Answer:
$1226.78<x<$1301.22
Step-by-step explanation:
The formula for calculating confidence interval is expressed as;
CI = xbar ± z×(s/√n)
Given
Mean (xbar) = $1264
z is the z score at 90% CI = 1.645
s is the standard deviation = $150
n is the sample size = 44
Substitute
CI = 1264±1.645(150/√44)
CI = 1264±1.645(150/6.63)
CI = 1264±1.645(22.624)
CI = 1264±37.22
CI = (1264-37.22, 1264+37.22)
CI = (1226.78, 1301.22)
Hence the confidence interval of the mean is $1226.78<x<$1301.22
Solve the equation in the interval [0,360). Use an algebraic method.
Answer:
70.9,109.1,204.0,336.0
Step-by-step explanation:
The solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given equation is 6sin² θ - 7 sinθ = 5
Lets arrange in an order
6sin² θ - 7 sinθ - 5 = 0
a=6, b=-7 and c = -5
sinθ = 7±√49+120/12
Simplifying under the square root:
sinθ =7±17/12
Taking the positive solution first
sinθ =24/12
sinθ =2 (Not valid)
Now let's try the negative solution:
sinθ =7-17/12
sinθ =-10/12
sinθ =-5/6
θ= sin⁻¹(-5/6)
θ= −50.48⁰ ,−129.52⁰
we need to restrict our solution to the given interval [0,360), so we add 360 degrees to the negative angle:
θ=360−50.48 = 309.52 and 360 −129.52 =230.48
Therefore, the solution set for the equation 6sin² θ - 7 sinθ - 5 = 0 in the interval [0,360)is {θ∈ [0,360)∣θ = 230.48 ,309.521}
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14) Find the product of seven times five and two
thousandths.
Answer:
35.015
Step-by-step explanation:
see attached image
Question
9. Deb ordered a set of red and yellow pins. She received 220 pins, and 40% of them were red. How many yellow pins did Deb
receive?
I’ve never been good with math, can u help?
In the following expression, both A and B are variables that can take positive values.
2\sqrt(A)-(B)/(5)
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
(Choice A)
Keeping A constant and increasing B
(Choice B)
B
Keeping A constant and decreasing B
(Choice C)
C
Increasing A and keeping B constant
(Choice D)
D
Decreasing A and keeping B constant
Answer:
(Choice B) Keeping A constant and decreasing B
(Choice C) Increasing A and keeping B constant
Step-by-step explanation:
Let us analyze these two options.
2√a - b /5
(Choice B) Keeping A constant and decreasing B
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
But if A is kept constant and B is decreased to 20
2√100 - 20/5
= 2(10) - 4
= 20 -4= 16
We see the expression value has increased from 14 to 16.
Similarly analyzing Option C
(Choice C) Increasing A and keeping B constant
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
Now increasing A to 121 and keeping B constant would give
Let a = 100 and b= 30
2√121 - 30/5
= 2(11) - 6
= 22 -6= 16
This also increases the expression's value
But the other two choice A and D do not give the same result.
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
(Choice A)
Keeping A constant and increasing B
2√100 - 40/5
= 2(10) - 8
= 20 -8= 12
This decreases the value .
Also
(Choice D)
Decreasing A and keeping B constant
2√81 - 40/5
= 2(9) - 8
= 18 -8= 10
This also decreases value
The correct choices are B and C
Answer:
the acutal solution is B and D
The cost of a new laptop is $750 which generates a sales tax amount of 37.50. What is the sales tax rate.
Answer:
5 percent.
Step-by-step explanation:
Divide tax by the cost to see the percentage of the tax.
750/37.50=0.05
5 percent.
What is the slope of the line shown below?
Answer:
m=-2
Step-by-step explanation:
Tell whether (1,-1) is a solution of y
9x - 10
Answer:
yes, it is
Step-by-step explanation:
plug in the point (1, -1) (x,y) into the equation y = 9x - 10
-1 = 9(1)-10
-1 = 9-10
-1=-1
The concentration C of certain drug in a patient's bloodstream t hours after injection is given by
C(t)= t/3t^2+5
Required:
a. Find the horizontal asymptote of C(t). (Answer must be in slope-intercept form.)
b. Determins what happens to the concentration of the drug as t increases. As t increases, what value will c(t) approach.
c. Determine the time at which the concentration is highest.
Answer:
a) The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) The time at which the concentration is highest is approximately 1.291 hours after injection.
Step-by-step explanation:
a) The horizontal asymptote of [tex]C(t)[/tex] is the horizontal line, to which the function converges when [tex]t[/tex] diverges to the infinity. That is:
[tex]c = \lim _{t\to +\infty} \frac{t}{3\cdot t^{2}+5}[/tex] (1)
[tex]c = \lim_{t\to +\infty}\left(\frac{t}{3\cdot t^{2}+5} \right)\cdot \left(\frac{t^{2}}{t^{2}} \right)[/tex]
[tex]c = \lim_{t\to +\infty}\frac{\frac{t}{t^{2}} }{\frac{3\cdot t^{2}+5}{t^{2}} }[/tex]
[tex]c = \lim_{t\to +\infty} \frac{\frac{1}{t} }{3+\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{\lim_{t\to +\infty}\frac{1}{t} }{\lim_{t\to +\infty}3+\lim_{t\to +\infty}\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{0}{3+0}[/tex]
[tex]c = 0[/tex]
The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) From Calculus we understand that maximum concentration can be found by means of the First and Second Derivative Tests.
First Derivative Test
The first derivative of the function is:
[tex]C'(t) = \frac{(3\cdot t^{2}+5)-t\cdot (6\cdot t)}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}-\frac{6\cdot t^{2}}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right)[/tex]
Now we equalize the expression to zero:
[tex]\frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right) = 0[/tex]
[tex]1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]\frac{3\cdot t^{2}+5-6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]5-3\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{5}{3} }\,h[/tex]
[tex]t \approx 1.291\,h[/tex]
The critical point occurs approximately at 1.291 hours after injection.
Second Derivative Test
The second derivative of the function is:
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}-\frac{(12\cdot t)\cdot (3\cdot t^{2}+5)^{2}-2\cdot (3\cdot t^{2}+5)\cdot (6\cdot t)\cdot (6\cdot t^{2})}{(3\cdot t^{2}+5)^{4}}[/tex]
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}- \frac{12\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
[tex]C''(t) = -\frac{18\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
If we know that [tex]t \approx 1.291\,h[/tex], then the value of the second derivative is:
[tex]C''(1.291\,h) = -0.077[/tex]
Which means that the critical point is an absolute maximum.
The time at which the concentration is highest is approximately 1.291 hours after injection.
How many yards will the players have run ?? Please help
Answer:
125.3 yards
Step-by-step explanation:
He wants them to run the so 110^2+60^2 =which is 125.3.
Hope this helps plz mark brainliest :D
In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" and
mNQP = 33. Justify why QNP must be isosceles.
Answer/Step-by-step explanation:
Let's find the measure of the angles of ∆QNP.
∆QMN is am isosceles ∆, because it has two equal sides. Therefore, its base angles would be the same. Thus:
m<MNQ = ½(180 - 48) (one of the base angles of ∆QMN)
m<MNQ = ½(132) = 66°
Next, find m<QNP
m<QNP = 180° - m<MNQ (linear pair angles)
m<QNP = 180° - 66° (Substitution)
m<QNP = 114°
Next, find m<P
m<P = 180 - (m<QNP + m<PQN) (sum of ∆)
m<P = 180 - (114 + 33)
m<P = 180 - 147
m<P = 33°
Thus, in ∆QNP, there are two equal angles, namely, <P and <PQN.
An isosceles ∆ had two equal base angles. Therefore, ∆QNP must be an isosceles ∆.
An isosceles triangle is that the triangle must have two sides of equal length.
Triangle QNP is isosceles triangle because, QN = PN
In triangle QMN,
Since, QM = QN
So, ∠QMN = ∠QNM
By property of triangle:
∠MQN + ∠QNM + ∠QMN = 180
48 + 2 ∠QNM = 180
∠QNM = [tex]\frac{180-48}{2}[/tex] = 66 degree
So, ∠QMN = ∠QNM = 66 degree
from figure,
∠QNM + ∠QNP = 180
∠QNP = 180 - 66 = 114 degree.
In triangle QNP,
∠QNP + ∠PQN + ∠QPN = 180
∠QPN = 180 - 33 - 114 = 33 degree
Since, ∠QNP = ∠QPN = 33 degree
Therefore, triangle QNP is isosceles triangle.
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Please help me! I’ve been trying to find this for an hour );
Answer:
I got (4x+3)(3x+1)
Hope I help Please mark me BrainIIest please and thank you :)
Step-by-step explanation:
3
If a is 63% of x and c is
8
the closest equivalent of the ratio of a to c?
ã of x, which of the following is
O
С C
E
Answer:
The closest equivalent of the ratio of a to c will be:
a/c=1.680
Step-by-step explanation:
As 'a' is 63% of x
so
[tex]a=0.63x[/tex]
As 'c' is 3/8 of x
so
c=3/8
Thus, the closest equivalent of the ratio of a to c will be:
a/c = (0.63x)/(3/8x)
= 1.680
Therefore, the closest equivalent of the ratio of a to c will be:
a/c=1.680
David cycled 4 laps on a bicycle path surrounding a lake. Each lap was the same length. If he cycled a total of 13.2 mi, what was the length of each lap around the lake? Write your answer in feet.
it's probably 17424 feet
Find the x-and y-intercepts.
2x – 3y = -6
Answer:
y intercept is 2 x =-3
Step-by-step explanation:
2x-3y=-6
subtract 2
-3y=-2×-6
divide by -3
y=2/3+2
×
0=2/3x+2
-2=2/3×
-3=x
Help me out here pleaseeeeeeeeeeeeeeeeeee
Answer:
im 90% sure its A
Step-by-step explanation:
y=1/x-2+1 the domain and range of this function
Answer:
Domain=(-infinity,0)
Range: (-infinity,-1)
Step-by-step explanation:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.
Is this a function please help I’m failing
Answer:
No
Step-by-step explanation:
This relation is not a function. This line has repeating x-values, it only has one so each y-value cannot have a unique x-value. For this reason, no vertical line will ever be a function.
Find the next three terms of the sequence: 33, 25, 18, 12, …….
a) 7, 2, -1
b) 8, 3, 0
c) 7, 3, 0
d) 6, 2, -1
pls help and show work
The required terms are 7, 3 and 0. The correct option is (c).
What is an arithmetic sequence?
An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given sequence is as below,
33, 25, 18, 12, …….
The difference between the consecutive terms is given as,
D₁ = 25 - 33
= -8
D₂ = 18 - 25
= -7
D₃ = 12 - 18
= -6
It is clear that the difference between the consecutive terms are in arithmetic progression.
Thus, the next differences can be found as,
D₄ = -6 + 1
= -5
D₅ = -5 + 1
= -4
And, D₆ = -4 + 1
= -3
The next three terms of the sequence can be written as,
12 - 5 =7, 7 - 4 = 3, 3 - 3 = 0.
Hence, the next three terms of the given sequence are 7, 3 and 0.
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change 0.18 into a ratio
I WILL GIVE BRAINLIEST
Tell whether the following equations represent a linear function.
10x + 2y = 4
−x² + 3y = 19
6x + 1/2y = 3
Answer:
Tell whether the following equations represent a linear function.
10x + 2y = 4--linear equation✓
−x² + 3y = 19--quadratic equation
6x + 1/2y = 3--linear equation✓
School lunch costs $1.25 per day. If there are 21 school days
this month, how much would it cost to eat at school all
month?. SHOW YOUR WORK., i need help asap
Answer:
$26.25
Step-by-step explanation:
1.25 per day
21 days
1.25 × 21 = 26.25
combine like terms 2.4m- 125 + 1.8b+ 92.4
Answer:
2.4m+1.8b−32.6
Step-by-step explanation:
Group like terms together
1. 2.4 m + \left( - 125 + 92.4 \right) + 1.8 b2.4m+(−125+92.4)+1.8b
2 . Add or subtract the numbers
2.4 m- 32.6 + 1.8 b2.4m−32.6+1.8b
3 . Rearrange the expression
2.4 m + 1.8 b- 32.62.4m+1.8b−32.6
Answer:
2.4m+1.8b-32.6
Step-by-step explanation:
2.4m- 125 + 1.8b+ 92.4
2.4m+1.8b-32.6
What type of dance does a geometry teacher like
Answer:
line dancing, square dancing, etc
Step-by-step explanation:
Answer: square dancing, circle dancing, line dancing.
Hope this helps... Stay safe and have a great day/night!!! :D
What is the degree of the polynomial, 2y23+3x25-16x26?
25
23
26
16
Please help me will give brainliest for the person that answers it correctly.
Answer:
This graph has a slop of 0
Step-by-step explanation
see the included picture of the graph
I have 12 coins x of them are R5 coins and the rest are R1 coins. An expression in the in terms of x for the number of R1 coins I have is
Answer:
ans= 12-x=r1 coin...
Step-by-step explanation:
hope u can do..
In the diagram, LaTeX: \Delta ABC\cong\Delta DFE
Δ
A
B
C
≅
Δ
D
F
E
. Find the values of x and y.
Answer:
x = 13
y = 8
Step-by-step explanation:
Lola plans to visit her friend in another state. The distance to her friend is
1297 miles. If she leaves on Friday and drives 7 hours at a time at 60 mph,
when will she get there?
Answer: In three days
Step-by-step explanation:
What is the volume of a cylinder ft, with a height of 9 feet in a base diameter of 16ft? Round to the nearest tenths place ?
1809.56ft³ <<<<<<<<<<<<<<<<Answer
Answer:
452.7 ft³
Step-by-step explanation:
sooooo first you find the radius of the base.
Radius=16/2=8
now you find the area of the base:
Area of a circle=2(pi)(radius)=50.3 ( rounded up to the nearest 10ths)
now to get the volume:
volume of a cylinder=Base*hight=50.3*9= 452.7 ft³
Whats the correct answer need help right now
I’ll be giving extra points(brainliest)
Answer:
The correct answer would be D. It would not be a linear function because the rate of change is not constant.
Step-by-step explanation:
The rate of change is not constant since it is not adding by a same number each time.