measure of the spacing between the bars.
6.25" + 5x = 36"
5x = 29.75"
x = 5.95"
please help me with this
Answer:
3/4
Step-by-step explanation:
The 0 <= theta <= pi/2 makes it so the angle must be in the first quadrant. From there, you can use the fact that sin = opposite / hypotenuse.
Thus the opposite side length would be 5, the hypotenuse would be 5, and the adjacent side length would be 3 (by Pythagorean theorem).
Recall that cot = cotangent = 1 / tan. And recall that tan is opposite of adjacent. So tan(theta) = 4/3, and cot (theta) = 3/4.
b) Find the least number that must be subtracted from 2120 so that the result is a perfect square.
Answer: 4
I’m sorry, I could not find any other methods except for finding the closest perfect square which was 2116. (46^2)
Can someone help me wit this please
Answer:
Hi
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graph the line passing through (−4,−1) whose slope is m=-4/5
Answer:
[tex]y=-\frac{4}{5}x-\frac{21}{5}[/tex]
Step-by-step explanation:
The fastest way is to use point-slope form with [tex]m=-\frac{4}{5}[/tex] and [tex](x_1,y_1)=(-4,-1)[/tex]:
[tex]y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}[/tex]
To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting m = -4/5, x = -4, and y = -1, we can solve for b:
-1 = (-4/5)(-4) + b
-1 = 3.2 + b
b = -4.2
Therefore, the equation of the line is:
y = (-4/5)x - 4.2
To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:
y = (-4/5)x - 4.2
y = (-4/5)(0) - 4.2
y = -4.2
So the y-intercept is (0,-4.2).
Using this point and the given point (-4,-1), we can draw a straight line passing through both points.
Here is a rough sketch of the graph:
|
|
| *
| /
| /
| /
-----*--------
|
|
|
|
|
The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.
PLEASE SOMEONE HELP ME !!!!
At the end of October, Allen Springer's check register
balance was $812.45. His bank statement balance was
$624.77. An examination of his statement and check
register showed that an ATM withdrawal of $200 had
not been entered in the register, Check 201 for $92.49
was outstanding, and Check 202 for $80.17 was cashed
but not recorded in the register. Reconcile the checking
account.
The reconciled balance is $600.13.
2.3 CD is a tangent to the circle ABDEF at D. Chord AB is produced to C. Chord BE cuts chord AD in H and chord FD in G. ACFD and AB = EF. Let D₁ = x and D₁ = y A C B 1 3 H 2 1 N 2 D G 1 2 2 2.3.1 Name with reasons THREE other angles equal to x. 2.3.2 Show that BDE = x + 2y 2.3.3 Prove that BCDH is a cyclic quadrilateral. 1 Assignment/ Term 2 E (4) (4) [28] TOTAL [50]
The three angles equal to x are: ∠x = ∠BAD = ∠BED = ∠BFD
It is proved that, ABHD ||AFED and proved that AB BD = FD BH
Here, we have,
from the given figure, we get,
CD is a tangent to the circle ABDEF at D.
Chord AB is produced to C.
Chord BE cuts chord AD in H and chord FD in G.
ACFD and AB = EF.
we have,
AC || FD
FE = AB
i) The three angles equal to x are:
∠x = ∠BAD = ∠BED = ∠BFD
as the angles on the same chord.
ii) ∠DBH = ∠DFE [angle on same chord DE ]
∠BDH = ∠FDE [angle inscribed by equal chord]
∠BHD = ∠FED [ when two angles of a triangle are equal so the other will
also equal ]
so, we get, by AAA similarity ΔBHD ≡ Δ FDE
iii) now, we have, from ΔBHD ≡ Δ FDE
BD/BH = FD/FE
=> BD/BH = FD/AB
=> AB.BD = FD.BH [by cross multiplication]
Hence, Proved.
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complete question:
CD is a tangent to circle ABDEF at D Chord AB IS produced to C Chord BE cuts chord AD in H and chord FD in G ACI/FD and FE = AB Let ZD4 = and ZD = y 1 2 3 Determine THREE other angles that are equal tox Prove that ABHD ||AFED Hence or otherwise, prove that AB BD = FD BH
NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular decagon below. Find its area. Round to the nearest tenth if necessary.
[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{nr^2}{2}\sin(\frac{360}{n}) ~~ \begin{cases} r=\stackrel{ circumcircle's }{radius}\\ n=sides\\[-0.5em] \hrulefill\\ n=10\\ r=13 \end{cases}\implies A=\cfrac{(10)(13)^2}{2}\sin(\frac{360}{10}) \\\\\\ A=845\sin(36^o)\implies A\approx 496.7[/tex]
Answer:
496.7 square units
Step-by-step explanation:
A regular polygon is a polygon with equal side lengths and equal interior angles, meaning all of its sides and angles are congruent.
The radius of a regular polygon is the distance from the center of the polygon to any of its vertices.
The given figure is a regular decagon (10-sided figure) with a radius of 13 units.
To find the area of a regular polygon given its radius, use the following formula:
[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=nr^2\sin \left(\dfrac{180^{\circ}}{n}\right)\cos\left(\dfrac{180^{\circ}}{n}\right)$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute n = 10 and r = 13 into the formula and solve for A:
[tex]A=10 \cdot 13^2 \cdot \sin\left(\dfrac{180^{\circ}}{10}\right)\cdot \cos\left(\dfrac{180^{\circ}}{10}\right)[/tex]
[tex]A=10 \cdot 169 \cdot \sin\left(18^{\circ}\right) \cdot \cos \left(18^{\circ}\right)[/tex]
[tex]A=496.678538...[/tex]
[tex]A=496.7\; \sf square \; units[/tex]
Therefore, the area of a regular decagon with a radius of 13 units is 496.7 square units (to the nearest tenth).
Ken's living room and computer room have the dimensions shown.
What is the total volume of the rooms, in cubic feet?
Answer:
The total volume is 1660 cubic feet.
Step-by-step explanation:
The volume of a room is:
Vol = l × w × h
We calculate the two rooms separately, then add them together for the final answer.
The large room is:
Vol = 14 × 9 × 10
= 1260
The smaller room is:
Vol = 8 × 5 × 10
= 400
The total volume is
1260 + 400
= 1660
The total volume of the two rooms is 1660 cubic feet.
50 POINTS
The Jordans are considering buying a house with a market value of $250,000. The assessed value of the house is a dollars. The annual property tax is $2.45 per $100 of assessed value. What is the property tax on this house?
To find the property tax on the house, we need to calculate the assessed value and then multiply it by the property tax rate.
The property tax rate is $2.45 per $100 of assessed value, which can be written as 0.0245 (since $2.45 divided by $100 is 0.0245).
To calculate the assessed value, we need to find the assessed value as a percentage of the market value. Let's assume the assessed value is x.
x/100 * $250,000 = $a
We don't have the value of 'a,' so we can't directly calculate the assessed value.
Could you please provide the value of 'a' (the assessed value) so that we can calculate the property tax on the house?
~~~Harsha~~~
Answer:
$4,593.75
Step-by-step explanation:
To find the property tax on the house, we need to first determine the assessed value of the house.
If the market value of the house is $250,000, and the assessed value is a dollars, then we can set up the following equation:
a = 0.75 x 250,000
where 0.75 represents the assessment rate, which is typically a percentage of the market value used to determine the assessed value for tax purposes.
Simplifying the equation, we get:
a = 187,500
Therefore, the assessed value of the house is $187,500.
To find the property tax, we can use the given tax rate of $2.45 per $100 of assessed value.
First, we need to convert the assessed value from dollars to hundreds of dollars, which we can do by dividing by 100:
187,500 / 100 = 1,875
Next, we can multiply the assessed value in hundreds of dollars by the tax rate per hundred dollars:
1,875 x 2.45 = 4,593.75
Therefore, the property tax on the house is $4,593.75.
help is it 32 or what help
Answer:
45
Step-by-step explanation:
In addition to low iron levels, some of your patients have had high potassium levels while
taking NT71C. While reviewing the data during rounds, you and your colleagues estimate
that the patients need 5.2µg of iron and 1.3mg of potassium each day. The iron
supplements you've purchased contain 1.2µg of iron and 0.3mg of potassium per dose,
while the patient's daily meals contain 0.4µg of iron and 0.1 mg of potassium per serving.
What balance of iron supplement dose and ordinary food servings should you use to
meet the patients' nutritional needs?
To determine the balance of iron supplement dose and ordinary food servings needed to meet the patients' nutritional needs, let's assign variables to represent the quantities:
Let:
- x = number of iron supplement doses per day
- y = number of ordinary food servings per day
Based on the information given, we can establish the following equations:
Equation 1: Iron Balance
1.2µg * x + 0.4µg * y = 5.2µg
Equation 2: Potassium Balance
0.3mg * x + 0.1mg * y = 1.3mg
We can solve this system of equations to find the values of x and y that satisfy both equations.
Multiplying Equation 1 by 10 and Equation 2 by 1000 will help us eliminate the decimal points:
Equation 1 (revised): 12µg * x + 4µg * y = 52µg
Equation 2 (revised): 300µg * x + 100µg * y = 1300µg
Now, we can use any method to solve the equations. Let's solve them using the substitution method:
From Equation 1 (revised), we can express x in terms of y:
12µg * x = 52µg - 4µg * y
x = (52µg - 4µg * y) / 12µg
x = (13µg - µg * y) / 3µg
x = 13/3 - y/3
Substituting this value of x into Equation 2 (revised):
300µg * (13/3 - y/3) + 100µg * y = 1300µg
Simplifying and solving for y:
(3900µg - 100µg * y + 100µg * y) / 3 = 1300µg
3900µg / 3 = 1300µg
1300µg = 1300µg
The equation is satisfied for any value of y. This means that there is no unique solution for the system of equations. In other words, any combination of iron supplement doses (x) and ordinary food servings (y) that satisfy the equation 1.2µg * x + 0.4µg * y = 5.2µg will also satisfy the equation 0.3mg * x + 0.1mg * y = 1.3mg.
Therefore, there are multiple ways to achieve the balance of iron and potassium needed to meet the patients' nutritional needs. The specific values of x and y will depend on the preferences of the patients and the dosing recommendations by healthcare professionals.
Deriving the Law of Cosines Follow these steps to derive the law of cosines. 1. The relationship between the side lengths in AABD is 2²=²+h² by the Pythagorean theorem 2. The relationship between the side lengths in ACBD is a² = (b-x)² +h² by the law of sines
This is the Law of Cosines, which relates the Lengths of the sides of a triangle to the cosine of one of its angles.CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))
To derive the Law of Cosines, follow these steps:
Step 1: Consider the triangle AABD, where A and B are vertices and AB is the side opposite the angle ABD.
Apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have:
AB² = AD² + BD²
Step 2: Now, consider the triangle ACBD, where C is another vertex and AC is the side opposite the angle ACD.
Apply the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. In this case, we have:
AC / sin(ACD) = BD / sin(ABD)
Rearrange the equation to isolate AC:
AC = (BD / sin(ABD)) * sin(ACD)
Step 3: Notice that BD = b - x, where b is the length of AB and x is the length of CD.
Substitute this expression for BD in the equation from step 2:
AC = ((b - x) / sin(ABD)) * sin(ACD)
Step 4: Square both sides of the equation obtained in step 3:
AC² = ((b - x) / sin(ABD))² * sin²(ACD)
Step 5: Recall that sin²(ACD) = 1 - cos²(ACD). Substitute this expression in the equation from step 4:
AC² = ((b - x) / sin(ABD))² * (1 - cos²(ACD))
Step 6: Rearrange the equation to isolate cos²(ACD):
cos²(ACD) = 1 - (AC² / ((b - x) / sin(ABD))²)
Step 7: Simplify the equation:
cos²(ACD) = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²
Step 8: Finally, recall that cos²(ACD) = 1 - sin²(ACD) = 1 - (CD / AC)². Substitute this expression in the equation from step 7:
1 - (CD / AC)² = 1 - AC² / (b - x)² * (sin(ABD) / sin(ACD))²
Rearrange the equation to obtain the Law of Cosines:
CD² = AC² + (b - x)² - 2 * AC * (b - x) * (sin(ABD) / sin(ACD))
This is the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
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What the meaning of statement this?
This symbol " [tex]\phi = {u : u\neq u}[/tex]" given in set statement means that the set is empty and has no element in it.
What is the meaning of [tex]\phi = {u : u\neq u}[/tex]?[tex]\phi = {u : u\neq u}[/tex] is a set notation that represents the empty set. In set theory, the empty set, denoted by the symbol [tex]\phi[/tex] or {}.
An empty set is defined as a set that does not contain any elements and it is just empty or null.
For this question, [tex]\phi = {u : u\neq u}[/tex] , the set is defined using a condition or property.
The condition given is u ≠ u, which is always false for any element. So we can say that it implies that there is no element that satisfies the condition u ≠ u, meaning there are no elements in the set.
Hence, the set is empty.
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The quantities
�
xx and
�
yy are proportional.
�
xx
�
yy
3
33
30
3030
10
1010
100
100100
16
1616
160
160160
Find the constant of proportionality
(
�
)
(r)left parenthesis, r, right parenthesis in the equation
�
=
�
�
y=rxy, equals, r, x.
�
=
r=r, equals
The Constant of proportionality (r) in the equation x = ry is 1/11.
The constant of proportionality (r) in the equation x = ry, where x and y are proportional, we can use the given pairs of values for x and y and solve for r.
Let's consider the given pairs of values:
x = 3, y = 33
x = 30, y = 3030
x = 10, y = 1010
x = 100, y = 100100
x = 16, y = 1616
x = 160, y = 160160
We can select any pair of values and set up the equation x = ry. Let's choose the pair x = 3 and y = 33:
3 = r * 33
To find r, we divide both sides of the equation by 33:
r = 3 / 33 = 1 / 11
Therefore, the constant of proportionality (r) in the equation x = ry is 1/11.
We can verify this by substituting other pairs of values into the equation and checking if the equation holds true. For example, let's substitute x = 160 and y = 160160:
160 = (1/11) * 160160
160 = 14560
The equation holds true, confirming that the constant of proportionality is indeed 1/11.
Hence, the constant of proportionality (r) in the equation x = ry is 1/11.
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Pat receives a series of four annual federally subsidized student loans, each for $5400 at 6.5%. To defray rising costs for her senior year, 3 years after acquiring the first loan she takes out a private student loan for $4100 at 7.5% interest with a term of 10 years and capitalizes the interest for her last year of college. She graduates 9 months after getting the private loan. Payments on all loans are deferred until 6 months after graduation. Find her monthly payment.
Pat's approximate monthly Payment would be $304.32 to repay all her loans after the deferment period.
The Pat's monthly payment, we need to consider the terms and interest rates of each loan. Let's break down the calculation step by step:
1. Federally subsidized student loans:
- Pat receives four annual loans, each for $5400 at an interest rate of 6.5%.
- Since the loans are annual, we need to calculate the interest for each year and add it to the principal amount.
- The total principal amount for the four loans is $5400 * 4 = $21,600.
- The interest for each year is $21,600 * 6.5% = $1,404.
- Therefore, the total amount owed for the federally subsidized loans is $21,600 + ($1,404 * 4) = $27,816.
2. Private student loan:
- Pat takes out a private student loan for $4100 at an interest rate of 7.5% for a term of 10 years.
- The loan is capitalized, which means the interest is added to the principal amount.
- The total principal amount for the private loan is $4100.
- The interest for each year is $4100 * 7.5% = $307.50.
- Since Pat capitalizes the interest for her last year of college, the loan will accrue interest for a total of 9 months.
- Therefore, the total interest accrued for the private loan is ($307.50 * 9) = $2767.50.
- The total amount owed for the private loan is $4100 + $2767.50 = $6867.50.
3. Total amount owed:
- To find the total amount owed by Pat, we add the amounts from the federally subsidized loans and the private loan.
- Total amount owed = $27,816 + $6867.50 = $34,683.50.
4. Monthly payment:
- The monthly payment is calculated based on the total amount owed and the repayment term.
- The term is 10 years for the private loan, but since payments are deferred until 6 months after graduation, the actual term is 10 years - 0.5 years = 9.5 years.
- The number of monthly payments is 9.5 years * 12 months/year = 114 months.
- Therefore, the monthly payment is $34,683.50 / 114 months ≈ $304.32.
So, Pat's approximate monthly payment would be $304.32 to repay all her loans after the deferment period.
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Simplify: −6ru2−ur2−22u2r2
The simplified form of[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex]is [tex]-u^2(7r + 22r^2)[/tex].
To simplify the expression[tex]-6ru^2 -ur^2 - 22u^2r^2[/tex], we can combine like terms and factor out common factors.
First, let's look at the variables r and u separately:
For r:
We have terms[tex]-6ru^2[/tex] and [tex]-ur^2.[/tex] We can factor out r from these terms:
[tex]r(-6u^2 - u^2)\\r(-7u^2)[/tex]
For u:
We have term[tex]-22u^2r^2[/tex]. We can factor out[tex]u^2[/tex]from this term:
[tex]u^2(-22r^2)[/tex]
Combining the simplified terms for r and u, we get:
[tex]r(-7u^2) + u^2(-22r^2)[/tex]
Now, we can factor out the common factor of[tex]-u^2[/tex]:
[tex]u^2(7r + 22r^2)[/tex]
Therefore, the simplified expression is[tex]-u^2(7r + 22r^2)[/tex] .
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Consider the rhombus above. What is the measure of angle BDA? (NOTE: not drawn to scale)
The measure of angle BDA is 3
How to calculate the measure of angle BDA?From the question, we have the following parameters that can be used in our computation:
ABC = 4x - 2
DBC = 3x - 3
The figure is a rhombus
This means that
ABC = 2 * DBC
So, we have
4x - 2 =2 * (3x - 3)
When evaluated, we have
4x - 2 = 6x - 6
When solved for x, we have
2x = 4
So, we have
x = 2
This also means that
BDA = DBC = 3x - 3
So, we have
BDA = 3(2) - 3
Evaluate
BDA = 3
Hence, the measure of angle BDA is 3
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..........................................................................................................................
Answer:
B) m = (9/10)v------------------------
Direct variation equation in terms of given values:
m = kv, where k- coefficient10 cm³ of oil has a mass of 9 grams:
v = 10, m = 9Substitute values of m and v and find the value of k:
9 = 10kk = 9/10Substitute the value of k back to initial equation:
m = (9/10)vThe matching choice is B.
Answer:
[tex]m= \frac{9}{10}*v[/tex]
Step-by-step explanation:
Since the mass of cooking oil is directly proportional to the oil's volume, we can write the following equation:
m = kv
where k is the constant of proportionality.
We know that when v = 10, m = 9, so we can plug these values into the equation to solve for k:
9 = k * 10
k =[tex]\frac{9}{10}[/tex]
Now, we can plug k =[tex]\frac{9}{10}[/tex] into the original equation to get the following equation:
m =[tex]\frac{9}{10}[/tex] v
Write two numbers that multiply to the value on top and add to the value on bottom.
6
-7
Answer:
-1 and -6
Step-by-step explanation:
If you multiply negative times negative or minus times minus it will turn to plus so
- x - = +
-1 x -6 = +6
If you add negative plus negative or minus plus minus it remain negative or minus
- + - = -
-1 + -6 = -7
The two numbers that multiply to 6 and add to -7 are -1 and -6.
We are given two conditions:
xy = 6
x + y = -7
We can rearrange equation 2 to express one variable in terms of the other.
x = -7 - y
Now we can substitute this expression for x in equation 1:
(-7 - y) y = 6
Expanding the equation:
-7y - y²= 6
Rearranging the equation to bring it to a quadratic form:
y² + 7y + 6 = 0
We can now solve this quadratic equation to find the values of y.
Factoring the quadratic equation:
(y + 6)(y + 1) = 0
Setting each factor equal to zero and solving for y:
y + 6 = 0 --> y = -6
y + 1 = 0 --> y = -1
So we have two possible values for y: -6 and -1.
Substituting these values back into equation 2 to find the corresponding values of x:
For y = -6:
x + (-6) = -7
x = -1
For y = -1:
x + (-1) = -7
x = -6
Therefore, the two numbers that multiply to 6 and add to -7 are -1 and -6.
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What are the base angles z & j of the equal sided triangle below? Type in the single angle only - not the sum of the two! numerical answer only
Answer:
58° + x = 180°
x = y = 122°
z = j, so 122° + 2z = 180°
2z = 58°
z = j = 29°
The Peace Barber Shop employs four barbers. One barber, who also serves as the manager, is paid a salary of $1,800 per month. The other barbers are paid $1,300 per month. In addition, each barber is paid a commission of $4 per haircut. Other monthly costs are: store rent $800 plus 60 cents per haircut, depreciation on equipment $500, barber supplies 40 cents per haircut, utilities $300, and advertising $200. The price of a haircut is $11.
Instructions
Determine the variable cost per haircut and the total monthly fixed costs.
Compute the break-even point in i) units and ii) dollars.
Determine the net income, assuming 1,500 haircuts are given in a month.
a.i) The variable cost per haircut is $5.
a.ii) The monthly fixed costs are $2,800
b.i) The break-even point in units is approx. 467 haircuts.
b.ii) The break-even point in dollars is $5,137.
c) The net income, assuming 1,500 haircuts are given in a month, is $6,200.
How to solve the cost problems?We shall first break down the costs to estimate the variable cost per haircut and the total monthly fixed costs.
Then, we shall use the results to calculate the break-even point in units and dollars. Lastly, we compute the net income.
a.i) Variable cost per haircut (VC):
Total variable cost per haircut = Commission + Store rent + Barber supplies
Given:
Commission for each haircut per barber = $4
Rent for store per haircut = $0.60
Barber supplies per haircut = $0.40
Price of a haircut (P): $11
VC = $4 + $0.60 + $0.40
= $5
So, the variable cost per haircut is $5.
a.i)Total monthly fixed costs (TFC)
Total monthly fixed costs: Manager's salary + Depreciation on equipment + Utilities + Advertising
Given:
Manager's salary = $1,800
Depreciation on equipment = $500
Utilities =$300
Advertising = $200
TFC = $1,800 + $500 + $300 + $200
= $2,800
Therefore, the total monthly fixed costs are $2,800.
b) Break-even point:
The break-even point is the point: total revenue = total costs.
b.i) Break-even point in units = TFC divided by contribution margin per unit
contribution margin = price - VC
= $11 - $5
= $6
break-even point in units = $2,800 / $6
= 466.67
So, the break-even point in units is ≈ 467 haircuts.
b.ii) Break-even point in dollars:
Break-even point (in dollars) = break-even point (in units) * P
= 467 * $11
= $5,137
Thus, the break-even point in dollars is $5,137.
c) The net income:
Total costs(TC) - Total Revenue (TR):
TR = Number of haircuts * P
= 1,500 * $11
= $16,500
Total Cost (TC) = TVC + TFC
TC = (Variable cost per haircut * Number of haircuts) + Total fixed costs
= ($5 * 1,500) + $2,800
= $7,500 + $2,800
= $10,300
Net income = TR- TC
= $16,500 - $10,300
= $6,200
Hence, the net income, assuming 1,500 haircuts are given in a month, is $6,200.
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Apply the distributive property to factor out the greatest common factor.
24+32p= _____
Answer:
8(3+4p)
Step-by-step explanation:
8 goes into 24 and 32, so it can be factored out:
[tex]24+32p=8(3+4p)[/tex]
Answer:
8(3 + 4p)
Step-by-step explanation:
Factor 24 + 32p
First, factor out the GCF. In this case, the GCF is 8, and we have
8(3 + 4p)
We can't factor anymore so the answer is 8(3 + 4p)
6.- María le dice a Susy: "Cuando yo tenga la
edad que tú tienes, tu edad será 2 veces la que
tengo y sabes que cuando tenía 10 años, tu
tenías la edad que tengo". ¿Cuánto suman las
edades actuales de ambas?.
Maria's current age is 15 and Susy's current age is 5.
We have,
Let's denote Maria's current age as M and Susy's current age as S.
We can use the given information to set up a system of equations and solve for their ages.
According to the first statement, "When I have the age that you are, your age will be 2 times that I have," we can write the equation:
M + S = 2(M - S)
Expanding and simplifying:
M + S = 2M - 2S
S + 2S = 2M - M
3S = M
According to the second statement, "When I was 10 years old, you were the age that I am," we can write the equation:
M - 10 = S
Now we have a system of equations:
3S = M
M - 10 = S
To solve the system, we can substitute the value of M from the first equation into the second equation:
3S - 10 = S
Simplifying:
2S = 10
S = 5
Substituting the value of S back into the first equation:
3(5) = M
M = 15
Therefore,
Maria's current age is 15 and Susy's current age is 5.
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The complete question:
Maria tells Susy: "When I have the age that you are, your age will be 2 times that I have and you know that when I was 10 years old, you were the age that I am".
How much do the current ages of both?
show work if possible
Answer:
C. 33
Step-by-step explanation:
(√121) (√9) = (√11*11) (√3*3)
= (√11^2) (√3^2)
= (11)(3)
= 33
You are contracted to fabricate a gate with specifications shown below. What angle are the bars placed in the top arc so they are equally spaced between bars?
18 degrees
30 degrees
36 degrees
25 degrees
Answer:
The correct answer is 30 degrees.
A survey was given to 320 people asking whether people like dogs and/or cats.
102 said they like dogs
196 said they like cats
72 said they don't like cats or dogs.
How many said they liked both cats and dogs?
people liked both cats and dogs.
Answer:
50 people
Step-by-step explanation:
After removing the people who liked neither, we are left with,
320 - 72 = 248
now, out of these 248, 196 like cats
248 - 196 = 52 so 52 dont like cats
also, 102 like dogs so 248 - 102 = 146
so 146 dont like cats
these 146 cannot be included in liking both
similarly the 52 cannot be included in liking both
so we are left with 248 - 52 - 146 = 50
so 50 people like both cats and dogs
Find the equation of a line parallel to y=x−1 that contains the point (−3,−2). Write the equation in slope-intercept form.
Answer:
y = x + 1
Step-by-step explanation:
Parallel lines have same slope.
y = x - 1
Compare with the equation of line in slope y-intercept form: y = mx +b
Here, m is the slope and b is the y-intercept.
m =1
Now, the equation is,
y = x + b
The required line passes through (-3 ,-2). Substitute in the above equation and find y-intercept,
-2 = -3 + b
-2 + 3 = b
[tex]\boxed{b= 1}[/tex]
Equation of line in slope-intercept form:
[tex]\boxed{\bf y = x + 1}[/tex]
The equation is :
↬ y = x + 1Solution:
We KnowIf two lines are parallel to each other, then their slopes are equal. The slope of y = x - 1 is 1. Hence, the slope of the line that is parallel to that line is 1.
We shouldn't forget about a point on the line : (-3, -2).
I plug that into a point-slope which is :
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Slope is 1 so
[tex]\sf{y-y_1=1(x-x_1)}[/tex]
Simplify
[tex]\sf{y-y_1=x-x_1}[/tex]
Now I plug in the other numbers.
-3 and -2 are x and y, respectively.
[tex]\sf{y-(-2)=x-(-3)}[/tex]
Simplify
[tex]\sf{y+2=x+3}[/tex]
We're almost there, the objective is to have an equation in y = mx + b form.
So now I subtract 2 from each side
[tex]\sf{y=x+1}[/tex]
Hence, the equation is y = x + 1Triangle with one square corner
Please help me im not good at math
Answer:
2m - 72
Step-by-step explanation:
2x Malik's age = 2 × m, m represents his age because it is unknown
72 less means -72
