Answer:
c)
Step-by-step explanation:
α also known as type I error depicts the probability of rejecting the true null hypothesis. So, when α=0.05 then it means that there is 5% probability or chance of rejecting the true null hypothesis.
So, in hypothesis testing α=0.05 means that there is a maximum 5 percent chance that a true null hypothesis will be rejected.
8. Find the inverse of the function.
Y=-3/x+4
Yo sup??
y=-3/x+4
cross multiply
x+4=-3/y
x=-3/y-4
f(y)=-3/y-4
or
f(x)=-3/x-4
=-4x-3/x
The correct answer is option 4
Hope this helps.
Answer:
It is -4x-3/x.
Rs 144 is distributed among 2 boys and 3 girls in such a way that each girl gets three times as much as each boy gets. Find how much each boy should get.
Answer:
Each boy gets approximately Rs 13.09
Step-by-step explanation:
We are given the following in the question:
Total money = Rs 144
Let x be the amount each girl gets and y be the amount each boy gets.
The money is distributed among 2 boys and 3 girls. Thus, we can write:
[tex]3x + 2y = 144[/tex]
Also, each girl gets three times as much as each boy gets.
Thus, we can write:
[tex]x = 3y[/tex]
Substituting these values, we get,
[tex]3(3y) + 2y = 144\\11y = 144\\\\y =\dfrac{144}{11} \approx 13.09\\\\x = 3(\dfrac{144}{11}) \approx 39.27[/tex]
Thus, each boy gets approximately Rs 13.09
Answer: each boy should get $39.27
Step-by-step explanation:
Let x represent the amount that each boy should get.
Let y represent the amount that each girl should get.
The total amount of money that would be distributed among the 2 boys and 3 girls is 144 Rs. This is expressed as
2x + 3y = 144 - - - - - - - - - - - -1
The money is shared in such a way that each girl gets three times as much as each boy gets. This is expressed as
y = 3x
Substituting y = 3x into equation 1, it becomes
2x + 3 × 3x = 144
2x + 9x = 144
11x = 144
x = 144/11 = 13.09
y = 3x = 3 × 13.09
y = $39.27
what is the segment of AD?
A) 5
B) 6
C) 4.5
D) 3
Answer:
i am pretty sure it is B
Step-by-step explanation:
The present above is a 10 in by 10 in by 10 in cube. How many square inches of wrapping paper do you need to wrap the box?
Answer:
600 in^2.
Step-by-step explanation:
There are 6 faces on a cube so the area we need is:
6 * 10 * 10
= 600 in^2.
Statistics encompasses all scientific disciplines in which random occurrences are analyzed. In addition, statistics references any random occurrence which is reported using percentages or proportions. True or false?
Answer: FALSE
Step-by-step explanation: Statistics is the Science of collecting, organising,sumarising,analysing information to reach at a reasonable conclusion or outcome. Statistics also helps to measure levels of confidence in any conclusion or outcome.
Statistics has been applied in several fields like Medicine, pharmacy, Engineering,Biology etc it helps in determining especially in numerical representation the impact of certain conditions or activities or information.
Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.
cot x sec4x = cot x + 2 tan x + tan3x
(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x
1 + sec2x sin2x = sec2x
sine of x divided by one minus cosine of x + sine of x divided by one minus cosine of x = 2 csc x - tan2x + sec2x = 1
Answer:
Step-by-step explanation:
1.
cot x sec⁴ x = cot x+2 tan x +tan³x
L.H.S = cot x sec⁴x
=cot x (sec²x)²
=cot x (1+tan²x)² [ ∵ sec²x=1+tan²x]
= cot x(1+ 2 tan²x +tan⁴x)
=cot x+ 2 cot x tan²x+cot x tan⁴x
=cot x +2 tan x + tan³x [ ∵cot x tan x [tex]=\frac{ \textrm{tan x }}{\textrm{tan x}}[/tex] =1]
=R.H.S
2.
(sin x)(tan x cos x - cot x cos x)=1-2 cos²x
L.H.S =(sin x)(tan x cos x - cot x cos x)
= sin x tan x cos x - sin x cot x cos x
[tex]=\textrm{sin x cos x }\times\frac{\textrm{sin x}}{\textrm{cos x} } - \textrm{sinx}\times\frac{\textrm{cos x}}{\textrm{sin x}}\times \textrm{cos x}[/tex]
= sin²x -cos²x
=1-cos²x-cos²x
=1-2 cos²x
=R.H.S
3.
1+ sec²x sin²x =sec²x
L.H.S =1+ sec²x sin²x
=[tex]1+\frac{{sin^2x}}{cos^2x}[/tex] [[tex]\textrm{sec x}=\frac{1}{\textrm{cos x}}[/tex]]
=1+tan²x [tex][\frac{\textrm{sin x}}{\textrm{cos x}} = \textrm{tan x}][/tex]
=sec²x
=R.H.S
4.
[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}} = \textrm{2 csc x}[/tex]
L.H.S=[tex]\frac{\textrm{sinx}}{\textrm{1-cos x}} +\frac{\textrm{sinx}}{\textrm{1+cos x}}[/tex]
[tex]=\frac{\textrm{sinx(1+cos x)+{\textrm{sinx(1-cos x)}}}}{\textrm{(1-cos x)\textrm{(1+cos x})}}[/tex]
[tex]=\frac{\textrm{sinx+sin xcos x+{\textrm{sinx-sin xcos x}}}}{{(1-cos ^2x)}}[/tex]
[tex]=\frac{\textrm{2sin x}}{sin^2 x}[/tex]
= 2 csc x
= R.H.S
5.
-tan²x + sec²x=1
L.H.S=-tan²x + sec²x
= sec²x-tan²x
=[tex]\frac{1}{cos^2x} -\frac{sin^2x}{cos^2x}[/tex]
[tex]=\frac{1- sin^2x}{cos^2x}[/tex]
[tex]=\frac{cos^2x}{cos^2x}[/tex]
=1
Need help with #1 #4 #7 plz giving 15 points
Answer:
Q1: p = - 33
Q2: d = - 99
Q3: t = - 13
Step-by-step explanation:
Q1: [tex]$ \textbf{-} \frac{\textbf{p}}{\textbf{3}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{8} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{3}[/tex]
We solve this taking LCM.
We get: [tex]$ \frac{-p - 24}{3} = 3 $[/tex]
[tex]$ \implies - p - 24 = 9 $[/tex]
[tex]$ \implies \textbf{p} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 33} $[/tex]
Q4: [tex]$ \frac{\textbf{d}}{\textbf{11}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{4} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]
Again we proceed like Q1 by taking LCM.
We get: [tex]$ \frac{d - 44}{11} = - 13 $[/tex]
[tex]$ \implies d - 44 = - 13 \times 11 = - 143 $[/tex]
[tex]$ \implies d = - 143 + 44 $[/tex]
[tex]$ \implies \textbf{d} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 99} $[/tex]
Q7: 5t + 12 = 4t - 1
We club the like terms on either side.
[tex]$ \implies 5t - 4t = - 1 - 12 $[/tex]
[tex]$ \implies (5 -4)t = - 13 $[/tex]
[tex]$ \implies \textbf{t} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{- 13} $[/tex]
Hence, the answer.
A square is 3 inches on each side. A small square, x inches on each side, is cut out from each corner of the original square. Represent the area of the remaining portion of the square in the form of a polynomial function A(x)
Here's the polynomial function representing the area of the remaining portion of the square:
A(x) = 9 - 4x + x^2
1. **Initial area:** The original square has a side length of 3 inches, so its initial area is 3 * 3 = 9 square inches.
2. **Removing squares:** When small squares of side length x are cut out from each corner, the remaining shape becomes a smaller square with a side length of (3 - 2x) inches.
3. **New area:** The area of this smaller square is (3 - 2x) * (3 - 2x) = 9 - 6x + 4x^2 = 4x^2 - 6x + 9.
4. **Simplifying:** We can rearrange this expression to get a simpler polynomial function: A(x) = 9 - 4x + x^2.
Therefore, A(x) = 9 - 4x + x^2 represents the area of the remaining portion of the square after the small squares are cut out, as a function of the side length x of the removed squares.
Tyler has two savings accounts that his grandparents opened for him. The two accounts pay 10% and 12% in annual interest; there is $400 more in the account that pays 12% than there is in the other account. If the total interest for a year is $158, how much money does he have in each account?
Answer: the amount of money in the account that earns 10% interest is $500
the amount of money in the account that earns 12% interest is $900
Step-by-step explanation:
Let x represent the amount of money in the account that earns 10% interest.
Let y represent the amount of money in the account that earns 12% interest.
There is $400 more in the account that pays 12% than there is in the other account. This means that
y = x + 400
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering the account that earns 10% interest.
P = x
R = 10
T = 1 year
I = (x × 10 × 1) = 0.1x
Considering the account that earns 12% interest.
P = y
R = 12
T = 1 year
I = (y × 12 × 1) = 0.12x
If the total interest for a year is $158, it means that
0.1x + 0.12y = 158 - - - - - - - - - - -1
Substituting y = x + 400 into equation 1, it becomes
0.1x + 0.12(x + 400) = 158
0.1x + 0.12x + 48 = 158
0.22x = 158 - 48 = 110
x = 110/0.22 = 500
y = x + 400 = 500 + 500
y = 900
Sandra earned $8,000.00 from a summer job and put it in a savings account that earns 3% interest compounded continuously. When Sandra started college, she had $8,327.00 in the account which she used to pay for tuition. How long was the money in the account? Round your answer to the nearest month.
____ years and ____ months
Answer: 1 year and 4 months
Step-by-step explanation:
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = 8000
r = 3% = 3/100 = 0.03
A = 8327
Therefore,
8327 = 8000 x 2.7183^(0.03 x t)
8327/8000 = 2.7183^(0.03t)
1.040875 = 2.7183^(0.03t)
Taking log of both sides, it becomes
Log 1.040875 = log 2.7183^(0.03t)
0.0174 = 0.03tlog2.7183
0.0174 = 0.03t × 0.434 = 0.01302t
t = 0.0174/0.01302
t = 1.336
0.336 × 12 = 4.032
Therefore, the money waa in the account for 1 year and 4 months
Start with x2 + 4x = 12 and complete the square, what is the equivalent equation? A) (x + 2)2 = 16 B) (x + 2)2 = 14 C) (x + 4)2 = 16 D) (x + 4)2 = 28
Answer: The answer is A
Step-by-step explanation: Add the coefficient of x to the both sides.
X²+4x=12
X²+4x+4=12+4
X²+4x+4=16
X²+2x+2x+4=16
X(x+2)+2(x+2)=16
(X+2)(x+2)=16
(X+2)²=16
The equivalent equation is (x+2)²=16
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: The expression x²+4x-12=0
Thus simplifying the equation we get
x²+2.2x+4-12-4=0
(x+2)²-4²=0
(x+6) (x-2)=0
x=-6,2
or the equation can also be rewritten as (x+2)²=16
Thus the equivalent equation is (x+2)²=16
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Suppose Paul went to the store and bought 4 peaches to add to the basket.Write two new numerical expressions to represent the total number of fruit in the basket.
The question involves creating numerical expressions to represent the total number of fruits in a basket after adding 4 peaches. By assuming the initial fruit count as x, two expressions are x + 4, representing the total number of fruits, and 2(x + 4), indicating a scenario where the total fruit count doubles after adding the peaches.
Explanation:The question asks for two new numerical expressions to represent the total number of fruit in the basket, given that Paul added 4 peaches. To create these expressions, we need to assume there was an initial number of fruit in the basket before Paul added the peaches. Let's denote the initial number of fruit as x. Therefore, our two new numerical expressions could be:
x + 4: This expression represents the total number of fruit in the basket after adding 4 peaches to the initial amount.2(x + 4): This expression might represent a scenario where, for some reason, the number of fruits, after adding the 4 peaches, is doubled. It exemplifies how numerical expressions can model different real-world scenarios beyond simple addition.These examples show how basic algebraic expressions can be used to represent situations involving changes in quantity.
Three brothers Charlie Robert and Nicholas have 21 video games Charlie has twice as many games as Robert. Robert has 5 fewer games than Nicholas what would be the equation
Answer:
The equation would be [tex]4x-15=21[/tex].
Step-by-step explanation:
Given;
Total Number of Video games = 21
Let the number of video game Nicholas has be 'x'.
Now Given:
Robert has 5 fewer games than Nicholas.
so we can say that;
number of video game Robert has = [tex]x-5[/tex]
Also Given:
Charlie has twice as many games as Robert.
so we can say that;
number of video game Charlie has = [tex]2(x-5)=2x-10[/tex]
we need to write the equation.
Solution:
Now we can say that;
Total Number of Video games is equal to sum of number of video game Nicholas has, number of video game Robert has and number of video game Charlie has.
framing the equation we get;
[tex]x+x-5+2x-10=21\\\\4x-15=21[/tex]
Hence The equation would be [tex]4x-15=21[/tex].
On Solving we get;
Adding both side by 15 we get;
[tex]4x-15+15=21+15\\\\4x=36[/tex]
Dividing both side by 4 we get;
[tex]\frac{3x}{4}=\frac{36}{4}\\\\x=9[/tex]
Hence Nicholas has = 9 video games
Robert has = [tex]x-5= 9-5=4[/tex] video games
Charlie has = [tex]2x-10 = 2\times9-10=18-10=8[/tex] video games
Answer:
The equation would be [tex]4x-15=21.[/tex]
Step-by-step explanation:
Given:
Three brothers Charlie Robert and Nicholas have 21 video games Charlie has twice as many games as Robert. Robert has 5 fewer games than Nicholas.
Now, to find the equation.
Let the games Nicholas has be [tex]x.[/tex]
Robert has games [tex]x-5.[/tex]
And Charlie has [tex]2(x-5).[/tex]
Now, the equation is:
[tex](x)+(x-5)+2(x-5)=21.[/tex]
[tex]x+x-5+2x-10=21\\2x-5+2x-10=21\\4x-15=21[/tex]
[tex]4x-15=21.[/tex]
Therefore, the equation would be [tex]4x-15=21.[/tex]
Students are getting signatures for a petition to increase sports activities at the community center. The number of signatures they get each day is 3 times as many as the day before. The expression 3 to the 6th power represents the number of signatures they got on the sixth day. How many signatures did they get on the first day?
Answer:
Students got 3 signature on the first day.
Step-by-step explanation:
We are given the following in the question:
The number of signatures they get each day is 3 times as many as the day before.
Thus, the number of signature forms a G.P with common ratio, r = 3.
The expression 3 to the 6th power represents the number of signatures they got on the sixth day. Thus we can write:
[tex]a_6 = 3^6[/tex]
The [tex]n^{th}[/tex] term in a G.P is given by
[tex]a_n = a_1r^{n-1}[/tex]
where [tex]a_1[/tex] is the first term in the G.p
Putting values, we get,
[tex]3^6 = a_1(3)^{6-1}\\3^6 = a_1(3)^5\\\Rightarrow a_1 = 3[/tex]
Thus, the first term of G.P is 3.
Hence, students got 3 signature on the first day.
Peter is Distributing pamphlets about dog care and samples of dog biscuits. The dog biscuits come in packages of 12 in the pamphlets are in packages of 20 how many packages of dog biscuits and pamphlets will Peter need
Answer:
3 packeges of Pamphlets and 5 packages of dog biscuits.
Step-by-step explanation:
Peter have to distribute a pamphlet with one dog buscuit to each person they need equal amount of pamphlets and biscuitsby taking LCM of both 12 and 20 theanswer is 60. Peter needs 60 pamphlets and 60 dog biscuits. So he require 3packages of pamphlets and 5packages of dog biscuits.
A frustum is made by removing a small cone from a similar large cone.Work out the frustum radius of cone=4.5cm radius of frustum=3cm height of the frustum =3cm height of the cone=9cm
The radius of the cone is found by comparing the ratios of heights and radii in a similar triangle. By applying the given values, the radius of the cone is found to be 9 cm.
Explanation:In mathematics, problems related to finding the dimensions of cones and frustums are common. As the problem mentions, a frustum is created when a smaller, similar cone is removed from a larger cone. To calculate the dimensions of the frustum, we use the properties of similar triangles.
For similar triangles:
Base ratios are equal to height ratios.
Therefore:
Height ratio (height of frustum/height of cone) = Base ratio (radius of frustum/radius of cone)
Applying the given values, it becomes:
3/9 = 3/Radius of cone
Hence, the radius of the cone is 9 cm.
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Final answer:
The volume of a frustum can be calculated using the formula [tex]\(V = \frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\)[/tex]. Given the dimensions provided for the frustum with the larger cone having a radius of 4.5 cm, the frustum a radius of 3 cm, and height of 3 cm, the volume of the frustum is approximately 134.25π cubic centimeters.
Explanation:
To work out the volume of a frustum that is formed by removing a small cone from a larger, similar cone, you can make use of the formula for the volume of a frustum:
V = [tex]\(\frac{1}{3}\pi h (r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})\),[/tex]
where:
h is the height of the frustum,
r₁ is the radius of the larger base (radius of the original cone),
r₂ is the radius of the smaller base (radius of frustum).
Given:
Radius of the large cone (r₁) = 4.5 cm,
Radius of the frustum (r₂) = 3 cm,
Height of the frustum (h) = 3 cm.
The height of the original cone (9 cm) is not needed to calculate the volume of the frustum. Plugging the given values into the formula:
[tex]\(V = \frac{1}{3}\pi \times 3 \times (4.5^{2} + 3^{2} + 4.5 \times 3)\)[/tex]
[tex]\(V = \pi (20.25 + 9 + 13.5)\)[/tex]
[tex]\(V = \pi (42.75)\)[/tex]
[tex]\(V = 134.25\pi \text{cm}^{3}\)[/tex]
Therefore, the volume of the frustum is approximately 134.25π cubic centimeters.
Does the graph represent a function ? Why or Why not ?
Answer:yes
Step-by-step explanation: the answer does represent a function because if you were to put points in the line wherever, and connect them by drawing a line vertically, it would not cross two points.
In Don's congruence flowchart for problem 6-29, one of the ovals "AB/FD= 1". In Phil's flowchart, one of the ovals said, "AB=FD". Discuss with with your team whether these ovals say the same thing. Can equality statements like Phil's always be used in congruence flowcharts?
Yes, they are saying the same thing. In fact, if a ratio equals one, it means that numerator and denominator are equal.
This is the reason why you can always use A=B or A/B, as they are totally equivalent.
Given: △ABC; AB=BC, m∠BDA = 60°, BD=4 cm, BD ⊥ BA . Find: DC, AC.
Answer:
DC = 10.93 cm , AC = 9.8 cm
Step-by-step explanation:
From trigonometry;
⇒ Tan 60 = AB/BD
⇒AB = BD Tan 60 ( where BD = 4 cm )
⇒ AB = 6.93 cm
Also, AB=BC , therefore;
⇒ BC = 6.93 cm
⇒ Cos 60 = BD/AD
⇒ AD = BD/ Cos 60 = 4/Cos 60
⇒ AD = 8 cm
From Pythagoras theorem;
⇒ [tex]AC^{2}[/tex] = [tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex](6.93)^{2}[/tex] + [tex](6.93)^{2}[/tex]
⇒ AC = [tex]\sqrt{96.05}[/tex] = 9.80 cm
⇒ DC = BD + BC = 4 + 6.93
⇒ DC = 10.93 cm
The amount of money in Tara's account with respect to the day of the month was recorded for 31 days. The correlation coefficient was calculated to be r = −0.9870. Interpret the meaning of the correlation coefficient in terms of the scenario.
There is a weak, negative correlation between the amount of money in Tara's account and the day of the month.
There is a strong, positive correlation between the day of the month and the amount of money in Tara's account.
There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
There is a weak, positive correlation between the day of the month and the amount of money in Tara's account.
There is no correlation between the amount of money in Tara's account and the day of the month.
Answer:
There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
Step-by-step explanation:
r is between -1 and +1. r values close to -1 are strongly negative. r values close to +1 are strongly positive. r values close to 0 are weak.
r = -0.9870 is strongly negative. So there is a strong, negative correlation between the amount of money in Tara's account and the day of the month.
Final answer:
The correlation coefficient r = -0.9870 shows a strong, negative correlation between the day of the month and the amount of money in Tara's account, meaning as the days pass, her account balance generally decreases. So, the correct statement is 'There is a strong, negative correlation between the amount of money in Tara's account and the day of the month.'
Explanation:
The correlation coefficient, denoted as r, measures the strength and direction of the linear relationship between two variables. Given that the correlation coefficient in the scenario is r = −0.9870, this indicates a strong, negative correlation between the amount of money in Tara's account and the day of the month. This means that as the days of the month increase, the amount of money in Tara's account tends to decrease, and this pattern is quite consistent, considering the high absolute value of the coefficient, which is close to -1.
Leon wants to estimate the height of a building. Leon's eyes are 6 feet above ground. He stands 25 feet from the building and sights the top of the building at a 77° angle of elevation. What is the building's height to the nearest tenth of a foot?
Answer:
114.29 ft
Step-by-step explanation:
tan ∅ = Opp/Adj
tan 77 = x/25
x = 25 tan 77
x = 108.29ft
Plus 6ft = 114.29 ft
FUNCTIONS: In the space provided, type the answer in descending order as it applies without any spaces between the letters, numbers, or symbols.
Type the composition (fog)(x) of the given functions:
f(x) = x^2 + 2x − 6 and g(x) = x + 5.
Answer:
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
Step-by-step explanation:
Given:
[tex]f(x) = x^2+2x-6[/tex]
[tex]g(x)=x+5[/tex]
We need to find [tex](f o g)(x)[/tex].
Solution:
Now we can say that;
[tex](f o g)(x)[/tex] = [tex]f(g(x))[/tex]
[tex](fog)(x) = (x+5)^2+2(x+5)-6[/tex]
Now Applying distributive property we get;
[tex](fog)(x) = (x+5)^2+2\times x+2\times5-6\\\\(fog)(x) = (x+5)^2+2x+10-6\\\\(fog)(x) = (x+5)^2+2x+4[/tex]
Now Solving the exponent function we get;
[tex](fog)(x) = x^2+2\times x\times 5+5^2+2x+4\\\\(fog)(x) = x^2+10x+25+2x+4\\\\(fog)(x) = x^2+12x+29[/tex]
Hence The composition [tex](fog)(x)[/tex] of the given function is [tex]x^2+12x+29[/tex].
Janine is saving money to buy a car. She has a total of $1400 left to save, and she plans to save a certain percentage of $1400 each month: In August, Janine will save 25% of $1400. In September, Janine will save 40% of $1400. In October, Janine will save 15% of $1400. In November, Janine will save the remaining amount. Which option correctly explains what Janine plans to save each month?
Answer:
August=$350
September=$560
October=$210
November= $280
Step-by-step explanation:
Total amount left to save $1400.
We calculate the amount save each mount since we are already given the percentages.
For the month of August she saves 25% of $1400, we convert the percentage to equivalent cash
[tex]\frac{25}{100}*1400\\=350[/tex]
for the month of August, she saved $350,
Next For the month of September she saves 40% of $1400, we convert the percentage to equivalent cash
[tex]\frac{40}{100}*1400\\=560[/tex]
for the month of September, she saved $560,
Next For the month of October she saves 15% of $1400, we convert the percentage to equivalent cash
[tex]\frac{15}{100}*1400\\=210[/tex]
for the month of October, she saved $210,
total amount saved by October = $350+$560+$210=$1120
Amount saved by November=1400-1120=$280
Joel has a goal to practice his clarinet for 4 1/2 per week. The list below shows the number of hours Joel has a practiced so far for the week. Monday 1 1/2 hours Wednesday 1 1/4 hours Thursday 1 hour How many more hours does he need to practice this week to meet his goal
0.75 hours more is needed to practice to meet his goal
Solution:
Given that,
Goal per week of Joel = [tex]4\frac{1}{2} = \frac{2 \times 4 + 1}{2} = \frac{9}{2}[/tex]
From given,
The list below shows the number of hours Joel has a practiced so far for the week
[tex]Monday = 1\frac{1}{2}\ hours = \frac{3}{2}\ hours[/tex]
[tex]Wednesday = 1\frac{1}{4}\ hours = \frac{5}{4}\ hours\\\\Thursday = 1\ hour[/tex]
How many more hours does he need to practice this week to meet his goal
Find the difference
Hours needed = Goal per week of Joel - (monday + wednesday + thursday)
[tex]Hours\ needed = \frac{9}{2} - (\frac{3}{2} + \frac{5}{4} + 1)\\\\Hours\ needed = 4.5-(1.5+1.25+1)\\\\Hours\ needed = 4.5 - 3.75 = 0.75\\\\Hours\ needed = 0.75 = \frac{3}{4}[/tex]
Thus 0.75 hours more is needed to practice to meet his goal
Joel needs to practice \( \frac{3}{4} \) hours more this week to meet his goal.
First, we need to calculate the total number of hours Joel has practiced so far. We will add the hours practiced on Monday, Wednesday, and Thursday.
[tex]Monday: \( 1 \frac{1}{2} \) hours = \( 1 + \frac{1}{2} \) hours = \( \frac{3}{2} \) hours[/tex]
[tex]Wednesday: \( 1 \frac{1}{4} \) hours = \( 1 + \frac{1}{4} \) hours = \( \frac{5}{4} \) hours[/tex]
[tex]Thursday: \( 1 \) hour = \( \frac{4}{4} \) hours (to keep the denominator consistent)[/tex]
Now, let's add these hours together:
[tex]\( \frac{3}{2} + \frac{5}{4} + \frac{4}{4} = \frac{6}{4} + \frac{5}{4} + \frac{4}{4} = \frac{15}{4} \) hours[/tex]
Joel's goal is to practice [tex]\( 4 \frac{1}{2} \)[/tex] hours per week, which is [tex]\( 4 + \frac{1}{2} \) hours = \( \frac{8}{2} + \frac{1}{2} \) hours = \( \frac{9}{2} \) hours.[/tex]
To find out how many more hours Joel needs to practice, we subtract the total hours he has already practiced from his goal:
[tex]\( \frac{9}{2} - \frac{15}{4} \)[/tex]
To subtract these fractions, we need a common denominator, which is 4:
[tex]\( \frac{18}{4} - \frac{15}{4} = \frac{3}{4} \) hours[/tex]
Therefore, Joel needs to practice [tex]\( \frac{3}{4} \)[/tex] hours more to meet his weekly goal.
Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 10.8 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids? The foil costs $0.24 per square foot.
Answer:
Therefore the team saves $5.18.
Step-by-step explanation:
i) there are two triangular pyramids
ii) the base of each pyramid is an equilateral triangle with an area of 10.8 square feet.
iii) the base of the pyramids are not covered with foil.
iv) since there are two pyramids the total area not covered
= 10.8 [tex]\times[/tex] 2 = 21.6 square feet
v) the cost of foil = $0.24 per square foot.
vi) the team save altogether by covering only the lateral area of the two pyramids
= 21.6 [tex]\times[/tex] 0.24 = $5.18
Therefore the team saves $5.18.
True or false? All occurrences of the letter u in "Discrete Mathematics" are lowercase. Justify your answer
The given statement "All occurrences of the letter u in "Discrete Mathematics" are lowercase" is true.
Here's why:
There are no occurrences of the letter "u" in "Discrete Mathematics" at all.
Therefore, the question of whether they are uppercase or lowercase becomes irrelevant due to the absence of the letter itself.
Because the statement involves a vacuous quantification, meaning it deals with an empty set, it automatically becomes true.
In such cases, it doesn't matter what property is being attributed to the empty set because there are no elements for that property to be true or false for.
Two friends entered a contest jointly and won; however, there is only one prize and it cannot be split. Some methods of selecting who receives the prize are given below. A: Place both names in equal amounts into a hat and draw one without looking. B: Ask a stranger to flip a coin. C: Roll a die and evaluate the outcome as either even or odd. D: Throw a stone closest to an object. E: Play a hand of blackjack. F: Ask a random stranger to select. The methods that are fair include _____ because _____ is flawed due to increased chances of winning based on one's skill, ______ is flawed due to poor randomization, and ______ is flawed due to unequal probabilities of winning and losing.
Answer:
The methods that are fair include __A, B and C__ because __D__ is flawed due to increased chances of winning based on one's skill, ___F___ is flawed due to poor randomization, and ___E___ is flawed due to unequal probabilities of winning and losing.
Step-by-step explanation:
A. Place both names in equal amounts into a hat and draw one without looking:
If you place both names in equal amounts into a hat, then the probability of picking any one of the names would be equal.
For example, if you put 20 pieces of paper containing each name in a hat, then,there will be 40 names in the hat. The probability of picking any one or the other randomly would be:
P = 20/40 =1/2
B. Ask a stranger to flip a coin:
A coin has only two faces, head and tail. Hence, if one person picks head and the other picks tail, the probability of landing on either head or tail is given as:
P = 1/2
C. Roll a die and evaluate the outcome as either even or odd:
A die has 6 faces with equal number of faces with equal number of even numbers and odd numbers, 3. Hence, the probability of rolling an even or odd number is given as:
P = 3/6 = 1/2
D. Throw a stone closest to an object:
This method is not fair because then it depends solely on who can throw the farthest i.e. the physical ability of the throwers.
E. Play a hand of blackjack
This method is flawed because it has unequal probabilities of winning and losing.
F. Ask a random stranger to select:
This method is unfair because it then depends solely on the random picker. The picker could have personal preferences or a bias based on maybe height, beauty, weight, basically anything characteristic. Hence, it is unfair.
Final answer:
Fair methods for deciding who gets the prize include placing both names in a hat, flipping a coin, and rolling a die as they provide equal chances of winning, while throwing a stone, playing blackjack, or asking a stranger can introduce bias or skill, making them unfair.
Explanation:
The methods that are fair include placing both names in a hat, asking a stranger to flip a coin, and rolling a die because these methods provide equal probabilities of winning or losing. Method D: Throwing a stone closest to an object is flawed due to increased chances of winning based on one's skill, which means it's not random. E: Playing a hand of blackjack is flawed due to poor randomization, as the cards dealt can create significantly different chances of winning. F: Asking a random stranger to select is flawed due to unequal probabilities of winning and losing if the stranger holds a bias, even if unintended.
Tossing a coin is a fair way to decide because both outcomes (heads or tails) have equal chances of occurring, which is a 50% chance each way. This is consistent with the principle of randomness and independent events, where the outcomes of past coin tosses do not influence the results of future tosses.
The U.S. Post Office is interested in estimating the mean weight of packages shipped using the overnight service. They plan to sample 300 packages. A pilot sample taken last year showed that the standard deviation in weight was about 0.15 pound. If they are interested in an estimate that has 95 percent confidence, what margin of error can they expect?A. Approximately 0.017 pounds B. About 0.0003 pounds C. About 1.96 D. Can't be determined without knowing the population mean.
Answer: A. Approximately 0.017 pounds
Step-by-step explanation:
Formula to find the margin of error :
[tex]E=z^*\dfrac{s}{\sqrt{n}}[/tex] , where z* = critical value for confidence interval , s= standard deviation , n= sample size.
As per given , we have
s= 0.15 pound
n= 300
Critical value for 95% confidence = 1.96
Then, Margin of error for 9%% confidence interval will be :
[tex]E=(1.96)\dfrac{0.15}{\sqrt{300}}\\\\=0.0169740979142\approx0.017[/tex]
Hence, they can expect a margin error of 0.017 pound (approximately.)
Thus , the correct answer is A. Approximately 0.017 pounds
What’s the Value for k?
Answer:
Step-by-step explanation:
The sum of the angles on a straight line is 180 degrees. Therefore,
Angle XYZ + angle MYZ = 180
Angle XYZ + 115 = 180
Angle XYZ = 180 - 115 = 65 degrees
The sum of the angles in a triangle is 180 degrees. It means that
Angle XZY + angle YXZ + angle MYZ = 180
Therefore,
4k + 5 + 6k + 10 + 65 = 180
4k + 6k + 5 + 10 + 65 = 180
10k + 80 = 180
10k = 180 - 80 = 100
Dividing the left hand side and the right hand side of the equation by 10, it becomes
10k/10 = 100/10
k = 10
Juan wants to paint somthing in the shape of a right rectangle prism. The prism is 17 in long 11 in wide and 9 in high. He had enough paint to cover 850 sq in. Dose he have enough paint? Explain your reasoning
Juan does not have enough paint to cover shape of a right rectangle prism
Solution:
Given that,
Juan wants to paint something in the shape of a right rectangle prism
From given,
Length = 17 inches
Width = 11 inches
Height = 9 inches
The surface area of prism is given as:
[tex]A=2(wl+hl+hw)[/tex]
Where, "l" is the length and "w" is the width and "h" is the height
Substituting the values we get,
[tex]A = 2(11 \times 17 + 9 \times 17 +9 \times 11)\\\\A = 2(187+153+99)\\\\A = 2 \times 439 \\\\A = 878[/tex]
Thus surface area of prism is 878 square inches
Given that,
He had enough paint to cover 850 sq in
No he cannot paint since surface area is 878 square inches which is greater than 850 square inches
So, he does not have enough paint