Answer:
Amount invested at 4% is $16,000
Amount invested at 9% is $6,000
Step-by-step explanation:
Let one vestment be x
if total investment is $22,000 then
other investment will $22,000 - x
simple interest earned in any year is given by
SI = p*r*t/100
where SI is the interest earned
t is the time period of investment
r is the rate of annual interest
_____________________________________
interest on one account 4%
p = x
t = 1 year
SI = x*4*1/100 = 4x/100
_____________________________
interest on one account 9%
p = 22,000 - x
t = 1 year
SI = (22,000 - x)*9*1/100 = (198000 - 9x)/100
_____________________________________
it is given that total interest earned was $1180
thus sum of SI calculated for the 9% and 4% investment will be equal to 1180
4x/100 + (198000 - 9x)/100 = 1180
=> (4x+198000 - 9x)/100 = 1180
=> 198000 - 5x = 1180*100
=> -5x = 118,000 - 198000
=> -5x = -80,000
=> x = -80,000/-5 = 16,000
Thus,
Amount invested at 4% is $16,000
Amount invested at 9% is $(22,000 - 16,000) = $6,000
Factories A and B produce computers. Factory A produces 3 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.03 and the probability that an item produced by factory B is defective is 0.045. A computer is selected at random and it is found to be defective. What is the probability it came from factory A?
Answer:
P(A∣D) = 0.667
Step-by-step explanation:
We are given;
P(A) = 3P(B)
P(D|A) = 0.03
P(D|B) = 0.045
Now, we want to find P(A∣D) which is the posterior probability that a computer comes from factory A when given that it is defective.
Using Bayes' Rule and Law of Total Probability, we will get;
P(A∣D) = [P(A) * P(D|A)]/[(P(A) * P(D|A)) + (P(B) * P(D|B))]
Plugging in the relevant values, we have;
P(A∣D) = [3P(B) * 0.03]/[(3P(B) * 0.03) + (P(B) * 0.045)]
P(A∣D) = [P(B)/P(B)] [0.09]/[0.09 + 0.045]
P(B) will cancel out to give;
P(A∣D) = 0.09/0.135
P(A∣D) = 0.667
5- How many 50ml glasses can you fill from a 2 litre bottle?
Answer:
2 litre = 200 ml
so 200/50 = 4 glasses
Answer:
It's 40 of 50ml glass
Step-by-step explanation:
It's basically 2 litre/50ml
But 1000ml = 1 litres ;
Meaning 2 litres = 1000 × 2 = 2000ml
Therefore 2 litre/50ml = 2000/50
= 40
Brainliest to whoever gets this correct What was the equation of the graph below before it was shifted to the right 1.5 units?
9514 1404 393
Answer:
(c) G(x) = x³ -x
Step-by-step explanation:
Replacing x with x+1.5 will shift the graph back left by 1.5 units.
G(x) = ((x +1.5) -1.5)³ -((x +1.5) -1.5)
G(x) = x³ -x . . . . . . equation of graph before shift right
Given: g(x) = Square Root of x - 4 and h(x) = 2x - 8. What are the restrictions on the domain of gxh? x is greater than or equal to what?
[tex]g(x) = \sqrt{x - 4}[/tex]
[tex]h(x) = 2x - 8[/tex]
g x h = [tex]\sqrt{x-4}.(2x-8)[/tex]
Looking at the equation we know that there's no way to have a negative root, so we need x - 4 to be greater than or equal to 0
[tex] x - 4 \geq 0[/tex]
[tex]x \geq 4[/tex]
Answer:
It's 6
Step-by-step explanation:
A yogurt costs 45p. How many yogurts can be bought for ten pounds?
Step-by-step explanation:
21
may be, I am not sure about this answer. But it can be
What equation can be solved to find one of the missing side lengths of a triangle?
Answer:
Step-by-step explanation:
1 find out what kind of its is
if its equivelent you might use 60 as thee angles then find out
Members of a public speaking club are competing to see who can recite a speech fastest. Who speaks the most words per minute?
Bailey
Gail
Naomi
Wade
Answer:
Wade
Step-by-step explanation:
Wade equals to 165
Naomi equals to 112
Gail equals to 123
And bailey equals to 150
Solve the formula d = rt for r
Answer: r=d/t
Step-by-step explanation:
This is an equation manipulation problem. Since you are looking for r, you want to get it alone. To do so, you would divide t on both sides. Therefore, you get r=d/t.
Express the solution of the following initial value problem in terms of an integral.
dy/dx = 2 + x, y(2 ) = -6
Answer:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
Step-by-step explanation:
Solution:-
- We are given the following initial value problem:
[tex]\frac{dy}{dx} = 2 + x , y ( 2 ) = -6[/tex]
- We will first isolate the variables:
[tex]dy = ( 2 + x ).dx[/tex]
- Perform integration for both sides of the equation:
[tex]\int {dy} = \int {( 2 + x )}.dx + c\\\\y = 2x + \frac{x^2}{2} + c\\[/tex]
Where,
c: The constant of integration
- We will solve for the constant of integration by using the initial value y ( 0 ) = -6 as follows:
[tex]-6 = 2(0) + \frac{0^2}{2} + c\\\\c = -6[/tex]
- The final solution can be expressed as follows:
[tex]y = 2x + \frac{x^2}{2} - 6[/tex]
18. El equipo de docentes del Área de Formación Humanística decide repartir 195 ejemplares de libros de lectura a 4 estudiantes clasificados previamente por méritos propios. Pero el reparto se hará tomando en cuenta las inasistencias a las clases durante el primer ciclo. ¿Cuántos libros recibe cada estudiante si sus inasistencias han sido de 1; 2; 4 y 5 días, respectivamente?
Answer:
Each of the students absent for 1, 2, 4 and 5 days get 57, 53, 45 and 40 copies of the the reading books respectively.
Step-by-step explanation:
English Translation
The team of teachers from the Humanistic Training Area decides to distribute 195 copies of reading books to 4 students previously classified on their own merits. But the distribution will be made taking into account absences from classes during the first cycle. How many books does each student receive if their absences have been 1; two; 4 and 5 days, respectively?
Solution
Because the more the number of days absent, the less the number of books each of the 4 students deserve, we have to employ an elaborate scheme.
If 195 copies are distributed equally between 4 People, each person gets 48.75 copies of the books.
Now, if we add another 48.75 copies of books to the total number of books, each person gets 60.9375 books.
But, we can then divide 48.75 extra books on top according to the number of days absent and subtract each person's number from the assumed 60.9375 books, with an extra 48.75 books.
Total number of days absent = 1 + 2 + 4 +5 = 12
(48.75/12) = -4.0625 copies for each absent day.
The student with only 1 absent day gets 60.9375 - 4.0625 = 56.875 copies = 57 copies
The student with 2 absent days, gets = 60.9375 - (2×4.0625) = 52.8125 copies = 53 copies
The student with 4 absent days, gets = 60.9375 - (4×4.0625) = 44.6875 copies = 45 copies
The student with 5 absent days, gets = 60.9375 - (5×4.0625) = 40.425 copies = 40 copies
Hence, each of the students absent for 1, 2, 4 and 5 days get 57, 53, 45 and 40 copies of the the reading books respectively.
Hope this Helps!!!
What’s the correct answer for this?
Answer:
PO = 36
Step-by-step explanation:
Since both the chords are equal in length so they must be equidistant from the centre.
And
PG = GO
-x+10 = -3(x+2)
-x+10 = -3x-6
-x+3x = -6-10
2x = -16
Dividing both sides by 2
x = -8
Now
PO = PG + GO
PO = -(-8)+10+(-3)((-8)+2)
PO = 8+10+(-3)(-6)
PO = 18+18
PO = 36
Use the mapping to determine which of the following are elements of the range.
Name
Amy
Carol
Devon
Harrison
Jackson
Labron
Mason
Natalie
Paul
Sylvester
Birthday
January 5
January 7
February 24
March 1
April 7
May 30
July 20
August 1
November 13
November 26
Answer:
The elements of the range are the birthdays.
Step-by-step explanation:
A function is a distinct sort of relation in which each element of the domain is combined with precisely one element in the range. A mapping displays how the elements are combined.
A mapping figure comprises of two parallel columns. The 1st column signifies the domain of a function, and the other column for its range.
Lines or arrows are drawn from domain to range, to signify the relation between any two elements.
A function denoted by the mapping, in which each element of the range is combined with accurately one element of the domain is called one-to-one mapping.
From the diagram provided it is clear that the function denoted by the mapping is an one-to-one mapping.
The elements of the range are:
Birthday : {January 5 , January 7 , February 24 , March 1 , April 7 , May 30 , July 20 , August 1 , November 13 , November 26 }
Thus, the elements of the range are the birthdays.
Answer:
Amy
Devon
Labron
Step-by-step explanation:
The life cycle of a darkling beetle is shown here. Which stage represents the change from larva to adult?
[tex]1 + 1[/tex]
Answer:
D
Step-by-step explanation:
The diagramatic representation of the life cycle of a darkling beetle is shown in the attached file below.
The metamorphosis of the darkling bettle takes four stages:
egg → larva → pupa→ adult
After laying the eggs by an adult darkling bettle, the eggs are encased in a fluid-like covering to prevent it from damage as a result of environmental factors. The egg metamorphosize into the larva stage; a period of feeding and growth. They then in turn proceed into the pupa stage where they are being enclosed in a cocoon. In the cocoon, they undergo modifications and become sexually matured before they enters into adulthood.
Thus, the stage that represent the change fromm larva to adult is the pupa stage and it is shown in the diagram as option D
i need help on this. ive been struggling. TwT
lateral area
surface area
volume
Answer:
total surface area Stot = 753.9816 m2
lateral surface area Slat = 351.85808 m2
top surface area Stop = 201.06176 m2
bottom surface area Sbot = 201.06176 m2
Answer:
Lateral area = 352 Square m
Surface area = 756. 3 square m
Volume = 1408 cubic m
Step-by-step explanation:
[tex]lateral \: area = 2\pi \: rh \\ = 2 \times \frac{22}{7} \times \frac{16}{2} \times 7 \\ = 22 \times 16 \\ = 352 \: {m}^{2} \\ \\ surface \: area = 2\pi \: r(h + r) \\ = 2 \times 3.14 \times 8(7 + 8) \\ = 6.28 \times 8 \times 15 \\ = 6.28 \times 120 \\ = 756.3 \: {m}^{2} \\ \\ volume = \pi {r}^{2} h \\ = \frac{22}{7} \times {8}^{2} \times 7 \\ = 22 \times 64 \\ = 1408 \: {m}^{3} \\ [/tex]
A missiles is fired at a target and the probability that the target is hit is 0.7 . Find how many missiles should be fired so that the probability that the target is not hit is less than 0.001 .
Answer:
(C)
Step-by-step explanation:
We want the probability of at least one hit in
missiles to be at least 80%.
The total surface area of this cuboid is 112 cm,
Find the value of x.
X cm
2 cm
10 cm
Answer:
x=3
Step-by-step explanation:
The rectangular prism is made of 1-inch cubes.
If two more layers of cubes are placed on top of the rectangular prism, how many more cubes are
added to the prism?
What would be the volume of the new rectangular prism?
UZU
Z77-ULZ|
UZZIUZ
FI/ UUUUU
/307111700ZZWJZ13
777777
AHHOZZU
N
NI
3 in.
more cubes are added to the prism.
The volume of the new rectangular prism is
Answer:
Additional cubes added to the rectangular prism= 72cubes
Volume of new rectangular prism = 108in³
Step-by-step explanation:
The question is incomplete without the diagram and not clear to understand.
Let's determine how to find answers to the above using the following:
The diagram used for solving the question has been attached.
From the diagram, the base of the rectangular prism has length =6inches and width = 6inches
Height = 1inch
If 2more layers are added, then height becomes 3inches sinch the two additional layer has same dimensions as the base.
The bottom layer has 6 by 6 dimension
Area = 6×6 = 36in²
Since 1 cube = 1 inch
Number of cubes in the base = 36cubes
Since two layers were added, Additional cubes added to the rectangular prism = 2×36 = 72cubes
Volume of rectangular prism = length×breadth×height
= l×b×h
dimension of new rectangular prism
Length = 6in
Breadth = 6in
Height = 3in
Volume of new rectangular prism = 6×6×3
Volume = 108in³
5. Which statement is true about the triangles?
Hey there! I'm happy to help!
It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.
Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.
Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.
The answer is A) ΔABC ~ ΔDEF.
I hope that this helps! Have a wonderful day!
a country's population in 1993 was 94 million. in 1999 it was 99 million
Answer:
i dont get it
Step-by-step explanation:
The area of the surface of a circular pond is needed. A measure about the pond gives a circumference of about 47 feet. Find the area.
Answer:
55.95 ft²
Step-by-step explanation:
Circumference formula: C = 2πr => r = C / (2π)
Area formula: A = πr²
Substituting C / (2π) for r in the above equation, we get:
C 47 ft
A = π( ----------- )² = π ( -------------- )²
2π (2π)
or ...
π(47 ft)² 2209 ft²
A = ---------------------- = -------------------- = 55.95 ft²
4π² 4(3.14159)²
2)
Simplify -2(x + 4) + 5x + 10
First distribute through the set of parentheses.
When we distribute, we multiply the number outside
times each of the terms located inside the set.
So we have -2(x) + -2(4) or -2x - 8.
Now we have -2x - 8 + 5x + 10.
Combine like terms → your numbers and your "x" terms.
-2x + 5x is 3x and -8 + 10 is 2.
So we have 3x + 2.
3x + 2 cannot be simplified any further.
Professor Jennings claims that only 35% of the students at Flora College work while attending school. Dean Renata thinks that the professor has underestimated the number of students with part-time or full-time jobs. A random sample of 78 students shows that 36 have jobs. Do the data indicate that more than 35% of the students have jobs
Answer:
[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(z>2.074)=0.019[/tex]
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
Step-by-step explanation:
Information given
n=78 represent the random sample taken
X=36 represent the students with jobs
[tex]\hat p=\frac{36}{78}=0.462[/tex] estimated proportion of students with jobs
[tex]p_o=0.35[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the proportion of students with jobs is higher than 0.35, the system of hypothesis are:
Null hypothesis:[tex]p \leq 0.35[/tex]
Alternative hypothesis:[tex]p > 0.35[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{0.462 -0.35}{\sqrt{\frac{0.35(1-0.35)}{78}}}=2.074[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(z>2.074)=0.019[/tex]
If we use a significance level os 0.05 we see that the p value is lower than the significance level so then we can conclude that the true proportion of students with jobs is higher than 0.35 for this case. If we decrease the significance level to 1% the result changes otherwise not.
HELP PLEASE!! Stefano owns a restaurant where his customers create their own pasta dishes. The customer chooses exactly one type of noodle, sauce, vegetable, and meat. The following table shows the options available to customers. HELP PLEASE!! WILL GIVE EXTRA POINTS
Answer:
180 ways
Step-by-step explanation:
U just multiply the number of sauce, noodle, vegetable, and meat
So 3 times 3 times 4 times 5
Correct me if this is wrong
Answer:
180
Step-by-step explanation:
you multiply 3X3X4X5 thus it equals 180
What is the product x^2-16 over 2x+8 • x^3-2x^2+x over x^2+3x-4
Answer:
[tex]\dfrac{x^3-5x^2 +4x}{2x+8}[/tex]
Step-by-step explanation:
The basic idea is to factor each expression and cancel common factors from numerator and denominator.
[tex]\dfrac{x^2-16}{2x+8}\cdot\dfrac{x^3-2x^2 +x}{x^2+3x-4}=\dfrac{(x-4)(x+4)}{2(x+4)}\cdot\dfrac{x(x-1)^2}{(x+4)(x-1)}\\\\=\dfrac{(x-4)x(x-1)}{2(x+4)}\cdot\dfrac{(x+4)(x-1)}{(x+4)(x-1)}\\\\=\boxed{\dfrac{x^3-5x^2 +4x}{2x+8}}[/tex]
If eight trash bags last for thirty days then twenty eight trash bags will last for how many days
Answer:
105 days
Step-by-step explanation:
30 divided by 8 to get the rate which equals 3.75
28*3.75= 105 days
One of the reasons health care costs have been rising rapidly in recent years is the increasing cost of malpractice insurance for physicians. Also, fear of being sued causes doctors to run more precautionary tests (possibly unnecessary) just to make sure they are not guilty of missing something. These precautionary tests also add to health care costs. Data in the Excel Online file provided below are consistent with findings in the Reader's Digest article and can be used to estimate the proportion of physicians over the age of 55 who have been sued at least once.
Required:
a. Formulate hypotheses that can be used to see if these data can support a finding that more than half of physicians over the age of 55 have been sued at least once.
b. Use Excel or Minitab and the file LawSuit to compute the sample proportion of physicians over the age of 55 who have been sued at least once. What is the p-value for your hypothesis test?
c. At α= 0.01, what is your conclusion?
Answer:
a) The null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
b) Sample proportion (p) = 0.6
Sample size (n) = 200
P-value = 0.0029
c) Conclusion: there is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
Step-by-step explanation:
The question is incomplete: there is no attached file with the data.
a) We want to test if more than half of the physiscians over the age of 55 have been sued at least once.
Then, the claim that will be stated in the alternative hypothesis should be that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
The null hypothesis should state that this proportion is not signficantly different from 0.5.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
b) As we do not have the file, we will work with a sample with size n=200 and sample proportion of 0.6.
This sample proportion can be calculated from the data as
[tex]p=x/n=120/200=0.6[/tex]
where x is the number of subjects in the sample that have been sued at least once.
The claim is that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi>0.5[/tex]
The significance level is 0.01.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{200}}\\\\\\ \sigma_p=\sqrt{0.00125}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.6-0.5-0.5/200}{0.035}=\dfrac{0.098}{0.035}=2.758[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.758)=0.0029[/tex]
As the P-value (0.0029) is smaller than the significance level (0.01), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of physicians over the age of 55 that have been sued at least once is significantly higher than 0.5.
If the sinA=3/5 and the cos=4/5 then what is tan A
Answer:
tanA = sinA / cosA = 3/5 / 4/5 = 3/4.
Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
The question is incomplete. Here is the complete question.
Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.
Answer: L = 1; W = 9/4; A = 2.25;
Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:
A = x.y
A = x(-[tex]\frac{3}{4}.x + 3[/tex])
A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]
To maximize, we have to differentiate the equation:
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])
[tex]\frac{dA}{dx}[/tex] = -3x + 3
The critical point is:
[tex]\frac{dA}{dx}[/tex] = 0
-3x + 3 = 0
x = 1
Substituing:
y = -[tex]\frac{3}{4}[/tex]x + 3
y = -[tex]\frac{3}{4}[/tex].1 + 3
y = 9/4
So, the measurements are x = L = 1 and y = W = 9/4
The maximum area is:
A = 1 . 9/4
A = 9/4
A = 2.25
What is 719 ÷ 47
I don't know the answer so I will keep on typing untill it reached 20 words:)
Answer:
719/47 is 15.29787234
Imagine the United States only had two postage stamps, a 3 cent stamp and a 7 cent stamp. If you can put any number of stamps on an envelope that you want, what amounts of postage can and cannot be paid for?
Answer:
not possible: 1, 2, 4, 5, 8, 11possible: all othersStep-by-step explanation:
Obviously, all multiples of 3 and 7 can be paid.
1 cent can be added by adding a 7-cent stamp and taking away two 3-cent stamps. 2 cents can be added by adding three 3-cent stamps and taking away one 7-cent stamp. Hence any value more than 7 +2(3) = 13 cents can always be accommodated.
Amounts that are impossible:
1, 2, 4, 5, 8, 11 cents
All other positive integer amounts are possible.