The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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Which equation represents the vertical line passing through (5,-4)?
Answer:
x = 5
Step-by-step explanation:
Since the line is vertical,
the equation of the line then is x = (some value).
Since this particular line passes throught (5,-4), where the x coordinate is 5, we can deduce the equation of this line to be x = 5.
The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
the area of the rectangle is 80. 1 cm²
What is the area of a rectangle?
From the given information, let's say one side of rectangle = a
The other side = (36 - 2a)/2
= 18 - a cm
The angles between the diagonals of the rectangle is 78°
Then, the angle diagonal has with base will give
= (180° - 78°)/2
= 102/2
= 51°
We have the angle to be 51 degrees, using the tan ratio
Tan θ = opposite/ adjacent
Opposite of angle 51 degrees = a
Adjacent = 18 - a
Thus,
[tex]tan 51 = \frac{a}{18 - a}[/tex]
[tex]1. 2349 = \frac{a}{18-a }[/tex]
cross multiply
[tex]18 -a ( 1. 2349) = a[/tex]
[tex]22. 23 - 1. 2349a = a[/tex]
collect like terms
[tex]a + 1. 2349a = 22. 23[/tex]
[tex]2. 2349 a = 22. 23[/tex]
[tex]a = \frac{22. 23}{2. 2349}[/tex]
a = 9. 95
If a = 9. 95cm
Then, 18 - a = 18 - 9. 95 = 8. 05cm
The formula of area of a rectangle is given as;
Area = width × length
Area = 9.95 x 8.05
Area = 80. 1 cm²
Thus, the area of the rectangle is 80. 1 cm²
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Find parametrization for the tangent line at time t0=13.
Use the equation of the tangent line such that the point of tangency occurs when t=t0 .
(Write your solution using the form (*,*,*). Use t for the parameter that takes all real values. Simplify all trigonometric expressions by evaluating them. Express numbers in exact form. Use symbolic notation and fractions as needed.)
Where will this line intersect the - plane?
(Write your solution using the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.)
The parametrization for the tangent line at time [tex]t_{0}[/tex] is (41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
The point of intersection is (40, -4, 0)
What is the parametrization for the tangent line at time [tex]t_{0}[/tex] and point of intersection?The given curve is defined parametrically by the equations
x = 3t + 2
y = 4 cos t
z = 4 sin t
To find the parametrization for the tangent line at time t0 = 13, we need to find the point of tangency and the direction vector of the tangent line.
The point of tangency is the position of the curve at time t0, which is
(3 * 13 + 2, 4 cos 13, 4 sin 13) = (41, -4/3, 4/3)
The direction vector of the tangent line is the derivative of the curve at time t0, which is
(3, -4 sin 13, 4 cos 13) = (3, -4/3, 4/3)
Therefore, the parametrization for the tangent line is
(41 + 3t, -4/3 + 4t/3, 4/3 + 4t/3)
b. To find the point where this line intersects the -plane, we set z = 0 and solve for t. This gives us
4/3 + 4t/3 = 0
t = -1/2
Therefore, the point of intersection is
(41 - 3/2, -2, 0) = (40, -4, 0).
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the alexander family and jenkins family each used their sprinklers last summer. the water output rate for the alexander familys sprinkler was 20 L per hour. theh water output rate fro the jenkins familys sprinkler was 25 L per hour. the familes used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1450 L. How long was each sprinkler used?
Answer:
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.
Step-by-step explanation:
Lets start with 2 assumptions, what if we only used the Alexander's family sprinklers, We can define X as the variable
[tex]20x=1450[/tex]
[tex]x= 72.5[/tex]
If we just used the Alexanders it would of took 72 hours and 30 minutes.
Now lets look at the Jenkins family sprinkler, lets define it as Y.
[tex]25y=1450[/tex]
[tex]y = 58[/tex]
With only the Jenkins it would of took 58 hours.
Now, if they just of shared the work equally among the two sprinklers, the Alexanders family doing 725 L and the Jenkins with the other half.
It would of took the Alexanders
[tex]20x= 725[/tex]
[tex]x=36.25[/tex]
Jenkins
[tex]25y=725[/tex]
[tex]y=29[/tex]
Making it a combined time of 65.25 hours. 15 minutes long of our 65 hour time.
Now the Jenkins sprinkler generates 5 more L than Alexanders per hour. Which means it would only take the Jenkins family 1 hours to make 25 liters but Alexanders would take [tex]\frac{5}{4}[/tex] hours. We know that 1 hour contains 60 minutes, which means [tex]\frac{1}{4}[/tex] of a hour contains 15 minutes.
So it would take Alexanders family sprinkler 15 minutes more to produce the same amount per hour that the Jenkins does.
So from this we can conclude that if the Jenkins family sprinkler was used more we can cut the extra 15 minutes off, making the answer That the
Alexanders family sprinkler used for 35.25 hours
And the Jenkins family sprinkler was used for 29.75 hours.
I don’t know the answer for question number 1
The area of QOR from the given diagram is 2π square centimeters
How to calculate the area of a sectorA sector is said to be a part of a circle made of the arc of the circle along with its two radii.
The formula for calculating the area of a sector is expressed as;
A = r²β/2
where
r is the radius of the circle
β is the angle subtended
Given the following parameters
<QOR = 180 - <POQ
<QOR = 180 - 135
<QOR = 45 degrees
Determine the radius
L = rβ
π = r(π/4)
1 = r/4
r = 4
Determine the area of QOR
Area = 4²(π)/8
Area = 2π
Hence the area of QOR from the given diagram is 2π square centimeters
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Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to the actors. How many pages were there in the program?
Answer:
Step-by-step explanation:
Comment
Let the number of pages = x
Play = 1/3x
Actors = 1/4(x - 1/3 x)
Actors = 1/4(2/3x)
Actors = 2/12 x
Producer Director etc = 2 pages
Equation
Actors = 2 pages
2/12 x = 2
Solution
2x/12 = 2 Multiply both sides by 12
12*2x/12 = 2*12 Combine
2x = 24 Divide by 2
2x/2 = 24/2 Combine
x = 12
Answer
The program had 12 pages.
a mother is 25 years older than her son.
Write down the son's age and the mother's age
Answer:
mother age 37
sons age 12
Find the value of x. (5x-40) (5x)
the first equation is inside the triangle at the bottom left but "5x" is at the bottom right on the outside of the triangle.
The value of x is 22
How to solve for x?Based on the description in the question,
The angles 5x -40 and 5x are angles on a straight line
So, we have:
5x - 40 + 5x = 180
Evaluate the like terms
10x = 220
Divide by 10
x = 22
Hence, the value of x is 22
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Proofs and congruent triangles 2 forgot to put images last time 50 points ( serious answer or 1 star and report ) ( YOU NEED TO CHECK MY ANSWERS PLEASE )
Answer:
Step-by-step explanation:
Q3 asks for reasons of statements in a theorem proof.
1 Given is correct
2 Definition of right angle is correct
3 should be sum of interior angles in a triangle
4 is substitution
5 subtracting 90degree from left and right hand side
6 is definition of complementary
What is the angle for x
Answer:
X = 90°Step-by-step explanation:
that is a regular rhombus, by definition it has perpendicular diagonals, so in the center there are 4 90 ° angles, so your answer is x = 90 °
If 2y=x³ + 2x², find dy/dx when x=2.
Answer:
10
Step-by-step explanation:
[tex]\boxed{\textsf{If }y=x^n,\: \textsf{then }\dfrac{\text{d}y}{\text{d}x}=nx^{n-1}}[/tex]
Given equation:
[tex]2y=x^3+2x^2[/tex]
Isolate y by dividing both sides by 2:
[tex]\implies y=\dfrac{1}{2}x^3+x^2[/tex]
Differentiate with respect to x:
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=3 \cdot \dfrac{1}{2}x^{3-1}+2 \cdot x^{2-1}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{3}{2}x^2+2x[/tex]
Finally, substitute x = 2 into the differentiated equation:
[tex]\begin{aligned} \implies \dfrac{\text{d}y}{\text{d}x} & =\dfrac{3}{2}(2)^2+2(2)\\\\ & = \dfrac{3}{2}(4)+4\\\\ & = \dfrac{12}{2}+4\\\\ & = 6+4\\\\ & = 10\end{aligned}[/tex]
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Convert 45 32’ 55” into decimal degrees to the nearest two decimal places
The decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
Converting degrees into decimalThe given degree is:
45⁰ 32' 55''
This can be converted to decimal as shown below
[tex]45+\frac{32}{60} +\frac{55}{3600}[/tex]
This can be simplified further as:
[tex]45^o32'55'' = 45+0.53+0.0153\\\\45^o32'55'' = 45.55^0[/tex]
Therefore, the decimal equivalent of 45⁰ 32’ 55” is 45.55⁰
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An employer provides two payment options for employees. Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks. Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks. (Score for Question 1: ___ of 2 points)
Based on the information, it can be inferred that payment option A means a payment of $450, while option B means a payment of $300.
How much money does each payment option receive?The payment options contemplated by the employer are distributed as follows:
Option A
First week: $200Second week: $200 + $50 = $250Third week: $250 + $50 = $300Fourth week: $300 + $50 = $350Fifth week: $350 + $50 = $400Sixth week: $400 + $50 = $450Option B
First week: $200Second week: $220Third week: $240Fourth week: $260Fifth week: $280Sixth week: $300Note: This question is incomplete because there is some information missing. Here is the missing information:
Complete the tables to show how much money would be received for both payment options, each week, for 6 weeks.
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I don’t have an answer but by any chance did you complete the assignment?
Help would really be needed asap!
Answer:
C
Step-by-step explanation:
For lines AC and EF, line FC is a transversal.
Angles ACF and EFC are same side interior angles.
Since their measures add to 180°, then the lines are parallel.
Answer: Choice C
How many kilometers are equal to 750 meters?
Answer:
[tex]0.75[/tex]
Step-by-step explanation:
750metres÷1000
The sum of three numbers is 24. If two numbers are 16 and 22, what is the third?
Answer:
X=-14
Step-by-step explanation:
16+22+x=24
38+x=24
x=24-38
x=-14
Express the following
The sum of the exponential expression is e^8x + e^2x
Simplifying exponential functionExponential functions are inverse of logarithmic function
Given the exponential function below;
(e^4x)² + e^2x
Expand
e^8x + e^2x
Hence the sum of the exponential expression is e^8x + e^2x
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Women appear to marry about 3 years younger than men, but the two distributions are very similar in shape and spread.
The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."
What is a box plot?A boxplot is a type of graph that shows how the values in the data are distributed.
A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").
It can provide information about your outliers and their values.
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Full Question:
In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.
Complete this activity.
If the first element of the following pairs of numbers is a measure of hours and the second element is a measure of distance in miles, write an equation for D.
B = {(t, D ): (1, 50), (2, 100), (3, 150), . . .}
D =
t /2
50 t
50/ t
Answer:
D = 50t
Step-by-step explanation:
we see, with every additional hour the distance increases by 50.
that means in general that the number of hours are multiplied by 50 to get the distance.
in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.
A town planner is interested in getting some demographic data about the households in the city. The city has ten wards that vary in size. Which sampling method is most appropriate?
The best sampling method that Is most appropriate for the town planner is called Stratified Sampling.
What is the Sampling Method used?The best sampling method that I would recommend for the town planner is called Stratified Sampling.
The reason for using stratified sampling is because it is a method of sampling that involves dividing a population into smaller groups–called strata and in this case, the rows of houses can be used as a strata.
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On a recent trip to the convenience store, you picked up 3 gallons of milk, 6 bottles of water, and 6 snack-size bags of chips. Your total bill (before tax) was $29.10. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.70 more than a bottle of water, how much does each item cost?
Hi
the trick is to define price by referring only to one item.
Here the bootle of water is you reference.
there is 3 gallons of milk
6 bottles of water
6 bags of chips
let's call bottle of water " X"
water cost = X
milk = X+1.7
chips = X/2
So we have :
3 (X+1.7 ) + 6X + 6 ( X/2) = 29.1
3X+ 5.1 + 6X + 6X/2 = 29.1
3X +6X + 3X + 5.1 = 29.1
12X +5.1 = 29.1
12X = 29.1 - 5.1
12 X = 24
X = 24/12
X = 2
price of bottle is 2 dollars
then milk is 2 + 1.7 = 3.7
chips = 2/2 = 1
let's check = 3*3.7 + 6*2 + 6*1 = 11.1+12+ 6 = 29.1
Using the following table, construct and interpret a 90% confidence interval for the population standard deviation of the carbon in metric tons.
Nation
Brazil
Germany
Mexico
Emissions
Canada
361
844
398
Great Britain 577
631
The 90 percent confidence interval for the data is given as 396.02, 727.98
First we have to find the meanThe formula is fx/n
= Mean, μ = 562.2
sum up the data and divide by 5
sd =
Σ(xi - μ)2/N
= (361 - 562.2)² + ... + (631 - 562.2)²/5
= 151806.8/5
= 30361.36
sd = √30361.36
= 174.24511470914
1 - confidence level
= 1 - 0.90
= 0.1
df = 4
Using excel
T.INV.2T(0.1, 4) = ±2.13
562 +- 2.13 x 174.245/√5
562- 165.98, 562+ 165.98
= 396.02, 727.98
Hence the confidence interval can be calculated to be 396.02, 727.98
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Use the equation and type the ordered-pairs. y=3^x
The ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
How to type the ordered pairs?The equation is given as:
y = 3^x
Let x = 0, 1 and 2
y = 3^0 = 1
y = 3^1 = 3
y = 3^2 = 9
So, we have the following ordered pairs (0,1), (1,3) and (2,9)
Hence, the ordered pairs of the equation y = 3^x are (0,1), (1,3) and (2,9)
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i) Baraka bought ksh.20,000 worth of shares of a company each month. During the first three months, he bought the shares at a price of ksh.120, ksh.160 and ksh.210.Compute the average price paid by him for the shares after 3 months
The average price paid by him for the shares after 3 months is ksh. 163.33
AverageTotal value of shares bought = ksh.20,000Amount of shares bought in the first three months = ksh.120, ksh.160 and ksh.210Average price paid for the shares after 3 months
= (120 + 160 + 210) / 3
= 490 / 3
= 163.333333333333
Approximately,
ksh. 163.33
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Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.
csc ß- sin ß
Choose the correct answer below.
OA. 1
B. cos ßcot B
OC. sin²B
OD. 1-sin² B
OE. sin² ßtan² ß
OF. cos B
...
Using trigonometric identities, the simplified expression, without quotients, is given as follows:
A. [tex]\cos{\beta}\cot{\beta}[/tex]
Which trigonometric identities are used to solve this question?The cosecant of an angle is given by one divided by the sine of the angle, hence:
[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]
The sine and the cosine of an angle are related as follows:
[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]
[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]
The cotangent of an angle is:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]
Which is the simplified expression?The expression given is:
[tex]\csc{\beta} - \sin{\beta}[/tex]
Simplifying the cosecant:
[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]
Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:
[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]
Hence option A is correct.
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When
a number is
Substracted from 2, the
result equal 4 less
than one-fifth
the
of
number. Find the number
everythings in the image
Answer:
t= d/r t=5
Step-by-step explanation:
divide each side by d to isolate t
use geometric shapes to create a logo that will fit in a measuring 15 cm by 15 cm
A geometric shapes that can be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.
What are geometric shapes?It should be noted that geometric shapes are the figure of area that is closed by a boundary.
In this case, a geometric shapes that. an be used to create a logo that will fit in a measuring 15 cm by 15 cm is to use a square.
This is because all the sides in a square are equal.
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The stemplot below represents the number of bite-size snacks grabbed by 10 students in an activity for a statistics class. A stemplot titled number of snacks. The stems are 1, 2, 3, 4. The first column of leaves is 5, 0, 2, 2. Column 2 is 6, 1, blank, blank, Column 3 is 6, 3, blank, blank. Column 4 is 7, blank, blank, blank, Column 5 is 9, blank, blank, blank. Key 2 slash 4 is a student who grabbed 24 snacks. What is the correct set of data for the stemplot? 15, 16, 17, 19, 20, 21, 23, 32, 42 15, 16, 16, 17, 19, 21, 23, 32, 42 15, 16, 16, 17, 19, 20, 21, 23, 32, 42 15, 15, 16, 17, 19, 20, 21, 23, 32, 42
The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.
According to the question
Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:
Row one, 1| 5 6 6 7 9 :
This means there are 5 data set for the first row which are:
15, 16, 16, 17, 19
Row two, 2|0 1 3 :
There are 3 data here, which are:
20, 21, 23
Row 3, 3|2: = 32
Row 4, 4|2: = 42
So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.
Correct option is C.
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Given f (x) = x2 + 4x + 5, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?
h2 + 8h
2x + h + 4
8 + h
h + 4
By evaluating the quadratic function, we will see that the differential quotient is:
[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]
How to get (f(2 + h) - f(2))/h?Here we have the quadratic function:
[tex]f(x) = x^2 + 4x + 5[/tex]
Evaluating the quadratic equation we get:
[tex]\frac{f(2 + h) - f(2)}{h}[/tex]
So we need to replace the x-variable by "2 + h" and "2" respectively.
Replacing the function in the differential quotient:
[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]
If we simplify that last fraction, we get:
[tex]\frac{8h + h^2}{h} = 8 + h[/tex]
The third option is the correct one, the differential quotient is equal to 8 + 4.
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