Answer:
$421.72
Step-by-step explanation:
Compounded Monthly Interest Rate Formula: A = P(1 + 4/12)^12t
Simply plug in our known variables:
A = 120(1 + 0.06/12)²¹⁽¹²⁾
A = 120(1.005)²⁵²
A = 120(3.51437)
A = 421.724
consider a polynomial f(x)=ax^3 + bx^2 + x + 2/3.if x + 3 is a factor of f(x) and f(x) is divided by x + 2, then we get remainder as 5. find the values of a and b.
Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
The tens digit is y and the units digit is one half of that. What is the value of the number if I reverse its digits ?
Answer:
The number after reversing the digits is [tex]\bold{6y}[/tex]
Step-by-step explanation:
First of all, let us try to learn about representing a 2 digit number.
28 can be written as 20 + 8 OR 2 [tex]\times[/tex] 10 + 8
79 can be written as 70 + 9 OR 7 [tex]\times[/tex] 10 + 9
17 can be written as 10 + 7 OR 1 [tex]\times[/tex] 10 + 7
i.e. if we are given the unit's and ten's digits as U and T, we can write the two digit number as: T [tex]\times[/tex] 10 + U
Now, it is given that ten's digit is [tex]y[/tex].
Unit's digit is half of that i.e. [tex]\frac{y}{2}[/tex].
So, the number is
[tex]y \times 10 +\frac{y}{2}\\\Rightarrow 10 y +\frac{y}{2}\\\Rightarrow \dfrac{21}{2}y[/tex]
Now, the digits are reversed:
Unit's digit = [tex]y[/tex]
Ten's digit = [tex]\frac{y}{2}[/tex]
So, the number after reversing the digits:
[tex]\dfrac{y}{2}\times 10+y\\\Rightarrow 5y+y = \bold{6y}[/tex]
The number after reversing the digits is [tex]\bold{6y}[/tex].
12x+15y=34 and -6x+5y=3
Answer:
pls like and follow my page ....thank you
Step-by-step explanation:
using elimination method...you will have it as
12x+15y =34 .............1
-6x+5y = 3 ...............2
multiply equation 1 by 6 and equation 2 by 12
72x + 90y = 204.........4
-72x + 60y = 36..........5
asd equation 2 and 1...
0x + 150y = 240
y= 240/250 ..
after getting your answer ..
substitute for y in either of equation 1 and 2 to get your x
Find x
a) 21 √2
b)7
c)21 √2/2
d)21 √3/2
Answer:
C
Step-by-step explanation:
Use the sine ratio in the left, right triangle to find the common side to both triangles and the exact values
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , thus
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2 × opp = 21 ( divide both sides by 2 )
opp = [tex]\frac{21}{2}[/tex]
Now consider the right triangle on the right, using the cosine ratio
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{\frac{21}{2} }{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = [tex]\frac{21}{2}[/tex] × [tex]\sqrt{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → C
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495495 and standard deviation 118118 . You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to 118100=1.18118100=1.18 . 118100√=11.8118100=11.8 . 118100⎯⎯⎯⎯⎯⎯√=1.09118100=1.09 . 118118 .
The question is not typed properly! Complete question along with answer and step by step explanation is provided below.
Question:
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .
You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to
a. 118
b. 118/100=1.18
c. 118/√100= 11.8
d. cannot be determined
Answer:
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Step-by-step explanation:
From the given information,
The population mean SAT critical reading score is
[tex]\mu = 495[/tex]
The population standard deviation is
[tex]\sigma = 118[/tex]
You choose an SRS of 100 students and average their SAT Critical Reading score.
[tex]n = 100[/tex]
Since the sample size is quite large then according to the central limit theorem,
The mean sample will be the same as the population mean SAT critical reading score.
[tex]\bar{x} = \mu = 495[/tex]
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Hey ya'll, DONT DO THE WORK FOR ME just check it for me please, my assignment asked me.....Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework. He says that he spent 125% more time doing homework this week. Is he correct? Show your work to justify your decision.
Then, i answered with:
To find a percentage you just have to put the percent in decimal form then you multiply. 125% = 125/100 125% = 125/100 = 1.25 By doing this, we get 1.25, which is the same as 125% in decimal form. Therefore, Evan was correct. He spent 125% more time doing homework this week.
WAS MY ANSWER CORRECT OR NOTTTT
Answer:
No it was not
why... well he spent 25% time.
Step-by-step explanation:
Multiply the polynomials. (2x^2 + 6x + 6)(3x – 2)
Hey there! :)
Answer:
6x³ + 14x² + 6x - 12.
Step-by-step explanation:
Given:
(2x² + 6x + 6)(3x - 2)
Multiply each term in the first polynomial by both terms in the second:
3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =
6x³ + 18x² + 18x - 4x² - 12x -12 =
Combine like-terms:
6x³ + 14x² + 6x - 12.
Sphere A has a radius of 24 centimeters, and sphere B has a diameter of 42 centimeters. The radius of sphere A is multiplied
by what factor to produce the radius of sphere B?
o
+10000 N
o
o
Answer:
1.75
Step-by-step explanation:
The radius of Sphere A = 24 centimeters
The radius of sphere B = 42 centimeters
[tex]\text{Radius of Sphere B} \div \text{Radius of Sphere A}=42 \div 24\\=1.75[/tex]
Therefore, The radius of sphere A is multiplied by 1.75 to produce the radius of sphere B
Which is the value of g(-5) it g(x) = 3,4x - 8?
Answer:
g(-5)=-25
Step-by-step explanation:
f(x)=-3√(x-3)-1 which of the following graphs corresponds to the function above
Answer:
Step-by-step explanation:
graph attached
Answer:
graph y
Step-by-step explanation:
A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly of all applications were from minority members, and exactly of the open positions were filled by members of the minority. Find the mean of , where is the proportion of minority member applications in a random sample of that is drawn from all applications. Find the standard deviation of . Compute an approximation for , which is the probability that there will be or fewer minority member applications in a random sample of drawn from all applications. Round your answer to four decimal places.
Answer:
a) Mean of sample proportion = 0.16
Mean of random sample that are minority member applications = 336
b) Standard deviation of p = 0.008
In number terms, it is 16.8 applications.
c) Probability that there will be 15% or fewer minority member applications in a random sample of 2100 drawn from all applications = 0.1057
Step-by-step explanation:
Complete Question
A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly 16% of all applications were from minority members, and exactly 15% of the 2100 open positions were filled by members of the minority.
a. Find the mean of p, where p is the proportion of minority member applications in a random sample of 2100 that is drawn from all applications.
b. Find the standard deviation of p.
c. Compute an approximation for P (p ≤ 0.15), which is the probability that there will be 15% or fewer minority member applications in a random sample of 2100 drawn from all applications. Round your answer to four decimal places.
Solution
a) If the sample is a random sample, he proportion of the applications that will be minority member applications is still going to be approximately the same as the population proportion of the minority member applications.
Mean proportion = p = 0.16
The mean of the sample is then given with is given as
Mean = np
where n = sample size = 2100
p = mean proportion = 16% = 0.16
mean = 0.16 × 2100 = 336
b) The standard deviation of p is given as
σ = √[p(1-p)/n]
= √[0.16×0.84/2100] = 0.008
In real number terms,
= 0.008×2100 = 16.8 applications
c) Probability that there will be 15% or fewer minority member applications in a random sample of 2100 drawn from all applications
P(p ≤ 0.15)
We will use the normal approximation to the binomial distribution since, np and np(1-p) are both greater than 10.
Mean = 0.16
standard deviation = 0.008
To find P(p ≤ 0.15)
We first need to normalize or standardize 0.15
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (0.15 - 0.16)/0.008 = -1.25
To determine the required probability
We'll use data from the normal distribution table for these probabilities
P(p ≤ 0.15) = P(z ≤ -1.25) = 0.10565 = 0.1057 to 4 d.p.
Hope this Helps!!!
PLEASE HELP!!!
A sphere has a great circle whose area is equal to 16 Pi what is the volume of that sphere rounded to the nearest hundredth
Hi there! I haven't done math in a while but I do well and I hope this helps. First, we get our radius from our area, which is about 4 inches. From there, I used the volume formula and got the answer closest to C, or 267.95. Thanks, good luck :)
The ratio of cement : sand : aggregate in a mix of concrete is 1 : 3 : 3. Sang wants to make 112 kg of concrete. How much sand does he need?
Answer: 48
Step-by-step explanation:
The share of sand in the mixture is 3/7
To make 112 kgs. of concrete, he will need
3/7 x 112 = 48 units of sand
Answer:
48 kgsolution,
Ratio of cement:sand:aggregate
=1:3:3
Total of ratios=1+3+3
=7
Total concrete=112 kg
Amount of sand required:
[tex] \frac{ratio \: of \: sand}{total \: ratio} \times amount \: of \: concrete \\ = \frac{3}{7} \times 112 \\ = 48 \: kg[/tex]
Hope this helps...
Good luck on your assignment...
ANSWER ASAP PLEASE!!!!!!!!!!!! THANKS!!!!!!!!! :)
Answer: the answer is A
Step-by-step explanation:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL = 32
Step-by-step explanation:
We are told in the above question that:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
From the attached diagram, we can see that
JL : JK = JK: JM
Therefore,
JL/ JK = JK /JM
Where JL = Unknown
JK = 24
JM = 18
JL/ 24 = 24/18
Cross Multiply
24 × 24 = JL × 18
Divide both sides by 18
JL = (24 × 24) /18
JL = 576/18
JL = 32
What is Pascal's triangle.
Answer:
Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.
Answer:
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
Step-by-step explanation:
Liam wants to treat some friends to lunch. He has $50 and knows that lunch will cost about $8 per person, p. How many people can Liam buy lunch for?Part A- Write and solve an inequality to represent the Situation
Answer:
T ≥ 8x
50 ≥ 8x .......1
x ≤ 6
Liam can buy lunch for 6 people.
Step-by-step explanation:
Let x represent the number of people Liam can buy lunch for.
Given;
Lunch cost per person r = $8 per person
The total amount he has T = $50
The cost of buying lunch for c people is;
C = $8 × x
C = 8x
Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.
T ≥ C
Substituting C, we have;
T ≥ 8x
50 ≥ 8x ,.......1
Solving the inequalities;
8x ≤ 50
x ≤ 50/8
x ≤ 6.25
To the nearest whole number;
x ≤ 6
Liam can buy lunch for 6 people.
What will be the answer for this? Please help me, please and thank you
Answer:
10:1
Step-by-step explanation:
When you cross multiply the fractions together, you should get 30:3. When you simplify that, you get 10:1 as your answer.
Find the inequality represented by the graph
Answer:
y ≥ -2/3x +3
Step-by-step explanation:
incline is -2/3
and intercept with y-axis is 3
so the equation of the line is
y = -2/3x +3
Since the intended area in the graph I above the line, we now know enough to find the right one question:
y ≥ -2/3x +3
Answer: y>-2/3x+3 because the line is dotted its >
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all the headphones and music players in identical packages what is the greatest number of packages time can make
Answer:
He will have 13 packages containing 3 pairs of headphones and 1 music player each.
Step-by-step explanation:
He has 39 pairs of headphones and 13 music players.
He wants to sell both set of items in identical packages.
To do this he has to divide them in such a way that the same number of both set of objects are in every box.
Let us find the ratio of the pairs of headphones to music players:
39 : 13 = 3 : 1
Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.
So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.
what is the value of the discriminators of f f(x)=x^2-3x+18
Answer:
-63
Step-by-step explanation:
Compare ...
f(x) = x^2 -3x +18
to the standard form ...
f(x) = ax^2 +bx +c
and you will see that ...
a = 1, b = -3, c = 18.
__
The value of the discriminant is ...
d = b^2 -4ac
d = (-3)^2 -4(1)(18) = 9 -72 = -63
The discriminant is -63.
Please help me Thank u
Answer:
Step-by-step explanation:
Fist let's have a look :
(AB) is parallel with (CD) and there is a line crossing them both.Now the first question : What is the size x ?
We notice that x and 53° are vertically opposite so they are corresponding angles so the size of x is 53°The second question : what is the size of y ?
We notice that y and 53° are alternate angles so they are corresponding angles with same size y=53°The trick is to khow the situation where we have corresponding angles
A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed below, includes information they have either researched or measured. They need to build a tunnel from the point E to the point H on the sketch. a) Prove the three triangles ΔSFH, ΔEGL, and ΔSIL are similar. b) Use similar triangles to determine the length from H to E.
Answer:
a) Look step by step explanation
b) x = 498,22
Step-by-step explanation:
a) Two triangles are similar if all their angles are equal
Then in Δ SFH and Δ GEL we got:
∡ SFH = ∡ EGL right angles
∡ LEG = ∡ HSF since the same straight line (SL) is cut by parallel lines (vertical segments EG and SF )
∡ SHF = ∡ ELG The same straight line SL is cut by two parallel segments FH and GL ( horizontal segments)
The Δ SIL is similar to the two previous Δs according to:
∡ SIL is a right angle
∡ ILS = ∡ GLE = ∡ FHS
∡ ISL = ∡FSH = ∡GEL
The condition for similar triangles is satisfied
b)
From Δs FSH and GEL
SF/EG = 380/EL
225/180 = 380/EL
225*EL = 180*380
EL = 180*380/225
EL = 304
From Δs SIL and SFH
225/ (225 +475) = 380/ (380 + x + 304)
225 / 700 = 380 / 684 + x
225 * ( 684 + x ) = 700*380
153900 + 225*x = 266000
225*x = 266000 - 153900
225*x = 112100
x = 498,22
Given that x:2=7:5 Calculate the value of x
Answer:
x=2.8≈3
Step-by-step explanation:
x:2=7:5
[tex]\frac{x}{2}=\frac{7}{5}[/tex]
by cross-multiplication
x×5=2×7
5x=14
x=14/5
x=2.8≈3
i hope this will help you :)
PLZZZZZZ HLPPPPPPP MEEEEEEEE
Answer:
C. (x+4)(2x+3)
Step-by-step explanation:
We need to find the expression that represents the area of the rectangle.
The length of the rectangle is x + x + 1 + 1 + 1, that is, 2x + 3.
The width of the rectangle is x + 1 + 1 + 1 + 1, that is, x + 4.
So, if the area of the rectangle is the product of length and width, we have:
[tex]Area = length * width = (2x+3)(x+4)[/tex]
So the answer is C.
Write an equation of the line that is perpendicular to y = 1/2x +3 and passes through the point
(10,-5)
Answer:
y = -2x+15Step-by-step explanation:
[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]
how do you find percentage lost
Answer:
It depends
Step-by-step explanation:
It depends on the questions, some times you just substract the number from 100 which is the full percentage but sometimes it is like the example below.
lets say a city lost 2% of population each year population now?
98/100*98*100=0.9604= 96.04%
so the lost hear is 100-96.04=3.96
Triangles X Y Z and E G F are shown. Side X Y is 3.0 inches and angle Y Z X is 107 degrees. Side F G is 2.4 inches and side E F is 1.3 inches. Angle G E F is 48 degrees. Given ΔXYZ ≅ ΔEGF, find the measurements of the unknown sides and angles. ZX = in. EG = in. M∠X = ° m∠G = °
Answer:
ZX = 1.3 in
EG = 3.0 in
M∠X = 48°
M∠G = 25°
Step-by-step explanation:
As we can see in the attached figure that these two triangles are identical i.e their corresponding sides and angles are equal
Therefore if we say that
ZX = EF
So ZX = 1.3 in.
Now the same is applied for other sides and angles
EG = XY
So, EG = 3.0 in
M∠X = M∠E
hence, M∠X = 48°
For the M∠ G,
The angle is
= 180° - 107° - 48°
= 25°
Hence, the M∠ G is 25°
What is the solution to the following equation? 3(7x – 12) + 26 = 3x – 10
Answer:
x=0
Step-by-step explanation:
3(7x – 12) + 26 = 3x – 10
Distribute
21x -36 +26 = 3x-10
21x -10 = 3x-10
Add 10 on each side
21x-10+10 = 3x-10+10
21x = 3x
Subtract 3x from each side
21x-3x = 0
18x =0
x=0
Answer:
x=0
Step-by-step explanation:
3(7x – 12) + 26 = 3x – 10
21x-36+26-3x+10=0
18x-10+10=0
18x+0=0
18x=0
x=0
check : 3(7(0)-12)+26=3(0)-10
: -36+26=-10
-10=-10 it is correct
If ∠R is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for ∠Q.
Answer:
To solve a triangle is to find the lengths of each of its sides and all its angles. The sine rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle. The cosine rule is used when we are given either a) three sides or b) two sides and the included angle.
Step-by-step explanation:
We just saw how to find an angle when we know three sides. It took quite a few steps, so it is easier to use the "direct" formula (which is just a rearrangement of the c2 = a2 + b2 − 2ab cos(C) formula). It can be in either of these forms:
cos(C) = a2 + b2 − c22ab
cos(A) = b2 + c2 − a22bc
cos(B) = c2 + a2 − b22ca
Answer:
Law of cosines, two sides and the included angle known
Step-by-step explanation:
double check that the question is exactly the same to make sure you get the question correct
"If ∠P is given and the values of r and q are given, then explain whether the Law of Sines or the Law of Cosines should be used to solve for p."