Answer:
a) Mean = 4.55
Median = 4.7
Mode = 1.9
b) S = 2.3952
CV = 52.64 %
Range = 6.3
c) Yes, since the average and median values are both over "acceptable" ranges.
Step-by-step explanation:
Explanation is provided in the attached document.
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/26
Step-by-step explanation:
Probability of the first box to have the secret decoder ring is 18 out of 52:
18/52= 9/26Probability of the second box to have the ring is 17 out of 51, because one box with the ring already selected and not counted:
17/51= 1/3Probability that both of them have the secret decoder ring:
9/26*1/3= 3/26So the answer is 3/26
Question 8(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc DF. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees. 50° 90° 100° 140°
Answer: 90°
Step-by-step explanation:
As known ∡EGC=(arcEC+arcDF)/2
arcEC+arcDF=70°*2
5x+10+11x+2=140
16x+12=140
16x=128
x=128:16
x=8
So arcDF=11*x+2=11*8+2=90°
The measure of arc DF is 90°.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Given, Circle A with chords EF and CD that intersect at point G,
arc EC = 5x + 10°
arc DF = 11x + 2°
∠EGC = 70°
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite
so
∠EGC=(1/2)[arc EC+arc DF]
substitute the values
70 = 1/2(5x + 10 + 11x + 2)
70 = 1/2(16x + 12)
140 = 16x + 12
16x = 128
x = 128/16 = 8
so ac DF = 11x + 2
arc DF = 11(8) + 2
arc DF= 88 + 2 = 90°
Hence the value of arc DF is 90°.
Learn more about circle;
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The population, p, in thousands of a resort community is given by P(t)=700t/4t[tex]x^{2}[/tex]+9
Answer:
Step-by-step explanation:
pt=700 is basically evaluate it form the bottom to the top and u must mark me as brainly
Find the value of x.
Explanation:
For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.
x+125 = 180
x+125-125 = 180-125 ... subtract 125 from both sides
x = 55
PLEASE HELP ?
Convert by looking at the thermometer and measure to the nearest 5 degrees F.
31 degrees Celsius to Fahrenheit
Answer:
90º
Step-by-step explanation:
just look at where 31º on the right lines up with the value on the left (aka around 90º)
Answer:
87.8 °F ≈ 90°F
Step-by-step explanation:
[tex]x \ degrees \ F = 31 \ degree \ Celsius *\frac{9}{5} + 32\\x \ degrees \ F = 55.8 + 32\\\\x \ degrees \ Fahrenheit = 87.8 \ degrees \ Farenheit[/tex]
ANZ Corporation manufactures a product available in two models: ABC, and PQR. Despite the growing popularity of the PQR model, company profits have been declining steadily, and management is beginning to think there might be a problem with their costing system. Material and Labour costs are given below:
ABC PQR
Sales demand 30000 15000
Direct material cost/unit $45 $60
Direct labour cost/unit $30 $40
Production overheads are $600,000 each month.
These are absorbed on a sales demand basis.
Calculate the full production costs for ABC and PQR, using traditional costing method
Answer:
The full production costs are:
ABC = $22,900,000
PQR = $1,700,000
Step-by-step explanation:
Traditional costing method is a costing method that allocates or applies overhead based on a particular metric determined by a company. It therefore add both direct cost of production and production overheads absorbed to obtain the full cost of production.
Since production overheads in this question is absorbed on demand sales basis, the full production costs for ABC and PQR can be computed as follows:
ANZ Corporation
Computation of Full Production Costs
Particulars ABC PQR
Sales demand 30,000 15,000
Cost $ $
Direct cost:
Direct materials cost (w.1) 1,350,000 900,000
Direct labor cost (w.2) 900,000 600,000
Total direct cost 22,500,000 1,500,000
Indirect cost:
Production overhead (w.3) 400,000 200,000
Full production cost 22,900,000 1,700,000
Workings:
w.1: Computation of direct material cost
Direct material cost = Direct material cost per unit * Sales demand
Therefore;
ABC Direct material cost = $45 * 30,000 = $1,350,000
PQR Direct material cost = $60 * 15,000 = $900,000
w.2: Computation of direct labor cost
Direct labor cost = Direct labor cost per unit * Sales demand
Therefore;
ABC Direct material cost = $30 * 30,000 = $900,000
PQR Direct material cost = $40 * 15,000 = $600,000
w.3: Allocation of production overhead
Production overheads allocated to a model = Production overheads * (Model's Sales Demand / Total Sales demand)
Total Sales demand = 30,000 + 15,000 = 45,000
Therefore, we have:
Production overhead allocated to ABC = $600,000 * (30,000 / 45,000) = $400,000
Production overhead allocated to PQR = $600,000 * (15,000 / 45,000) = $200,000
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A one-sample t test will be carried out to see whether this is the case. What conclusion is appropriate in each of the following situations?
(a) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(b) n = 15, t = 1.66, a = 0.05
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(c) n = 26, t = 2.55, a = 0.01
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
(d) n = 26, t = 3.95
a. Reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
b. Reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
c. Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
d. Do not reject the null hypothesis. There is sufficient evidence that the true diameter differs from 0.5 in
You may need to use the appropriate table in the Appendix of Tables to answer this question.
Answer:
Option C - Do not reject the null hypothesis. There is not sufficient evidence that the true diameter differs from 0.5 in
Step-by-step explanation:
We are given;
n = 15
t-value = 1.66
Significance level;α = 0.05
So, DF = n - 1 = 15 - 1 = 14
From the one-sample t - table attached, we can see that the p - value of 0.06 at a t-value of 1.66 and a DF of 14
Now, since the P-value is 0.06,it is greater than the significance level of 0.05. Thus we do not reject the null hypothesis. We conclude that there is not sufficient evidence that the true diameter differs from 0.5 in.
Determine whether 52c2y4 is a monomial, binomial, trinomial, or other polynomial.
Answer: Monomial.
Step-by-step explanation:
Ok, when we have a polynomial with only one term, this is a monomial.
If the polynomial has two terms, this is a binomial.
If the polynomial has 3 terms, this is a trinomial.
And so on.
In this particular case we have:
52*c^2*y^4
Where c and y may be variables.
We can see that here we have only one term, so this would be a monomial.
(notice that the number of variables does not affect the type of polynomial in this case, only the number of terms)
Answer:
binomial.
Step-by-step explanation:
The polynomial −50c3z3−41y220z4 has 2 terms, so it is a binomial.
what is the answer to 100×338
Answer:
33800
Step-by-step explanation:
100 x 338 = 33800
Answer:
33800
Step-by-step explanation:
338x10=3380 then 3380x10=33800
-------------------------------------------------------
Good luck with your assignment...
6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
No solutionStep-by-step explanation:
6x – 3y = 3
–2x + 6y = 14
lets solve by substitution:
1) lets isolate y:
6x–3y=3
-3y=-6x+3
y=(-6x+3)/-3
y=2x-1
2) plug in 2x-1 for y in order to find x:
6x-3(2x-1)=3
6x-6x+3=3
3=3
since x cancels out, it means that there is no solution to this linear system of equations
Answer:
No Solution :)
Step-by-step explanation:
Perform the indicated operation and write the result in standard form: (-3+2i)(-3-7i)
A. -5+27i
B. 23+15i
C. -5+15i
D. 23-15i
E-5-27I
Answer:
23+15i
Step-by-step explanation:
(-3+2i) (-3-7i)
multiply -3 w (-3+2i) and multiply -7i w (-3+2i)
9-6i+21i-14i^2
combine like terms
9+15i-14i^2
i squared is equal to -1 so
9+15i-(14x-1)
9+14+15i
23+15i
hope this helps :)
How do I do this? I need the correct option
option A is correct answer.
because angle JKL is half of of arc JL .
so, angle JK is equal to 64°.
hope it helps...
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
- Find the circumference of the circle with the given radius or diameter. Use 3.14.
diameter = 10 cm
A. 15.7 cm
B. 314 cm
C. 78.5 cm
D. 31.4 cm
Answer:
C = 31.4 cm
Step-by-step explanation:
C = pi * d where d is the diameter
C = 3.14 * 10
C = 31.4 cm
Circumference = pi x diameter
= 3.14 x 10
= 31.4 cm
The answer is D. 31.4 cm.
how many solutions does this linear system hacve y=2/3x+2 6x-4y=-10
Answer:
the linear system has two valid solution.
Answer:one solution
Step-by-step explanation:
determine the polynomial equivalent to this expression.
x^2-9/x-3
A. x-3
B. -3x-9
C. x+3
D. x^2+3x
Answer:
[tex]\dfrac{x^2-9}{x-3}= \Large \boxed{x+3}[/tex]
Step-by-step explanation:
Hello,
We need to work a little bit of the expression to see if we can simplify.
Do you remember this formula?
for any a and b reals, we can write
[tex]a^2-b^2=(a-b)(a+b)[/tex]
We will apply it.
For any x real number different from 3 (as dividing by 0 is not allowed)
[tex]\dfrac{x^2-9}{x-3}=\dfrac{x^2-3^2}{x-3}=\dfrac{(x-3)(x+3)}{x-3}=x+3[/tex]
So the winner is C !!
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Determine whether the experiment is blind or double blind.Is the aspirin produced by World's Best Pharmaceutical Company better than that of a competitor at relieving headaches? 200 headache suffers are chosen at random. Migraned Testing Service administers the experiment and provides the results evaluation. Three levels are made: participants receive contents from Bottle A, Bottle B, or Bottle C. Other than the fact that one bottle contains placebo aspirin (but not which particular bottle contains placebo aspirin), no other information is given to the testing service regarding the bottles' contents.a. Blindb. Double blindc. Neither
Answer:
The correct answer is:
Double-blind (b)
Step-by-step explanation:
A blind/blinded experiment is one in which information which may influence the participant or experimenter is withheld throughout the process of the experiment either by masking (giving false identity) or completely blinded, to avoid biases that may arise from such knowledge by the participant or experimenter.
Blinding is of three types: single-blind, double-blind and triple-blind experiements and this is named with respect to three categories involved in the experiment; participant, researcher or a third party, which may include: analysts, monitoring committees stakeholders etc. The blinding type is explained as follows
Blinding Type participant researcher Third-party
single-blind blinded unblinded unblinded
double-blind blinded blinded unblinded
triple-blind blinded blinded blinded
In this example, the 200 headache sufferers (participants) and the Migrane testing service (researchers) do not know the contents of the bottles being administered, whereas the pharmaceutical company (third-party knows), hence it is a double-blinded experiment.
What are the trigonometric ratios? Write all six.
Step-by-step explanation:
Check that attachment
Hope it helps :)
Hey! :)
________ ☆ ☆_________________________________________
Answer:
There are six trigonometric ratios, which will be under “Explanation”
Step-by-step explanation:
Trigonometric ratios are a measurements of a right triangle.
Here are the all the six trigonometric ratios.
1. cotangent (cot)
2. cosecant (csc)
3. cosine (cos)
4. secant (sec)
5. sine (sin)
6. tangent (tan)
Hope this helps! :)
_________ ☆ ☆________________________________________
By, BrainlyMember ^-^
Good luck!
Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5
Answer:
see below
Step-by-step explanation:
Company A f(x) = 15(7x)
Company B g(x) = 100x + 5
If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less False
f Marguerite rents for 2 weeks, it will cost her less if she rents from Company B
A = 105(2) = 210
B = 100(2) + 5 = 205 B costs less True
If Marguerite rents for 1 week, it will cost her the same at either company
A = 105(1) = 105
B = 100(1) +5 = 105 True
If Marguerite rents for 1 week, it will cost her more if she rents from Company A
A = 105(1) = 105
B = 100(1) +5 = 105 False
h(x) = 5x – 5
h(x) = f(x) – g(x)
=15(7x) - ( 100x + 5)
= 105x - 100x -5
= 5x-5 True
h(x) = 5x + 5 False
Answer:
If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
If Marguerite rents for 1 week, it will cost her the same at either company.
h(x) = 5x - 5.
Step-by-step explanation:
Company A: f(x) = 15(7x)
Company B: g(x) = 100x + 5
h(x) = f(x) - g(x)
So, the function h(x) is the difference between Company A's rental and Company B's rental.
h(x) = (15(7x)) - (100x + 5)
= (105x) - (100x + 5)
= 105x - 100x - 5
= 5x - 5
h(x) = 5x - 5.
Let's say that Marguerite rents for 1 week. In Company A, that will cost her 15 * 7 = 105. In Company B, it will cost her 100 + 5 = 105. So, if Marguerite rents for 1 week, it will cost her the same at either company.
Let's say that Marguerite rents for 2 weeks. In Company A, that will cost her 15 * 7 * 2 = 30 * 7 = 210. In Company B, it will cost her 100 * 2 + 5 = 200 + 5 = 205. So, if Marguerite rents for 2 weeks, it will cost her less if she rents from Company B.
Hope this helps!
A hemoglobin test measures 29 grams of hgb per 200 milimiters of blood. If the patient has 11 quarts of blood in her body, how many grams of Hgb are present
Answer:
[tex] 11 quarts *\frac{946.353 ml}{1 quarter}= 10409.883 ml[/tex]
And for this case we can create the following proportion rule:
[tex]\frac{29 gr}{200 ml} =\frac{x}{10409.883 ml}[/tex]
And solving for x we got:
[tex] x= 10409.883 ml *\frac{29 gr}{200ml}= 1509.433 gr[/tex]
Step-by-step explanation:
For this problem we know that A hemoglobin test measures 29 grams of hgb per 200 milimiters of blood. and we want to know how many grams of Hgb are present in 11 quarts
First we need to convert the quarts to ml and we have:
[tex] 11 quarts *\frac{946.353 ml}{1 quarter}= 10409.883 ml[/tex]
And for this case we can create the following proportion rule:
[tex]\frac{29 gr}{200 ml} =\frac{x}{10409.883 ml}[/tex]
And solving for x we got:
[tex] x= 10409.883 ml *\frac{29 gr}{200ml}= 1509.433 gr[/tex]
Evaluate the expression. 1/2 x (4+8)
Answer:
Hey there!
1/2 x (4+8)
1/2 x (12)
6
Hope this helps :)
Answer: 6x
Step-by-step explanation:
.5x*(4+8)
.5x*(12)
6x
Hope it helps <3
In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential election. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Answer:
C.I = 0.7608 ≤ p ≤ 0.8392
Step-by-step explanation:
Given that:
Let consider a random sample n = 400 candidates where 320 residents indicated that they voted for Obama
probability [tex]\hat p = \dfrac{320}{400}[/tex]
= 0.8
Level of significance ∝ = 100 -95%
= 5%
= 0.05
The objective is to develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
The confidence internal can be computed as:
[tex]=\hat p \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }[/tex]
where;
[tex]Z_{0.05/2}[/tex] = [tex]Z_{0.025}[/tex] = 1.960
SO;
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }[/tex]
[tex]=0.8 \pm 1.960 \sqrt{4 \times 10^{-4}}[/tex]
[tex]=0.8 \pm 1.960 \times 0.02}[/tex]
[tex]=0.8 \pm 0.0392[/tex]
= 0.8 - 0.0392 OR 0.8 + 0.0392
= 0.7608 OR 0.8392
Thus; C.I = 0.7608 ≤ p ≤ 0.8392
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
What is the solution to the following system of equations?
|3x - 2y = 12
[6x - 4y= 24
It has infinitely many solutions.
It has no solution.
It has one solution (2, -3).
It has one solution (4,0)
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
¿Qué interés produce s/ 72,000 al 5% anual en 1 año, 1 mes, 10 días?
Answer: 3,988.8
Usaremos la fómula: I = C * i * n
I = 72 000 * 0.05 * (1 año + 1 mes + 10 día)
I = 72 000 * 0.05 * (1 + 0.08 + 0.0028)
I = 72 000 * 0.05 * 1.108
3,988.8
Step-by-step explanation:
Podemos obtener el interés que produce un capital con la siguiente fórmula:
I = C * i * n
Ejemplo: Si queremos calcular el interés simple que produce un capital de 1.000.000 pesos invertido durante 5 años a una tasa del 8% anual. El interés simple se calculará de la siguiente forma:
I = 1.000.000 * 0,08 * 5 = 400.000
Si queremos calcular el mismo interés durante un periodo menor a un año (60 días), se calculará de la siguiente forma:
Periodo: 60 días = 60/360 = 0,16
I = 1.000.000 * 0,08 * 60/360 = 13.333
Espero te ayude :3
Factories fully 18x-9
Answer:
Factor 9 out of 18x.
9(2x)−9
Factor 9 out of −9
9(2x)+9(−1)
Factor 9 out of 9(2x)+9(−1)
9(2x−1)
Answer:
9 ( 2x - 1 )
Step-by-step explanation:
→ Look for the HCF of the whole numbers
HCF of 18 and 9 is 9
→ Put 9 outside the brackets
9 ( ? - ? )
→ Perform the calculation 18x ÷ 9 to determine the first question mark
18x ÷ 9 = 2x ⇔ 9 ( 2x - ? )
→ Perform the calculation 9 ÷ 9 to determine the second question mark
9 ÷ 9 = 1 ⇔ 9 ( 2x - 1 )
If the sum of the first n terms of an AP is 1/2 (3n^2+7n),then find its nth term.Hence write its 20th term.
Answer:
62
Step-by-step explanation:
Sn=1/2(3n^2+7n)
S1=1/2(3+7)=5
S2=1/2(3*4+7*2)=26/2=13
We know
S1=a1=5
S2=a1+a2=13
S2-s1=a1+a2-a1
13-5=a2
a2=8
We know d=a2-a1
d=8-5=3
nth term of AP =an=5+(n-1)3
an= 2+3n
Therefore 20th term =
a20= 2+3(20)=62
Hence 20th term of AP is 62
I hope this helps
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer. It costs $4 to store one can of paint for one year and $500 to set up the plan for production of the primer. Let x be the number of cans of paint produced during each production run, and let y be the number of production runs. Then the setup cost is 500y and the storage cost is 2.c, so the total storage and setup cost is C = 500y +2.c. Furthermore, .cy = 16,000 to account for the annual demand. How many times a year should the company produce this primer in order to minimize the total storage and setup costs?
A. The company should have 6 production runs each year.
B. The company should have 8 production runs each year.
C. The company should have 10 production runs each year.
D. The company should have 11 production runs each year.
Answer:
B. The company should have 8 production runs each year.
Step-by-step explanation:
From the given information:
A paint manufacturer has a uniform annual demand for 16,000 cans of automobile primer
It costs $4 to store one can of paint for one year
$500 to set up the plan for production of the primer
Let x be the number of cans of paint produced during each production run
Let y be the number of production runs.
If the total storage and setup cost is C = 500y + 2c
and cy = 16000
Then c = 16000/y
From;
C = 500y + 2c
Replacing c with 16000/y, we have;
C = 500y + 2(16000/y)
C = 500y + 32000/y
in order to minimize the total storage and setup costs [tex]C_{min} = C[/tex]
Therefore [tex]\dfrac{dc}{dy}=0[/tex]
⇒ 500 - 32000/y² =0
y² = 32000/500
y² = 320/5
y² = 64
y = (√64)
y = 8
Therefore; The company should have 8 production runs each year in order to minimize the total storage and setup costs
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
