The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Let x be the number.
According to the problem.
50% of x = 10
x = 10 ÷ 50%
= 10×(50/100)
= (50÷5)/(100÷5) = 10/20
Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.
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PLEASE HELP ! Determine f of the quantity 2 plus h end quantity minus f of 2 all over h if f (x) = 5x − 6.
4
4h
5
5h
The value of the function is 5
What is function?A function is defined as a relation between a set of inputs having one output each.
Given function:
f(x) = 5x − 6
Now f(2+h) - f(2) /h
= 5(2+h)-6 - 10+6/h
=10+ 5h -10/h
=5h/h
=5
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Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds.
(n - 30) + n = 210
(n + 30) + n = 180
(n + 30) + n = 210
(n - 30) + n = 180
The equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
From the given information,
n = Tom's weight in pounds
If Jim weighs 30 pounds less than Tom
Jim weighs will be (n - 30)
Thus,
The sum of their weight
(n-30) + n
∴ (n-30) + n = 210
Hence, the equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210
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1. How many variables are involved in the chi-square test?
2. Which type of chi-square test is this?
A.goodness of fit B.test of independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table is the result of this rest statistically significant?
A. Yes B.No
The result of the respective questions are:
This chi-square test only takes into consideration one variable.The type of chi-square test this is is a Goodness of Fitdf= 3NOHow many variables are involved in the chi-square test?a)
This chi-square test only takes into consideration one variable.
b)
The type of chi-square test this is, is a Goodness of Fit
To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.
The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.
c)
Parameter
n = 4
Therefore
Degrees of freedom
df= n - 1
df= 4 - 1
df= 3
d)
In conclusion
Parameters
[tex]\alpha = 0.05[/tex]
df = 3
Hence
Critical value = 7.814728
Test statistic = 6.6
Test statistic < Critical value, .
NO, the result of this test is not statistically significant.
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Which of the following shows that the two composite figures cover the same area?
The area of a 2D form is the amount of space within its perimeter. It is measured in square units. The correct option is 9 units².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the different figures will be shown below.
Thus, the expression that shows that the two composite figures cover the same area is A = 4 + 3 + 2 = 9 units².
Hence, the correct option is 9 units².
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A suitcase measures 18 inches long and 12 inches high. What is the diagonal length of the suitcase?
Answer:
21.6 in
Step-by-step explanation:
Imagine the suitcase as a rectangle, with length of 18 in and width of 12 in. In order to find the diagonal length, simply use the Pythagorean Formula, a^2 + b^2 = c^2, and solve for c!
In this case, a = 18 and b = 12.
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Find the sum of s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)...
The sum of the equation is
[tex] \frac{859}{2772} [/tex]
How to find the sum
Given the expression
s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)
Let's find the LCM, which is 2772
s =
[tex] \frac{2772 - 693 + 462 - 308 +252 - 198}{2772} [/tex]
Add the numerators, do the addition before the substraction
s =
[tex] \frac{859}{2772} [/tex]
Thus, the sum of the equation is
[tex] \frac{859}{2772} [/tex]
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Suppose that poaching reduces the population of an endangered animal by 6% per year. Further suppose that when the population of this animal falls below 20, its extinction is inevitable (owing to the lack of reproductive options without severe in-breeding). If the current population of the animal is 1500, when will it face extinction? Comment on the validity of this exponential model.
If poaching reduces the population of an endangered animal by 6% and the criteria of population extinction is 20 with present population 1500 then it will take 3.62 years to reach to the mark of extinction.
Given Poaching reduces the population of endangered animals by 6% per year. The criteria of population extinction is 20. Present population being 1500.
Number of years taken by the population of endangered animals to reach to 20 mark can be calculated as under:
20=1500*[tex](1-0.06)^{n}[/tex]
20=1500*[tex]0.94^{n}[/tex]
20/1500=[tex]0.94^{n}[/tex]
0.133=[tex]0.94^{n}[/tex]
take log both sides
log(0.133)=log[tex]0.94^{n}[/tex]-------1
log(0.133)=nlog (0.94)
put the values log values:
log(0.133)=-0.8761
log(0.94)=-0.0268
Taking 1
-0.8761=n*(-0.0268)
n=0.8761/0.0268
n=3.269
Hence to reach level of 20 the population takes 3.2 years.
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Let t be the number of weeks Dr. Elder is on his diet and D(t) be a linear equation that models his weight in pounds. At the beginning of his diet, t=0, Dr. Elder weighs 265 pounds, D(0)=265. After nine weeks, t=9, he now weighs 229 pounds, D(9)=229. Find the slope
Using it's concept, it is found that the slope of the function is of -4.
What is the slope of a function?The slope of a function is given by the change in the output of the function divided by the change in the input.
For this problem, in 9 months, his weight changed from 265 pounds to 229 pounds, hence it changed -36 pounds, which means that the slope is of:
m = -36/9 = -4.
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Find the equation of the plane passing through the points A=(1,1,1), B=(1,4,5), C=(−3,-2,0).
Find the area of the triangle the 3 points from the first equation.
Find the angle between the 2 vectors; (1) from A to B and (2) from C to B.
Take any two pairs of the given points and make vectors out of them. For example, the vector from A to B is
[tex]\vec v_1 = \langle 1,4,5\rangle - \langle 1,1,1\rangle = \langle0,3,4\rangle[/tex]
and the vector from A to C is
[tex]\vec v_2 = \langle -3,-2,0\rangle - \langle1,1,1\rangle = \langle-4,-3,-1\rangle[/tex]
These vectors lie in the same plane (the one we want). We can get a third vector that is normal to the plane by taking their cross product (details omitted).
[tex]\vec n = \vec v_1 \times \vec v_2 = \langle 9,-16,12 \rangle[/tex]
If [tex]\vec u = \langle x,y,z\rangle[/tex] is an arbitrary vector, then the vector from any of the points A, B, or C to [tex]\vec u[/tex] will lie in our plane. That is, if we start from A,
[tex](\vec u - \langle1,1,1\rangle) \cdot \vec n = 0[/tex]
and this reduces to the equation of the plane,
[tex]\langle x - 1, y - 1, z - 1 \rangle \cdot \langle 9, -16, 12 \rangle = 0[/tex]
[tex]9 (x - 1) - 16 (y - 1) + 12 (z - 1) = 0[/tex]
[tex]\boxed{9x - 16y + 12z = 5}[/tex]
Area of triangle ABCThis follows immediately from the cross product identity
[tex]\|\vec x \times \vec y\| = \|\vec x\| \|\vec y\| \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between [tex]\vec x[/tex] and [tex]\vec y[/tex]. The left side corresponds to the area of the parallelogram spanned by [tex]\vec x[/tex] and [tex]\vec y[/tex]; half of this area would be that of a triangle. (see attached)
In our case, we have
[tex]\|\vec n\| = \|\vec v_1 \times \vec v_2\| = \sqrt{481}[/tex]
so the area of ABC is [tex]\boxed{\dfrac{\sqrt{481}}2}[/tex].
Angle between A to B and between C to BWe already know the first vector, [tex]v_1[/tex].
The vector from C to B is
[tex]\vec v_3 = \langle 1,4,5 \rangle - \langle -3,-2,0 \rangle = \langle 4, 6, 5 \rangle[/tex]
Recall the dot product identity,
[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]
Then
[tex]\vec v_1 \cdot \vec v_3 = \|\vec v_1\| \|\vec v_3\| \cos(\theta) \implies \cos(\theta) = \dfrac{38}{5\sqrt{77}} \implies \theta \approx \boxed{29.9914^\circ}[/tex]
Complete the sentence.
The amount of time it takes to eat an apple is most likely to be a function of
the
OA. size of the apple
B. orchard where the apple was harvested
O C. store where the apple was purchased
OD. color of the apple
A trader sold an article for N150 and
made a profit of 20%. What was the
cost price of the article?
Answer:
125
Step-by-step explanation:
N150=120%
? =100
150×100/120
=125
The cost price of the good is $125.
What is cost price?Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a given service.
Given that a good has been sold for $150 which made a profit of 20% we need to find the cost price of the good,
Let the cost price be x,
So,
x × 120% = 150
x = 150 × 100 / 120
x = 125
Hence the cost price of the good is $125.
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Find the 8th term of the sequence with formula tn= 7+2 (n-1)
Answer:
Your answer is 71
Step-by-step explanation:
7+2(n-1)
we have our n as 8
so,7+2(8-1)
9(7)=63
t+b = 41
t = 2b+2
Solve for t and b
Answer: b=13, t=29
Step-by-step explanation:
Substituting the first equation into the second,
[tex]2b+2+b=41\\\\3b+2=41\\\\3b=39\\\\b=13\\\\\implies t=2(13)+2=29[/tex]
witch hazel is listed at 12 per galon, less 34.5%. what is the net cost of the amount needed in filling the prescription
The net cost of the amount needed in filling the prescription is 7.86 per gallon
Net costCost of witch hazel = 12 per gallonDiscount = 34.5%Net cost = 12 - (34.5% of 12)
= 12 - (0.345 × 12)
= 12 - 4.14
= 7.86 per gallon
Therefore the net cost of the amount needed in filling the prescription is 7.86 per gallon
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A random variable is not normally distributed, but it is mound shaped. It has a mean of 11 and a standard deviation of 4.
If you take a sample of size 14, can you say what the shape of the sampling distribution for the sample mean is? Why?
Using the Central Limit Theorem, nothing can be stated about the shape of the sampling distribution for the sample mean, as the sample size is less than 30.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, we have a skewed variable and n < 30, hence nothing can be stated about the shape of the sampling distribution for the sample mean.
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solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?
Answer:
Step-by-step explanation:
cos (x/2)=cos x+1
cos (x/2)=2cos ²(x/2)
2 cos²(x/2)-cos (x/2)=0
cos (x/2)[2 cos (x/2)-1]=0
cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)
x/2=2nπ+π/2,2nπ+3π/2
x=4nπ+π,4nπ+3π
n=0,1,2,...
x=π,3π
or x=180°,540°,...
180°∈[0,360]
so x=180°
or
2cos(x/2)-1=0
cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)
x/2=360n+60,360n+300
x=720n+120,720n+300
n=0,1,2,...
x=120,300,840,1020,...
only 120° and 300° ∈[0,360°]
Hence x=120°,180°,300°
Divide: StartFraction 5 Over 8 EndFraction divided by three-fourths
The value gotten when 5/8 is divided by 3/4 is 5/6.
What is the value gotten from the division?A fraction is a non-integer that is made up of numerator and a denominator. An example is 5/8. Division is the process of grouping a number into equal parts using another number.
5/8 ÷ 3/4
5/8 × 4/3 = 5/6
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Pamela is 7 years younger than Jiri. The sum of their ages is 39. What is Jiri ‘s age?
Based on the task given, Pamela's age and juri's age is 16 and 23 years respectively.
EquationJuri's age = xPamela's age = x - 7Their total age = 39x + (x - 7) = 39
x + x - 7 = 39
2x = 39 + 7
2x = 46
x = 46/2
x = 23
Therefore,
Juri's age = x
= 23 years
Pamela's age = x - 7
23 - 7
= 16 years
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ram takes 20 minutes to inspect a car, while robert takes only 18 minutes.if both start inspecting car at 8.00 hours what is the first time at which both will have finished inspecting a car at the same point time
Answer:
11:00
Step-by-step explanation:
here we have to calculate the LCM of 20 and 18
20 = 2² × 5
18 = 2 × 3²
Then
LCM(20 , 18) = 2² × 5 × 3² = 20 × 9 = 180
The
After 180 minutes (3 hours) they will have finished inspecting a car at the same point time.
Then
At 8:00 + 3 = 11:00 Ram and Robert will have finished inspecting a car at the same point time.
Which point is a solution to the system?
Answer:
what solution bc i could answer this pls let me know the equation but......
Step-by-step explanation:
to find a solution you can add divide or subtract to find the solution like x=2
A well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece. What is the probability of getting a cookie with no more than 3 chips? Round your answer to four decimal places.
The probability of getting a cookie with no more than 3 chips is 0.714.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece.
Using poison ratio:
[tex]\rm P (X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}[/tex]
λ is the mean number of chocolate chips in a piece
[tex]\rm P (X = 6) = \dfrac{6^k e^{-6}}{k!}[/tex]
P(X ≥ 5) = 1 - P(X < 5)
P(X ≥ 5) = 1 - P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
[tex]\rm P(X \geq 5) = 1-[\dfrac{6^0 e^{-6}}{0!}+\dfrac{6^1 e^{-6}}{1!}+\dfrac{6^2 e^{-6}}{2!}+\dfrac{6^3 e^{-6}}{3!}+\dfrac{6^4 e^{-6}}{4!}][/tex]
After solving;
P(X ≥ 5) = 0.714
Thus, the probability of getting a cookie with no more than 3 chips is 0.714.
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what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)
⊰_________________________________________________________⊱
Answer:
The equation is-: y=3xStep-by-step explanation:
[tex]\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}[/tex]
[tex]\pmb{\tt{done \ !!}}[/tex]
⊱_________________________________________________________⊰
MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts
The amount of the radioactive substance is 374.6 g
How to determine the amount of radioactive substance?The given parameters are:
Initial, a = 424 mgRate, r = 6%Time, t = 2 hoursThe amount of the radioactive substance is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 424 * (1 - 6%)^t
At 2 hours, we have:
A(2) = 424 * (1 - 6%)^2
Evaluate
A(2) = 374.6
Hence, the amount of the radioactive substance is 374.6 g
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who knows how to sketch this kind of graph
The graph of f(x) = 0.5sin(4x) is sketched below
Graph of trigonometric functionsFrom the question, we are to sketch the graph of the given trigonometric function.
The given trigonometric function is
f(x) = 0.5sin(4x)
The graph of f(x) = 0.5sin(4x) is sketched below
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Set up an algebraic equation and then solve.
The width of a rectangle is 14 units less than the length. If the area is 120 square
units, then find the dimensions of the rectangle.
Length:
Width:
Answer:
Width: 6
Length: 20
Step-by-step explanation:
So the area of a rectangle can be defined as: [tex]A=wl[/tex] where w=width and l=length.
In this case we don't know what the length is, so let's just say the length is the variable l, and since the width is 14 units less than the length, we can express it as (l-14). this gives us the equation: [tex]A=l(l-14)=l^2-14l[/tex]. We can solve for l, since we're given the area which is 120. So let's set the equation equal to that:
Original Equation:
[tex]A=l^2-14l[/tex]
Substitute 120 as A (given)
[tex]120=l^2-14l[/tex]
There is many ways to solve this equation: factoring, quadratic equation, completing the square etc... but in this case I'll just complete the square
Add (b/2)^2 to both sides to complete the square
[tex]120+(\frac{-14}{2})^2=l^2-14l+(\frac{-14}{2})^2[/tex]
Simplify
[tex]169=l^2-14l+49[/tex]
Rewrite right side a square binomial
[tex]169=(l-7)^2[/tex]
Take the square root of both sides
[tex]13=l-7\\[/tex]
Add 7 to both sides
[tex]20=l[/tex]
to solve for width simply subtract 14 from the length which is 20, so the width is 6
Width: 6
L: 20
Which of the following has a slope of –2 and a y-intercept of 4?
y = 2x – 4
y = –2x – 4
y = –2x + 4
y = 2x + 4
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which equation has a slope of -2 and a y-intercept of 4?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
All of these equations are in [tex]\bf{y=Mx+b}[/tex] form.
The y-int. is b. The slope is M.
[tex]\bf{y\!=\!\!-2x+\!4}[/tex] | put in the values
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=\!\!y=-2x+4}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
The length of a rectangle is five times the width. If the area of the rectangle is 45
square inches, then find the length and width.
Step-by-step explanation:
sol;
l=5w
area=l*w
or,45=5w*w
or,45=5w2
or,45\5=w2
0r[tex]\sqrt{9}[/tex]=w
or,3=w
again,
l=5w
l=5*3
l=15
Therefore, length is 15 inch and width is 3 inch.
100POINTS WHY NOT
sally took money from her bank account to go out of town for an audition.she spot 54$ for a round trip ticket and 1/2 of the remaining money on her hotel bill.she spent $7.90 for food and arrived home with $15.10.How much money did Sally take from her bank account??
Answer:
$100
Step-by-step explanation:
Given information:
$54 = cost of ticketCost of hotel = 1/2 remaining money after purchase of ticket$7.90 = cost of food$15.10 = remaining moneyLet x = money taken from bank account
If Sally paid $54 for her ticket, then the money remaining at that point can be defined as: [tex]x-54[/tex]
If the cost of the hotel was half of the remaining money, then:
[tex]\textsf{Cost of hotel}=\dfrac{1}{2}(x-54)}[/tex]
To find how much money Sally took from her bank account, create an equation with the given information and solve for x.
[tex]\implies \textsf{Money in bank} - \textsf{ticket} - \textsf{hotel} - \textsf{ food} =\textsf{remaining money}[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}(x - 54)-7.90=15.10[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}x+27-7.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x-34.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x=50[/tex]
[tex]\implies x=100[/tex]
Therefore, Sally took $100 from her bank account.
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget: 2,020 − 22m
What does the coefficient of the expression represent? The number of months Megan will wait to sell the gadget The monthly depreciation value of the gadget The amount of money Megan will get when she sells the gadget The original value of the gadget
The coefficient (m) of the expression represents: C. the monthly depreciation value of the gadget.
What is depreciation?Depreciation can be defined as a process in which the monetary value of a physical asset decreases or falls over a period of time, especially due to wear and tear.
In this scenario, we can infer and logically deduce that the coefficient (m) of the given expression represents the monthly depreciation value of Megan's gadget.
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Answer:
it is C
Step-by-step explanation:
give the other guy brainliest, I am ok with hearts and good ratings.
Given f(x)-3x-1 and g(x)-2x-3, for which value of x does g(x)=f(2)?
Answer:
x = 4
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-1\\g(x)=2x-3\end{cases}[/tex]
f(2) means substitute x = 2 into function f(x):
[tex]\begin{aligned}g(x) & = f(2)\\ \implies 2x-3 & = 3(2)-1\\2x-3 & = 6-1\\2x - 3 & = 5\\2x - 3 + 3 & = 5 + 3\\2x & = 8\\\dfrac{2x}{2} & = \dfrac{8}{2}\\x & = 4\end{aligned}[/tex]
Therefore, g(4) = f(2).
f(2)
3(2)-16-15so
g(x)=52x-3=52x=8x=4