Answer:
2 + 109 = 111
Step-by-step explanation:
.............
If sin2 x + cos2 y = 2 sec2 z, then general solution of triplets (x, y, z) is
Answer:
x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I
Step-by-step explanation:
∴ LHS ≤ 2 and RHS ≥ 2
So, sin2 x = 1, cos2 y = 1 and sec2 z = 1
∴x=(n+12)π, y=mπ∴x=n+12π, y=mπ and z = rπ where n∈I, m∈I, r∈I
What is the approximate area of the unshaded region under the standard normal curve below? Use the portion of the standard normal table given to help answer the question.
A normal curve with a peak at 0 is shown. The area under the curve shaded is 1 to 2.
z
Probability
0.00
0.5000
1.00
0.8413
2.00
0.9772
3.00
0.9987
0.14
0.16
0.86
0.98
Answer:
0.14
Step-by-step explanation:
The z score is a score used in statistics to determine by how many standard deviations ti the raw score above or below the mean. If the raw score is above the mean then the z score is positive while If the raw score is below the mean then the z score is negative, It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, The area under the curve shaded is 1 to 2 = P(1 < z < 2) = P(z < 2) - P(z < 1) = 0.9772 - 0.8413 = 0.1359 ≈ 0.14
The area under the curve shaded is 1 to 2 is 0.14
What are probabilities?Probabilities are used to determine the chances of an event
The shaded region represents the probability of the z-scores
The shaded region 1 to 2 is represented as:
P(1 < z < 2) =
Using the probability of z-score, we have the formula
P(1 < z < 2) = P(z < 2) - P(z < 1)
From the given standard normal table:
P(z < 2) = 0.9772
P(z < 1) = 0.8413
So, we have:
P(1 < z < 2) = 0.9772 - 0.8413
P(1 < z < 2) = 0.1359
Approximate
P(1 < z < 2) = 0.14
Hence, the area under the curve shaded is 1 to 2 is 0.14
Read more about normal distribution at:
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A student says that a coordinate grid under a dilation with the center at the origin and scale factor 2 does not change the grid. The image is still a coordinate grid. How do you respond?
Answer:
Dilation changes (x,y) values not the grid or coordinate plane. Basically, dilating a graph or a coordinate grid means the original coordinates you may have had will be changed with the dilation. For example, a triangle plotted had its original area of 26 dilated to an area of 58.
In a mathematics class, half of the students scored 86 on an achievement test. With the exception of a few students who scored 46, the remaining students scored 77. Which of the following statements is true about the distribution of scores
Answer:
B. The mean is less than the median.
Step-by-step explanation:
Say there was 20 kids: 10 kids(half) scored 86's, 3 kids(a few) scored 45's, and 7 kids(the remaining) scored 77's.
The median would be- 81.5 (chronological order, find the middle number)
The mean would be- 76.85 (sum of all the scores divided by the number of scores)
The mode would be- 86 (most frequent number)
The mean(76.85) is less than(<) the median(81.5)
Choose the correct simplification of the expression (a^3/b^7)^2
Answer:
(a^3/b^7)^2 = (a^6/b^14)
find the factors of f(x), given that x = -2 is zero. f(x) = x³ + x² - 14x - 24
Answer:
x=-3 and x=4
Step-by-step explanation:
Since x=-2 is a zero of the function, we can find the other two factors by dividing f(x) by (x+2) using long division to obtain the other two roots. The quadratic obtained is x^2-x-12. Now factorising this quadratic will result in (x-4)(x+3)=0, x=-3 and 4 are the other rrots
The factorization of the function f(x) = x³ + x² - 14x - 24 will be (x + 2), (x + 3), and (x - 4).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The function is given below.
f(x) = x³ + x² - 14x - 24
Factorize the function, then we have
f(x) = x³ + x² - 14x - 24
f(x) = x³ + x² - 14x - 24
f(x) = x³ + 2x² - x² - 2x - 12x - 24
f(x) = x²(x + 2) - x(x + 2) - 12(x + 2)
f(x) = (x + 2)(x² - x - 12)
f(x) =(x + 2)(x² - 4x + 3x - 12)
f(x) = (x + 2)[x(x - 4) + 3(x - 4)]
f(x) = (x + 2)(x + 3)(x - 4)
The factorization of the function f(x) = x³ + x² - 14x - 24 will be (x + 2), (x + 3), and (x - 4).
More about the factorization link is given below.
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been stuck on this for a few days now, help on even one would be greatly appreciated!!!
Answer:
-5-9i
Step-by-step explanation:
-1-8i-4-i
-1-4-8i-i
-5-9i
Please help me answer the question
Answer:
fourth option
Step-by-step explanation:
Common difference is given by difference of two consecutive term
d = nth term - (n-1)th term
______________________________________
for all the series lets take second term as nth term
and first term as (n-1)th term
_________________________________________
for first series
n th term = -3 1/2 = -3.5
(n-1)th term = -5
therefore
d= -3.5 -(-5) = -3.5 +5 = 1.5
______________________________________
for second series
n th term = 4 1/2 = 4.5
(n-1)th term = 2 1/2 = 2.5
therefore
d= 4.5 -(2.5) =2
_________________________
for third series
n th term = 3
(n-1)th term =1.5
therefore
d= 3 - 1.5 = 1.5
__________________________________
for fourth series
n th term = -1.5
(n-1)th term = -4
therefore
d= -1.5 -(-4) = -1.5 + 4 = 2.5 = 2 1/2
___________________________________
Thus, based on above solution option four has common difference of 2 1/2
Convert the following:
4 quarts is equivalent to
ao liters (rounded to the hundredth)
Answer: 3.79 litres
Step-by-step explanation:
1 litre is equivalent to about 1.05668821 American quarts.
4 quarts would therefore be;
= 4/1.05668821
= 3.78541178
= 3.79 litres
Write six hundred twelve thousand, three hundred in the place-value chart. Then write the number in expanded
Answer:
612,300
600,000
10,000
2,000
300
00
0
A helicopter is at a cruising height of 1,200 feet. Suppose the angle of depression to the landing pad is 15°, which is located on top of a building that is 64 feet high. If the helicopter continues at the current cruising height, how far does the helicopter need to travel to be directly above the landing pad? Include a sketch that shows all known information and clearly shows what you need to find. Show all work and give the answer rounded to the nearest foot.
Answer:
we have a right triangle and to get the internal angle of the right triangle formed at the helicopter we subtract 62 degrees from 90 which equals 28 degrees
we now use the cosine to find the distance (d) from the helicopter
cosine 28 = 85/d
d = 85 / cosine 28 = 85 / 0.8829 = 96.2736 = 96 feet
You are an urban planner assessing the growth of a city. Ten years ago, the city's population was 250,823. Its current population is 325,823. By about what percentage has the city grown over the past ten years? Round to the nearest percent.
Answer:
Here is the answer i got-
Step-by-step explanation:
325823-250823=75000
325823’s 244367250percent is 75000
A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 52 in^2 and a perimeter of 30in. Find the dimensions of the brochure. The longer side is _____in. The shorter side is ______ in.
9514 1404 393
Answer:
9.562 in5.438 inStep-by-step explanation:
The sum of side lengths of a rectangle is half the perimeter, so is 15 inches for this brochure. If x is one of the side lengths, then (15 -x) is the other one, and the area is ...
x(15 -x) = 52
x^2 -15x = -52 . . . . multiply by -1 and expand
(x -7.5)^2 = -52 +56.25 = 4.25 . . . complete the square
x = 7.5 ±√4.25 ≈ {5.438, 9.562} . . . inches
The longer side is 7+√4.25 ≈ 9.562 inches; the shorter side is 7-√4.25 ≈ 5.438 inches.
F
13
5
H
12
G
se
Find mZH to the nearest degree.
67
O 18
O 45
O 23
Answer:
∠ H ≈ 23°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan H = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{FG}{HG}[/tex] = [tex]\frac{5}{12}[/tex] , thus
∠ H = [tex]tan^{-1}[/tex] ( [tex]\frac{5}{12}[/tex] ) ≈ 23° ( to the nearest degree )
What are the solutions of the system 7x + 3y=-3 and y= -2*?
Answer:
opt 4
Step-by-step explanation:
when x=0, 0+3y= -3, so y=-1 (0,-1) is solution
when x=3 , 21+3y=-3, 3y= -3-21= -24
y= -8 (3,-8) is also solution
1km make how many cm
Answer:
100000
Step-by-step explanation:
Solve 5x + 3 = -7x + 21
Why do interest rates on loans tend to be higher in a strong economy than in a weak one?
Amira starts an exercise programme on the 3rd of March. She decides she will swim every
3 days and cycle every 4 days. On which dates in March will she swim and cycle on the
same day?
Answer:
12 days
Step-by-step explanation:
The answer of the problem is the LCM of 3 and 4=12. Hence the answer is 12 days
On 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.
What is LCM?It is defined as the common number of two integers, which is the lowest number that is a multiple of two or more numbers. The full name of LCM is the least common multiple.
We have:
Amira starts an exercise program on the 3rd of March.
She will swim every 3 days and cycle every 4 days.
Total days =3 + 4 = 7 days = 1 week
The day she swims and cycles on the same day = LCM of 3 and 4
= 3, 6, 9, 12, 15
= 4, 8, 12, 16
= 12
Thus, on 12 March she will swim and cycle on the same day if Amira starts an exercise program on the 3rd of March.
Learn more about the LCM here:
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what is the number if 4 is subtracted from the sum of one fourth of 5 times of 8 and 10
Answer:18.5
Step-by-step explanation:
10+8=18
18*5=90
90/4
22.5-4=18.5
Which of the fractions below are less than 2/5? Select two.
Answer:
1/8 is less than
Step-by-step explanation:
i dont see any fractions below gona have to edit your answer
help asap!!
Find the length of AB
A. 2.89
B. 33.13
C. 378.63
D. 377.19
Answer:
C
Step-by-step explanation:
[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]
logx-log(x-l)^2=2log(x-1)
Answer:
x = 1.00995066776
x = 2.52925492433
Step-by-step explanation:
This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...
[tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]
The attached graph shows zeros at
x = 1.00995066776 and 2.52925492433
_____
Comment on the equation
Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068
Comment on the answer refinement
We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.
Choose two statements that are true for this expression.
5x3 – 6x2
25
y
+ 18
25
O A. The term
is a ratio.
B. There are three terms.
C. The entire expression is a difference.
O D. There are four terms.
Answer:
Step-by-step explanation:
I'm having difficulty reading your input: 25, y, + 18, 25. Please clarify your meaning.
5x3 – 6x2 is a polynomial expression with two terms.
The term is a ratio. False. See above.
The entire expression is a difference. True.
There are four terms. False. See above.
Two statements B and C are true for the expression 5x3 – 6x2 25y+ 18
How many options are correct for given expressio?
A. The term is a ratio. False
B. There are three terms.terms. True
C. The entire expression is a difference. True
D. There are four terms. False
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(3.5x10^8)x(4.0x10^-12)=
Answer:
Below
Step-by-step explanation:
● (3.5× 10^8) × (4×10^(-12))
● (3.5×4) × (10^8 × 10^(-12) )
● 14 × 10^ (-12+8)
● 14 × 10^(-4)
● 14/10^4
Geometry pls help !!! Find the value of AB.
AB = [?]
Answer:
AB = 16 Units
Step-by-step explanation:
In the given figure, CD is the diameter and AB is the chord of the circle.
Since, diameter of the circle bisects the chord at right angle.
Therefore, AE = 1/2 AB
Or AB = 2AE...(1)
Let the center of the circle be given by O. Join OA.
OA = OD = 10 (Radii of same circle)
Triangle OAE is right triangle.
Now, by Pythagoras theorem:
[tex] OA^2 = AE^2 + OE^2 \\
10^2 = AE^2 + 6^2 \\
100= AE^2 + 36\\
100-36 = AE^2 \\
64= AE^2 \\
AE = \sqrt{64}\\
AE = 8 \\
\because AB = 2AE..[From \: equation\: (1)] \\
\therefore AB = 2\times 8\\
\huge \purple {\boxed {AB = 16 \: Units}} [/tex]
find the area of this figure to the nearest hundredth. Use 3.14 to approximate pi.
Answer:
86.28 ft²
Step-by-step explanation:
The figure given consists of a rectangle and a semicircle.
The area of the figure = area of rectangle + area of semicircle
Area of rectangle = [tex] l*w [/tex]
Where,
l = 10 ft
w = 8 ft
[tex] area = l*w = 10*8 = 80 ft^2 [/tex]
Area of semicircle:
Area of semicircle = ½ of area of a circle = ½(πr²)
Where,
π = 3.14
r = ½ of 8 = 4 ft
Area of semi-circle = ½(3.14*4) = 6.28 ft²
Area of the figure = area of rectangle + area of semi-circle = 80 + 6.28 = 86.28 ft² (nearest hundredth)
Answer:
the area of the figrue is 105.12
Step-by-step explanation:
area of rectangle A= l · w10 x 8= 80area of simi-circle= 1/2(3.14 x r²)1/2 x 3.14 x 4²=25.1280+25.12=105.12 (nearest Hundredth)A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,722. Suppose that a random sample of 50 accounting graduates at a large university who received job offers resulted in a mean offer of $49,870 and a standard deviation of $3900. Do the sample data provide strong support for the claim that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722? Test the relevant hypotheses using α = 0.05. State your conclusion.A. Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.B. Do not reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.C. Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.D. Do not reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Answer:
Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.
Step-by-step explanation:
First of all let's define the hypothesis;
Null hypothesis;H0; μ = $48,722
Alternative hypothesis;Ha; μ > $48,722
Now, let's find the test statistic for the z-score. Formula is;
z = (x' - μ)/(σ/√n)
We are given;
x' = 48,722
μ = 49,870
σ = 3900
n = 50
Thus;
z = (49870- 48722)/(3900/√50)
z = 2.08
So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526
This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722
An athletic club charges a monthly membership
fee of $65. Members can also take classes for an
additional $15 per class. For this month only, the
club has a special that includes two free classes for
all new members. Which of the following functions
expresses the cost for the month for new members
who take x classes this month, where x > 2?
(A) C(x) = 2x + 65
(B) C(x) = 15x + 65
(C) C(x) = 2(x - 15) + 65
(D) C(x) = 15(x - 2) + 65
What is the true solution to the equation below? 2 in e in2×-in e in 10×= in 30 A x=30 B x=75 C x=150 D x=300
Answer:
Option B.
Step-by-step explanation:
Let as consider the given equation:
[tex]2\ln e^{\ln 2x}-\ln e^{\ln 10x}=\ln 30[/tex]
It can be written as
[tex]2(\ln 2x)-(\ln 10x)=\ln 30[/tex] [tex][\because \ln e^a=a][/tex]
[tex]\ln (2x)^2-(\ln 10x)=\ln 30[/tex] [tex][\because \ln a^b=b\ln a][/tex]
[tex]\ln \dfrac{4x^2}{10x}=\ln 30[/tex] [tex][\because \ln \dfrac{a}{b}=\ln a-\ln b][/tex]
[tex]\ln \dfrac{2x}{5}=\ln 30[/tex]
On comparing both sides, we get
[tex]\dfrac{2x}{5}=30[/tex]
Multiply both sides by 5.
[tex]2x=150[/tex]
Divide both sides by 2.
[tex]x=75[/tex]
Therefore, the correct option is B.
Answer:
b x=75
Step-by-step explanation: