Answer:
The answer is 3
Step-by-step explanation:
List all prime factors
15:1,3,5,
27:1,3,
Biggest one is 3
Answer:
the answer is 3
Step-by-step explanation:
cuz the prime factors of 27 is 1,3,and 27
while 15 is 1, 3 ,5 and 15
I hope this helps
Given right triangle JKL, what is the value of cos(L)?
Five-thirteenths
Five-twelfths
Twelve-thirteenths
Twelve-fifths
Pls help!!
The value of cos(L) in the triangle is Five-thirteenths
What are right triangles?Right triangles are triangles whose one of its angle has a measure of 90 degrees
How to determine the value of cos(L)?The value of a cosine function is calculated as:
cos(L) = Adjacent/Hypotenuse
The hypotenuse is calculated as
Hypotenuse^2 = Opposite^2 + Adjacent^2
So, we have:
Hypotenuse^2 = 12^2 + 5^2
Evaluate
Hypotenuse^2 = 169
Take the square root of both sides
Hypotenuse = 13
So, we have
Adjacent = 5
Hypotenuse = 13
Recall that
cos(L) = Adjacent/Hypotenuse
This gives
cos(L) = 5/13
Hence, the value of cos(L) in the triangle is Five-thirteenths
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Which of the following equations has a minimum value of (3,-10)? y = 2x2 + 40x + 203 y = x2 + 6x + 19 y = 2x2 − 12x + 8 y = -2x2 + 12x − 8
Answer:
y = 2x² − 12x + 8
Step-by-step explanation:
FIRST METHOD :
y = 2x² − 12x + 8
= (2x² − 12x) + 8
= 2 (x² − 6x) + 8
= 2 (x² − 6x + 9 − 9 ) + 8
= 2 (x² − 6x + 9) − 2×9 + 8
= 2 (x² − 6x + 9) − 18 + 8
= 2 (x² − 6x + 9) − 10
= 2 (x − 3)² − 10
Then ,the equation has a extremum value of (3,-10)
Since the number 2 in the equation y = = 2 (x − 3)² − 10 is greater than 0
(2 > 0) , the graph (parabola) opens upward
Therefore ,the extremum (3,-10) is a minimum.
SECOND METHOD :
the graph of a function of the form f(x) = ax² + bx + c
has an extremum at the point :
[tex]\left( -\frac{b}{2a} ,f\left( -\frac{b}{2a} \right) \right)[/tex]
in the equation : f(x) = 2x² − 12x + 8
a = 2 ; b = -12 ; c = 8
Then
[tex]-\frac{b}{2a} = -\frac{-12}{2 \times 2} = 3[/tex]
Then
[tex]f\left( -\frac{b}{2a} \right) = f(3) = 2(3)^2- 12(3) + 8 = 18 - 36 + 8 = -18 + 8 = -10[/tex]
the graph of a function f(x) = 2x² − 12x + 8
has an extremum at the point (3 , -10)
Since the parabola opens up ,then the extremum (3,-10) is a minimum.
Answer part ABCDE
B options is Z , T , chi-square, F
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistic can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this clinical trial (study), we should use a t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₀: μ ≠ 7
Next, we would calculate the t-test as follows:
[tex]t=\frac{7.08\;-\;7}{\frac{0.25}{\sqrt{14} } }\\\\t=\frac{0.08}{\frac{0.25}{3.7417 } }[/tex]
t = 0.08/0.0668
t = 1.198.
For the p-value, we have:
P-value = P(t < 1.198)
P-value = 0.1262.
Therefore, the p-value (0.1262) is greater than α = 0.10. Based on this, we should fail to reject the null hypothesis.
In conclusion, yes the mean discharge differs from 7 fluid ounces.
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(a+b)² - 11(a+b) -42
pls show the work
Answer:
(a+b)² - 11(a+b) -42
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms,
Group 1: -11b-11a
Group 2: a2+2ab
Group 3: b2-42
Pull out from each group separately :
Group 1: (a+b) (-11)
Group 2: (a+2b) (a)
Group 3: (b2-42) (1)
Looking for common sub-expressions :
Group 1: (a+b) (-11)
Group 3: (b2-42) (1)
Group 2: (a+2b) (a)
final answer:(a+b)² - 11(a+b) -42
Answer:
(a+b+3)(a+b-14)
Step-by-step explanation:
let a+b be x,
= x²-11x-42
=x²-(14-3)x-42
=x²-14x+3x-42
=x(x-14)+3(x-14)
=(x+3)(x-14))
replacing x by a+b,
=(a+b+3)(a+b-14)
The Tortoise and the Hare is a fable about a race with the
moral, “Slow and steady wins the race.” The Tortoise and the
Hare decide to “race” across the United States from
Washington D.C. to Los Angeles.
a. Charles Darwin studied the tortoises when he was on
the Galapagos in 1835. He thought they moved relatively quickly. “One large one, I found by pacing, walked at the rate of 60 yards in 10 minutes” he wrote in Zoology Notes.
i How many inches per minute does the Galapagos tortoise walk?
ii. How long would it take a Galapagos tortoise to walk across the U.S.? Use the most
appropriate unit for time.
b. The Hare can run up to 30mph.
i. How many inches per minute does the Hare run?
ii. How long would it take the Hare to complete the race across the U.S.? Use the
most appropriate unit for time.
c. In the fable, the Hare, confident that he is so far head, relaxes and takes a nap. How long would the Hare need to nap for the Tortoise to pass him and win the race?
a.i) The number of inches per minute that the Galapagos tortoise walks are 216 inches (6 x 36).
a.ii) The time it would take a Galapagos tortoise to walk across the U.S. in hours is 2,933 hours (1,056,000/(6 x 60).
b.i) The Hare runs 31,680 inches per minute (1,900,800/60).
b.ii) The time it would take the Hare to complete the race across the U.S. in hours is 20 hours (600/30).
c.) For the Tortoise to pass the Hare, the Hare needs to sleep for 2,913 hours (2,933 - 20) or 121.4 days (2,933/24).
What are the equivalent values for calculating distance?In this exercise, the following equivalent values are used for computing the distance and speed:
1 mile = 1,760 yards1 yard = 36 inches1 hour = 60 minutesDistance from Galapagos to the U.S. = 600 miles600 miles = 1,056,000 yards (600 x 1,760).Data and Calculations:Speed of Galapagos Tortoise per minute = 6 yards/ min (60 yards in 10 minutes)
Speed of Hare = 30mph
30 miles = 52,800 yards (30 x 1,760)
52,800 yards = 1,900,800 inches (52,800 x 36)
= 880 yards per minute (52,800/60)
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For a certain company, the cost function for producing x items is C(x)=40x+200 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200 . The maximum capacity of the company is 100 items.
Based on the cost and revenue functions to the company for selling x items, the domain of C(x) is [0, 100].
The range of C(x) is (200, 4,200).
What is the domain and range of C(x)?The domain would be the lowest capacity and the maximum capacity. As these are physical units to sell, the lowest unit would be 0 units as units can't be negative.
The maximum capacity is given as 100 items so the domain is:
= [0, 100]
The range is:
When x is 0, the function gives C(x) as:
= 40(0) + 200
= 200
When x is the maximum of 100, the C(x) is:
= 40(100) + 200
= 4,200
Range is:
(200, 4,200)
Full question is:
What is the domain and range of C(x)?
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An office has 7 male employees and 8 female employees. The manager randomly chooses 2 employees to
attend a football game. What is the probability that the manager chooses 2 femaleemployees?
From the 2 selected employees, the probability that they will both be females is; C: 4/15
How to find the Probability?We are given;
Number of male employees = 7
Number of female employees = 8
Total number of employees = 8 + 7 = 15
Now, 2 random employees are chosen and so the number of ways of selecting this is; 15C2
Now, out of the 2 selected employees, the probability that they will be female = 8C2/15C2 = 28/105 = 4/15
Thus, we can conclude that from the 2 selected employees, the probability that they will both be females is; C: 4/15
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Hava Racquets Company manufactures pickleball racquets in four different models.
For the year, the SoftNet line had a net loss of AED 40,000 from sales of AED 250,000,
variable costs of AED 180,000 and fixed costs of AED 110,000. If the Softnet is
eliminated, AED 30,000 of fixed cost will remain. What would be the incremental
effect to the Company if the Softnet would be eliminated?
Based on the AED 40,000 net loss that the SoftNet line brings to Hava Racquets company, the incremental effect if the Softnet line is eliminated is that the company would save AED 10,000.
What is the incremental effect?If Hava Racquets Company decides to scrap the Softnet line, then it means that they will no longer be incurring the AED 40,000 net loss that the line had brought to them.
They would instead incur a fixed cost of AED 30,000 which they can apply to their other operations.
This means that in exchange for a AED 40,000 loss, they would instead get a AED 30,000 loss.
The savings on these losses is:
= 40,000 - 30,000
= AED 10,000
This means that Hava Racquets Company will make a saving of AED 10,000 if they eliminate the line.
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find the coefficient of x^5 in the expression ( 1 - 2x) ^6
Answer:
-32x^5
Step-by-step explanation:
using binomial expression we have (1-2x)^6
need heeeelp please
Answer:
Initial population: 222 fish
After 7 years: 871 fish
Step-by-step explanation:
Initial population size:
Let t=0
∴P(0)=[tex]\frac{2000}{1+8e^0}[/tex]
=[tex]\frac{2000}{1+8}[/tex]
=[tex]\frac{2000}{9}[/tex]
=222 fish
After 7 years:
Let t=7
∴P(7)=871 fish
How can 25 e42 n=1 be rewritten?
Answer:
The 'n = 1' below sigma represents the lower bound. meaning the number from which you start adding.
'25' above sigma is the upper bound.
In general it means adding 42 from 1 to 25 times.
so 42(25).
Answer:
C. 42(25)
Step-by-step explanation:
Took the unit test review and this was the correct option choice.
Goodluck on your unit test, I am sure that you will do good :)
what is the range of the function f(x) = lxl + 5 ?
Answer:
All real numbers greater than or equal to 5
Step-by-step explanation:
The range of y=|x| is all real numbers greater than or equal to 0. Adding 5 to this makes the range all real numbers greater than or equal to 5.
Solve for x
Please write your work
Answer:
Step-by-step explanation:
12 + 2x + 24 = 27 + x
2x + 36 = 27 + x
x + 36 = 27
x = -9
2(-9) + 24 = -18 + 24 = 6
12 + 6 = 18
27 + (-9) = 18
STATISTICS:
Using the research question, "Do certain musical genres impact the task performance of those high in neuroticism?" determine the:
1. Dependent and Independent Variable:
2. Moderator OR Mediator:
The dependent variable here is task performance. The independent variable in the question is musical genres.
What is a dependent variable?This is the term that is used to refer tp the variable that is of interest. It is the variable that one is trying to determine.
The independent variable is the x variable. It is the variable that helps us check the impact that it has on the dependent variable.
The task performance is what we want to know here. To do so we want to use the genre of music.
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P: 2,012
1) El volumen de un cubo de arista 1 es Vc = 1³ y el
Volumen de una esfera de radior es
JE
V₁ = πr ²³ Entonces si en un cubo de arista 4cm
3
y se introduce una pelota de diametro 4 cm, al Calcular
aproximación con cuatro cifras decimales, por exceso.
Calcular el volumen que queda entre la esfera y el cubo.
(toma π =
3,141592654)
El volumen que queda entre la esfera y el cubo es: 30.49cm^3
¿Como calcular el volume sobrante?
El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.
Para el cubo que tiene una arista de 4cm, el volumen es:
V = (4cm)^3 = 64 cm^3
Para la esfera con un diametro de 4cm, el radio es:
R = 4cm/2 = 2cm
Y el volumen será:
V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3
El volumen que queda entre la esfera y el cubo es:
V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3
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Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.23%.
(a)
In which month does the amount of principal in a monthly payment first exceed the amount of interest?
(b)
How much interest is repaid for the term of the loan? (Round your answer to the nearest cent.)
$
(c)
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?
Yes
No
This exercise requires the ability to create Amortization Schedules Using a Spreadsheet program. Based on the information given about the Amortization of the loan, the principal payable per month became greater than the interest payable per month on the 159th month (given that the loan amount is $500,000.
In which month does the amount of principal in a monthly payment first exceed the amount of interest?The amount of principal in a monthly payment first exceeds the interest payment In 159th Month. The interest on this month is $1, 248.39 while the principal on this month is $1, 205.46.
It is to be noted that when a loan is taken, the constituents of the amounts being paid back is the Principal and part of the interest on the loan.
How do you Calculate Amortization of Loans?The yearly interest rate must be divided by 12.
Your monthly interest rate, for instance, will be 0.3525 percent if your annual interest rate is 4.23 percent (0.0423 annual interest rate x 12 months).
Additionally, you'll add 12 to the number of years remaining on your loan term.
How much interest is repaid for the term of the loan?The total amount of interest that is paid for the term loan is $383,385.54
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?Yes it would change. It would change to the 165th month. In this month, the interest paid is $1, 834.00 while the principal paid back is $1,846.77. See the attached image for answer C.
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QUESTION IS DOW BELOW 15 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
WILL GIVE BRAINLIEST FOR ACCURATE ANWSER
a. Applying the angle of intersecting chord theorem, m∠AEB = 57°.
b. Applying the , angle of intersecting tangents or secants theorem, VW = 106°.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chord theorem, the angle formed inside a circle (i.e. angle AEB) by two chords (i.e. AC and BD) have a measure that is equal to half of the sum of the measures of intercepted arcs AB and CD.
What is the Angle of Intersecting Tangents or Secants Theorem?According to the angle of intersecting tangents or secants theorem, the angle formed outside a circle (i.e. angle VZW) have a measure that is equal to half of the positive difference of the measures of intercepted arcs XY and VW.
a. m∠AEB = 1/2(measure of arc AB + measure of arc CD) [angle of intersecting chord theorem]
Substitute
m∠AEB = 1/2(53 + 61)
m∠AEB = 57°
b. 35 = 1/2(VW - 36) [angle of intersecting tangents or secants theorem]
Multiply both sides by 2
2(35) = VW - 36
70 = VW - 36
Add 36 to both sides
70 + 36 = VW
VW = 106°
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Sahil has a fish tank in the shape of a cuboid, as The tank is 3 cm shown in the diagram. water 55 cm 33 cm 28 cm Diagram M accurately 55 cm long 28 cm wide 33 cm high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the ta What is the greatest number of neon tetra fish Sahil can put in his tank?
Answer:
9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is
55 cm long
28cm wide
cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?
Step-by-step explanation:
Heyy I just need some help with question 13,17,19 if anyone could help me and show the work that would be amazing thank you!!
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer
In the diagram, angle ADE ≈ angle ABC the ratios blank and blank are equal.
Based on the angle-angle similarity theorem (AA), the pair of ratios that are equal is: AE/EC = AD/DB.
What is the Angle-angle Similarity Theorem (AA)?The angle-angle similarity theorem (AA) states that two triangles are similar to each other if they have two corresponding congruent angles, and therefore, the ratios of their corresponding side lengths are equal. This means their corresponding side lengths are proportional in measure.
Given that angle ADE ≅ angle ABC, we also know that:
Angle EAD ≅ CAB.
Thus, this implies that triangle EAD is similar to triangle CAB based on the angle-angle similarity theorem (AA). Therefore, the ratios of their corresponding side lengths are equal.
Thus, the ratios that are equal to each other would be:
AE/EC = AD/DB.
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Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions 2x+5+2x+3x= x +
One Solution 2x+5+2x+3x= x +
Infinitely Many Solutions 2x+5+2x+3x= x +
Since there is only one value of x, hence the equation given has only one solution
Equations and expressionsEquations are expressions separated using mathematical operations. Given the equation below;
2x+5+2x+3x = x
Collect the like terms
2x+2x+3x -x = -2
7x -x = -2
Simplify
6x = -2
x = -2/6
x = -1/3
Since there is only one value of x, hence the equation given has only one solution
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HELP ME ,HELP ME ,HELP ME PLEASE.IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
a) 88 degrees
The measure of the central angle is the same as the measure of the arc it intercepts.b) 44 degrees
Angle FEG is inscribed in arc FG, and thus has half the measure of arc FG.HELPPPP PLSSSSSSSS !?!?????
Answer:
(9/3) * 4 * 2
Step-by-step explanation:
:DDDD
Answer:
2(9 / 3) * 4
Step-by-step explanation:
this is one of the many ways to solve this
9/3 is 3
2 times 3 is 6
6 times 4 is 24
therefore 2(9 / 3) * 4 is 24
A truck rental is $30 plus $.30 /mi. Find out how many miles Ken traveled if his bill was $55.20 .
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
Let's consider the information given:
rental price: $30 + $0.30/miletotal bill for Ken: $55.20Let's setup an equation for the cost
set 'x' as number of miles traveled[tex]\hookrightarrow Cost = 30 + 0.3x[/tex]
set that equal to the total cost or bill and solve[tex]30 + 0.3x = 55.2\\0.3x = 25.2\\x=84[/tex]
Ken must have traveled 84 miles
Answer: 84 miles
Hope that helps!
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A positive integer is 10 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is frac(2,3), then find the two integers.
The two integers are are mathematically given as
x=3.70
y=13.7
What is the two integers?Generally, the equation for the two integers is mathematically given as
x + 10 = y
1/x + 2/y = 2/3
Substitute
1/x + 2/x+10 = 2/3
Multiply by 3
3/x + 6/x + 10 = 2
Multiply by x
2 + 6x/x + 10 = 2x
Multiply by x + 3
2(x + 10) + 6x = 2x(x + 3)
2x+20+6x=2x^2+6x
-2x^2+2x+20=0
x=3.70
hence y
x + 10 = y
3.70+ 10 = y
y=13.7
In conclusion, the two integers are
x=3.70
y=13.7
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Cai says you can divide both quantities in a ratio by the same nonzero number to
find an equivalent ratio. Explain why Cai is correct.(MATH)
Answer:
correct
Step-by-step explanation:
dividing both quantities in a ratio by the same non zero number does indeed find an equivalent ratio.
for example
60 : 36 ( divide both parts by 6 )
= 10 : 6 ← equivalent ratio ( divide both parts by 2 )
= 5 : 3 ← equivalent ratio in simplest form
in fact dividing the original by the HCF of the 2 quantities gives the ratio in simplest form immediately , that is
60 : 36 ( divide both parts by 12 )
= 5 : 3
Question 26: [4 points]
1% of a population have a certain disease and the remaining 99% are free from this disease. A test is used to detect this disease. This test is positive in 95% of the people with the disease and is also (falsely) positive in 2% of the people free from the disease.
If a person, selected at random from this population, has tested positive, what is the probability that she/he has the disease?
Let D be the event "have the disease" and FD be the event "free from the disease" Let the event TP be the event that the "test is positive".
A diagram with all the above information is shown.
[tex]P(D/TP) = \frac{P(D \: n \: TP)}{P(TP)} [/tex]
[tex]P(TP) = P(TP \: n \: D)+P(TP \: n \: FD) \\ P(TP) = 0.95×0.99 + 0.02×0.01 = 0.9407[/tex]
[tex]P(D/TP) = \frac{0.9405}{0.9407} = \frac{9405}{9407} [/tex]≈0.999787
Given that m/_a=40 and m/_b=61 find that the measure of angles x and y
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
x = 159°y = 140°[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:y + a = 180[/tex]
( linear pair )
[tex]\qquad❖ \: \sf \:y + 40 = 180[/tex]
[tex]\qquad❖ \: \sf \:y = 180 - 40[/tex]
[tex]\qquad❖ \: \sf \:y = 140 \degree[/tex]
And
[tex]\qquad❖ \: \sf \:x = a +( 180 - b)[/tex]
( Exterior angle = sum of opposite interior angles )
[tex]\qquad❖ \: \sf \:x = 40 + (180 - 61)[/tex]
[tex]\qquad❖ \: \sf \:x = 40 + 119[/tex]
[tex]\qquad❖ \: \sf \:159 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
x = 159°y = 140°Elena is 56 inches tall. (Note: 100 inches = 254 centimeters)
Round your answers to the nearest thousandth. Type the answers in the boxes below.
1. What is her height in centimeters? centimeters
2. What is her height in meters?
Elena's height in centimeters is 142.24 cm.
Elena's height in meters is 1.42 meters.
What is Elena's height in centimeters and meters?The mathematical operations that would be used to determine the answers ae division and multiplication.
Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the operation that is used to determine the product of two or more numbers.
In order to determine the height in centimeters, first determine how many cenitmeters make 1 inch
1 inch = 254 / 100
1 inch = 2.54 cm
Now, convert 56 inches to cm : 56 inches x 2.54 = 142.24 cm
In order to determine the height in meters, first find the unit of conversion of inches to meters
1 inch = 0.0254 meters
0.0254 x 56 = 1.42 meters
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a man borrowed GHC 1200 at the bank for 4 months at the rate of 5%.Calculate a. his simple interest
there are 12 months in a year, so then 4 months is really 4/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & 1200\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=\to \frac{4}{12}years\dotfill &\frac{1}{3} \end{cases} \\\\\\ I = (1200)(0.05)(\frac{1}{3})\implies I=20~GHC[/tex]
