Answer:
if x = 2
f(x) = -3x^2 + 180x -285
f(x) = -3*2*2 + 180*2 -285
f(x) = -12 + 360 -285
f (x) = 63
Step-by-step explanation:
Define “constant value”
A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.
The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.
Answer:
d. 25.25.
Step-by-step explanation:
A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.
1
1
A baseball weighs approximately
3
pound. A golf ball weighs about pound.
10
What expression can be used to find the combined weight of a baseball and a golf ball?
Answer:
6 pounds 10 ounces
Step-by-step explanation:
I take this to mean "a baseball weighs approximately 3 pounds and a golf ball three pounds ten ounces."
Adding these two weights together, we get 6 pounds 10 ounces.
Please help with this
The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
Answer:
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Step-by-step explanation:
The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]
[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Answer:
A
Step-by-step explanation:
Twice the difference of a number and 9 is 3. Use the variable b for the unknown number.
Answer:
b = 10.5
Step-by-step explanation:
2(b-9) = 3
then:
2*b + 2*-9 = 3
2b - 18 = 3
2b = 3 + 18
2b = 21
b = 21/2
b = 10.5
check:
2(10.5 - 9) = 3
2*1.5 = 3
determine the coordinator of the point
of intersection of lines
3x-2y=13 and 2y+x+1=0
Answer:
(3,-2)
Step-by-step explanation:
Given equations of line
3x-2y=13
2y+x+1=0
=> x = -1 -2y
Point of intersection will coordinates where both equation have same value of (x,y)
top get that we have to solve the both equations by using method of substitution of simultaneous equation.
using this value of x in 3x-2y=13, we have
3(-1-2y) -2y = 13
=> -3 -6y-2y = 13
=> -8y = 13+3 = 16
=> y = 16/-8 = -2
x = -1 - 2y = -1 -2(-2) = -1+4= 3
Thus, point of intersection of line is (3,-2)
Calculate, correct to one decimal plice
the acute angle between the lines
3x - 4y + 5 = 0 and 2x + 3y -1 = 0
A. 70.69
B. 50.2
C. 39.8
D. 19.4
Answer:
A. 70.69 is the correct answer.
Step-by-step explanation:
Given:
Two lines:
[tex]3x - 4y + 5 = 0 \\2x + 3y -1 = 0[/tex]
To find:
Angle between the two lines = ?
Solution:
Acute Angle between two lines can be found by using the below formula:
[tex]tan \theta = |\dfrac{(m_1 - m_2)}{ (1 + m_1m_2)}|[/tex]
Where [tex]\theta[/tex] is the acute angle between two lines.
[tex]m_1, m_2[/tex] are the slopes of two lines.
Slope of a line represented by [tex]ax+by+c=0[/tex] is given as:
[tex]m = -\dfrac{a}{b }[/tex]
So,
[tex]m_1 = -\dfrac{3}{- 4} = \dfrac{3}{4}[/tex]
[tex]m_2 = -\dfrac{2}{ 3}[/tex]
Putting the values in the formula:
[tex]tan \theta = |\dfrac{(\dfrac{3}{4}- (-\dfrac{2}{3}))}{ (1 + \dfrac{3}{4}\times (-\dfrac{2}{3 }))}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{3}{4}+\dfrac{2}{3}}{ (1 -\dfrac{1}{2})}|\\\Rightarrow tan \theta = |\dfrac{\dfrac{17}{12}}{ \dfrac{1}{2}}|\\\Rightarrow tan \theta = \dfrac{17}{6}\\\Rightarrow \theta = tan^{-1}(\frac{17}{6})\\\Rightarrow \theta = \bold{70.69^\circ}[/tex]
So, correct answer is A. 70.69
(a) A survey of the adults in a town shows that 8% have liver problems. Of these, it is also found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability that this person i. Has a liver problems? (3 Marks) ii. Is a heavy drinker (2 Marks) iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem? (2 Marks) iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker? (2 Marks) v. If a person is found to be a non –drinker, what is the probability that this person has liver problems. (2 Marks)
Answer:
i. Has a liver problems?
= 0.08
ii. Is a heavy drinker ?
= 0.066
iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?
= 0.303
iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
= 0.25
v. If a person is found to be a non –drinker, what is the probability that this person has liver problems?
= 0.104
Step-by-step explanation:
We have 2 Events in this question
Event A: People with liver problems
Event B : People without liver problems
Event A: People with liver problems
Let us represent people with liver problems as = (L)
a)8% have liver problems. = P(L)
Under liver problems we have:
b) 25% are heavy drinkers = P( L & H)
c) 35% are social drinkers = P( L & S)
d) 40% are non-drinkers. = P( L & N)
Event B( no liver problem)
Let us represent no liver problem as NL
We are not given in the question but Probability of having no liver problem = 100 - Probability of having liver problem
= 100 - 8% = 92 %
P(NL ) = 92%
From the question, For people without liver problems, we have:
a) 5% are heavy drinkers = P(NL & H)
b) 65% are social drinkers = P( NL & S)
c) 30% do not drink at all = P( NL & N)
An adult is chosen at random, what is the probability that this person
i. Has a liver problems?
P(L) = 8% or 0.08
ii. Is a heavy drinker ?
From the question, we have:
Probability of people that have liver problems and are heavy drinkers P(L & H) = 25% = 0.25
Probability of people that have do not have liver problems and are heavy drinkers P(NL & H) = 5% = 0.05
Probability ( Heavy drinker) =
P(L) × P(L & H) + P(NL) × P(NL & H)
= 0.25 × 0.08 + 0.05 × 0.92
= 0.066
iii. If a person is found to be a heavy drinker, what is the probability that this person has liver problem?
Probability (Heavy drinker and has liver problem) = [P(L) × P(L & H)] ÷ [P(L) × P(L & H)] + [P(NL) × P(NL & H) ]
= [0.25 × 0.08] ÷ [0.25 × 0.08] + [0.05 × 0.92]
= 0.303030303
Approximately = 0.303
iv. If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
P(L & H) = 25% = 0.25
v. If a person is found to be a non –drinker, what is the probability that this person has liver problems.?
People with liver problems are non-drinkers. = P( L & N) = 40% = 0.4
People without liver problems and do not drink at all = P( NL & N) = 30% = 0.3
Probability (non drinker and has liver problem) = [P( L & N) × P(L & H)] ÷ [P( L & N) × P(L & H)] + [ P( NL & N) × P(NL & H) ]
= [0.4× 0.08] ÷ [0.4 × 0.08] + [0.3 × 0.92]
= 0.1038961039
Approximately ≈ 0.104
Help please!!! Thank you
Answer:
Option (G)
Step-by-step explanation:
Let the length of the race = a miles
Since, Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
Time taken to cover 'a' miles with the speed = 12 mph,
Time taken '[tex]t_1[/tex]' = [tex]\frac{a}{12}[/tex]
Time taken to cover 'a' miles with the speed = 11 mph,
Time taken '[tex]t_2[/tex]' = [tex]\frac{a}{11}[/tex]
Since the time taken by David to cover 'a' miles was 10 minutes Or [tex]\frac{1}{6}[/tex] hours more than the time he expected.
So, [tex]t_2=t_1+\frac{1}{6}[/tex]
[tex]\frac{a}{11}=\frac{a}{12}+\frac{1}{6}[/tex]
[tex]\frac{a}{11}-\frac{a}{12}=\frac{1}{6}[/tex]
[tex]\frac{12a-11a}{132}=\frac{1}{6}[/tex]
a = 22 mi
Therefore, distance of the race = 22 mi
Option (G) is the correct option.
please help give bralienst not need explation
Answer:
4.5 cm
Step-by-step explanation:
The ruler says it all..... (why do you need help with this? What grade????)
Hope this helps, have a good day :)
Answer:Its 4.5 centimeters
Step-by-step explanation:
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
A customer can pay GH➣900.00 per month on a mortgage payment.
Interest rate is 12% annually compounded continuously, and mortgage
terms is 15 years. Determine the maximum amount the customer can pay within
the period.
Answer:
$74,748.11
Step-by-step explanation:
In order to make use of the amortization formula, we need to find the equivalent monthly interest rate.
When 12% interest is compounded continuously, the annual multiplier is ...
e^0.12 ≈ 1.127497
The equivalent multiplier when the interest is compounded monthly is the 12th root of this,
(e^0.12)^(1/12) = e^0.01 ≈ 1.0100502 = 1 + r
___
The amortization formula tells us that monthly payment amount A will pay off principal P in n months:
P = A(1 -(1 +r)^-n)/r = $900(1 -1.0100502^-180)/0.0100502
P = $74,748.11
The customer can pay off a 12% loan of $74,748.11 at the rate of $900 per month for 15 years.
You are ordering two pizzas. A pizza can be small, medium, large, or extra large, with any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8). How many possibilities are there for your two pizzas
Answer:
1048576
Step-by-step explanation:
Given the following :
Pizza order :
Size = small, medium, large, or extra large = 4 possible sizes
Toppings = any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8).
Combination of Toppings = 2^8
Four different sizes of pizza = 4
Number of possibilities in ordering for a single pizza :
(4 * 2^8) = 4 * 256 = 1024
Number of possibilities in ordering two pizzas :
(4 * 2^8)^2
(2^2 * 2^8)^2
From indices :
[2^(2+8)]^2
[2^(10)]^2
2^(10*2)
2^20
= 1048576
Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Cancel the common factor of the numerator and the denominator and write specified expression
Step-by-step explanation:
Hello,
I hope you mean to cancel the common factor that exists in numerator and denominator,right.
so, Let's look for the common factor,
here, the expression is,
=4(x-2)/ (x+5)(x-2)
so, here we find the common factor is (x-2)
now, we have to cancel it. And after cancelling we get,
=4/(x+5)
Note:{ we cancel the common factor if the common factors are in multiply form.}
Hope it helps
10/7p+13/8+15/2p=909/56 i NEED THiS solving multi step equations w fractions and #8 PLEASE
Answer:
P= 2
Step-by-step explanation:
10/7p+13/8+15/2p=-909/56
Combine like terms
10/7p+15/2p=-909/56-13/8
20p+105p/14=-909-13*7/56
125/14p=-909-91/56
125/14p= -1000/56
125/14p*14/125= -1000/56*14/125
simplify
P= 8/4=2
And for #8 n =1 I answered this question it
Search
In a random sample of 20 NBA basketball games the mean number of points scored by the home team was 100.4 with a standard deviation of 4.86.
Create and interpret a 95% confidence interval for the true mean number of points scored by an NBA basketball team at home.
You and your friend were watching a LA Lakers game where they were not playing at home. They only scored 98 points. Your friend says, "Wow, I bet if they were playing at home they would have scored a lot more points." Do you agree or disagree with your friend? Support your detailed answer.
Answer:
The 95% confidence interval is [tex]98.27 < \mu < 102.53[/tex]
This interval means that there 95% confidence that the true mean is within this interval
Yes i would agree with my friend because the lower and the upper limit 95% confidence interval for mean points scored at home is greater than 98 points
Step-by-step explanation:
From the question we are told that
The sample size is n = 20
The sample mean is [tex]\mu = 100.4[/tex]
The standard deviation is [tex]\sigma = 4.86[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 4.86 }{ \sqrt{20 } }[/tex]
[tex]E = 2.13[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]100.4 - 2.13 < \mu < 100.4 + 2.13[/tex]
[tex]98.27 < \mu < 102.53[/tex]
At α = 0.001, is the overall model significant?Group of answer choicesNo, F* < FcThe test is inconclusive because 0.001 < p < 0.10Yes, F* < Fc, and p < 0.05.Yes, F* > Fc, and p < 0.001.Yes, F* > Fc, and p > 0.05.
Answer:
No, F* < Fc
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis .
Annie tried to solve an equation step by step. Find Annie's mistake. *
Answer:
Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .
maybe you should type in the steps before it is answered. thanks
Answer:
answer= C
Step-by-step explanation:
“Type ‘equal, supplementary, complementary, or vertical in the space provided’”
Answer:
Supplementary
Step-by-step explanation:
When the sum of 2 angles equal 180°, they are called supplementary angles. And they also form a straight line together.
<AOB (40°) and <BOC (140°) are not equal angles.
<AOB (40°) and <BOC (140°) are not complementary angles. Complementary angles add up to equal 90°.
<AOB (40°) and <BOC (140°) are not vertical angles. Vertical angles are opposite angles formed when two lines intersect.
<AOB (40°) and <BOC (140°) are supplementary angles. They add up to equal 180°.
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700 t 11,000 The population before construction is 67,000. Determine the projected population 16 yr after construction of the park has begun. people
Complete question :
The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people
Answer:
486,200
Step-by-step explanation:
Given that the rate of change in population is represented by the function:
f(t) = 5,700√t + 11,000
To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation
f(t) = 5,700t^1/2 + 11,000
Taking the integral of f with respect to t:
∫(5,700t^1/2 + 11,000)
[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C
[(5700t^3/2)/ 3/2] + 11000t + C
Where C = constant
If population before construction = 67000
Then C = 67000
t = time = 16 years
Substitute values into the original change equation:
[(5700(16)^3/2)/ 3/2] + 11000t + 67000
[(5700 * 64) / 1.5] + 11000(16) + 67000
243200 + 176000 + 67000
= 486,200
How many cubic inches of a milkshake can you fit up to the brim of this cup without letting it overflow? The
cup is 10 inches tall, and the rim of the cup is 4 inches across. (Hint: the radius is half of the diameter.)
Assuming the cup is a right circular cylinder, it's volume is [tex]V=\pi r^2 h[/tex]
$h=10$, $r=\frac 42$
So the volume is $\pi\cdot(2)^2\cdot10=125.66$
hence you can fill up to 125.66 cubic Inches of milkshake
.
The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.
With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).
The margin of error:
A margin of error increases as the confidence level rises, resulting in a larger interval. A margin of error is reduced as confidence is increased, resulting in a narrower interval.By increasing sample size and confidence level, the margin of error lowers and grows.
Margin of error [tex](E) = Z_c * {\frac{\sigma}{\sqrt{n}}}[/tex]
Here [tex]Z_c[/tex] denotes the confidence level's critical value.Whenever it comes to sample size, n is the number of people who take part in the study.As a result, the margin of error lowers as the sample size grows, and the margin of error increases as the confidence level grows.Find out more about the margin of error here:
brainly.com/question/10501147
sin
3/5
4/5
3/4
5/4
Answer:
[tex]\boxed{\frac{3}{5}}[/tex]
Step-by-step explanation:
The trigonometric functions are described as follows:
[tex]sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}[/tex]
Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).
The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.
[tex]\boxed{\frac{3}{5}}[/tex] is the final answer!
is this correct if not which one?
Answer:
C.
Step-by-step explanation:
[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]
We can reduce the second term:
[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]
Since they now have a common denominator, we can add them:
[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]
The answer is C.
So, yes, you're answer was correct!
slope of -4/3x with point (7,20) find equation
Answer:
y= -4/3x+10 2/3
Step-by-step explanation:
To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.
I hope my explanation wasn't confusing and that my answer helped.
the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi
Answer:
James town is 5 meters higher than Takoradi .
Step-by-step explanation:
Given:
Height of James town = 2 meters below sea level
Height of Takoradi town = 7 meters below sea level
To find:
How much higher is James town that Takoradi = ?
Solution:
As we can see the standard of height is how much the town is below the sea level.
So, the height of town having lesser value will be at a higher level.
Value of Height of James town is lesser than that of Takoradi town.
Therefore, James town is at a higher level.
Difference of height = 7 meters - 2 meters = 5 meters
So, the answer is:
James town is 5 meters higher than Takoradi.
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
A plan for a dog park has a grassy section and a sitting section as shown in the figure. Which equation can be used to find the area of the grassy section?
Answer:
[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Step-by-step explanation:
The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]
where:
Base stands for the larger base (in our case the dimension "B" in the attached image)
base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)
and
height stands for the distance between bases (in our case the dimension "h" in the attached image.
Therefore the formula for the area of the grassy section becomes:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Answer:
1/2 (b+b) h
here is the actual picture
