Please help me with this problem, I've been trying for more than twenty minutes. pls help.
Answers
Answer:
The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.
We begin by multiplying out the left-hand side of the inequality to obtain:
(n²-17)(n²-100)≤0
This expression can be further simplified by multiplying out the terms in the brackets, which gives us:
n⁴ - 117n² + 1700 ≤ 0
To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:
n⁴ - 117n² + 1700 = 0
n² (n² - 117) + 1700 = 0
(n² - 19)(n² - 90) + 1700 = 0
(n² - 19)(n² - 90) = -1700
To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:
n² - 19 = 0 or n² - 90 = 0
n² = 19 or n² = 90
n = ±√19 or n = ±√90
Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime
Related Questions
Please give me detailed answer
Answers
The values of x, y and z are 5, 18 and 12 using the congruent triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
In congruent triangles all the sides are equal, with respect to the other triangle.
Calculation:Given that ΔUVW≅ΔTSR.
We can see that in TSR triangle the lengths of TR and TS are given as 50 and 53 now the remaining side RS is 5y-33 as we know that both triangles are similar we compare side RS with side VW
i.e..,
5y-33 = 57
5y = 90
y = 18
So we can now compare vertices vertex V is vertex R , vertex W is vertex S and vertex U is vertex T.
So equating the sides of triangles we get,
12x-7 = 53 and 3z+14 = 50
12x = 60 3z = 36
x= 5 z = 12
The values of x, y and z are 5, 18 and 12 using the similar triangles properties and triangles sum properties.
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pls help with both questions
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You are given the figure below as well as following. Explain how a and b are parallel. Explain giving measurements and angels. Angels should be part of your answer.
Answers
Answer:
Since angle 9 is 110 degrees, that means that angle 10 must be 70 degrees, because the angle is on a straight line, so the angles must add to be 180 degrees, because they are supplementary angles. Since p ll q (p is parallel to q), that means that angle 1 is 110 degrees and angle 2 is 70 degrees. Because angles 1, 2, 5, and 6 have to add to be 360 degrees and angles 1+2 equals 180 degrees, that means that 5+6 equals 180 degrees as well. Angle 6 equals 110 degrees so that means angle 5 is 70 degrees. On the other side, angle 8 is 70 degrees, and since the two angles are the same, p and q are the same.
it is expected that 35% of students in a math course offered at northern university will earn an a. using excel to approximate the binomial distribution with a normal distribution, find the probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn an a.
Answers
The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..
We have given that,
A data of students in a math course offered at northern university will earn .
Total number of randomly selected students enrolled in the course = 300
i.e total number of trials, n = 300
probability of success, p = 35% = 0.35
probability of failure, q = 1-0.35 = 0.65
np = 300× 0.35 =
n(1-p) = 300×0.65 =
both np and n(1-p) are greater than 10 , so we can use normal approximation here.
We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)
P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
Now, P(X>75) = 1 - P(X=<75)
but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)
where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.
Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as
=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081
=BINOM.DIST(75,300, 0.35, FALSE)
= 5.0305E-05
Now, the required probability, P(X> 75)
= 1 - P(X ≤75)
= 1 - 5.03095E-05 = 0.999949691
or using cumulative distribution function,
P(X>75) = 0.999873919
both are give approx. same results
.So, required probability is 0.9998.
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Consider two securities, a and b. security a and b have a correlation coefficient of 0.65. security a has standard deviation of 12, and security b has standard deviation of 25. calculate the covariance between these two securities.
a. 300
b. 461.54
c. 261.54
d. 195
e. 200
Answers
The correct answer is option D. The covariance between securities a and b is 195.
To calculate the covariance between securities a and b, we can use the formula:
covariance = correlation coefficient * standard deviation of security a * standard deviation of security b
Plugging in the given values, we get:
covariance = 0.65 * 12 * 25 = 195
Therefore, the answer is (d) 195.
The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.
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Evaluate the following 14/2+4*4-4
Answers
Answer:
14/2+4x4-4= 19
Step-by-step explanation:
calculate
7+19-4
which is 19
(BODMAS rule is used here)
14/2 + 4 × 4 - 4
7 + 4 × 4 - 4
7 + 16 - 4
7 + 12
19
please mark brainliest <3
H(x) = -4x - 3, find h (2)
Answers
Multiple -4•2 =-8
-8-3
Answer -11
Mark Brainly pls
Answer:
h(2) = (-11)
Step-by-step explanation:
h(x) = (-4x - 3), if h(2)
h(2) = (-4(2) - 3)
h(2) = -8 - 3
h(2) = (-11)
Thus, The answer is (-11) if h(2)
3. (8.4B) The graph below shows the relationship
between the number of dollars a worker earns,
and the number of hours worked. What does the slope of the graph represent? HELP PLEASE
Answers
The slope of the graph represent d)The number of hours worked to earned dollors
What is Slope of the graph?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)and Todhunter'sformulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which provides the same valueTo learn more about Slope of the Graph refer to:
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is this a function (1, 8.5)(2, 8)(3, 7.5)(4, 7)(5, 6.5)(6, 6)
Answers
Yes, because no x values repeat.
The above table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown.Which of the following statements is supported by the table and boxplot?answer choicesThe range of the distribution is 20 years.There were 43 people who attended the lecture.At least 50% of the people who attended the lecture were 43 years or younger.At least 75% of the people who attended the lecture were age 53 years or younger.At least 25% of the people who attended the lecture were 33 years old.
Answers
The boxplot shows that the majority of the people who attended the lecture were age 53 or younger, which means at least 75 percentage of the people were in that range.
The table and boxplot provide information about the ages of the people who attended a lecture last week. The boxplot shows that the majority of the people who attended the lecture were age 53 or younger. This is supported by the table, which shows that the median age is 53 and the interquartile range is between 36 and 53. This indicates that at least 75% of the people who attended the lecture were age 53 years or younger. The range of the distribution is 20 years, with the minimum age being 18 and the maximum age being 38. This suggests that there were at least two people in each age range, from 18 to 38. This also indicates that there were at least 43 people who attended the lecture. The boxplot also shows that at least 25% of the people who attended the lecture were 33 years old. This is supported by the table, which shows the lower quartile is 33.
Interquartile range = Maximum - Minimum
Interquartile range = 53 - 36 = 17
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2
Write the correct answer in the box. Substitute numerical values into the expression for all known variables.
Jeff wants to purchase a television for his first apartment. The television costs $750. He can get a zero-interest loan for the television if he pays $100
per month. At the same time, he puts away $200 per month in savings. To figure out when his savings will equal the remaining amount he owes on
the television, he starts writing a system of equations:
Equation 1: y=200x
Equation 2:
Write the second equation in the system.
y=??????
Answers
Answer:
Equation 2: y=750-100x
Step-by-step explanation:
A shoe store uses a 60% markup for all of the shoes it sells. What would be the selling price of a pair of shoes that has a wholesale cost of $55?
Answers
Answer:The selling price of shoes after a markup of 60% of the price will be equal to $81.60
Step-by-step explanation:
i don't think this is right
how do you solve -40 -(-12/5) =
Answers
Answer:
Below
Step-by-step explanation:
-40 -(-12/5) = -200/5 + 12/5 = -188/5 = - 37 3/5
7. Sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants
she packed. The total number of pairs of pants and shirts was 16.
A. Let x = the number of pants she packed and let y = the number of shirts she packed. Write a system of
equations to represent the problem.
B. Solve the system of equations using substitution to find the number of shirts and pairs of pants Sylvia
brought.
Answers
The system of equations is x + y = 16 and y = 2x - 2
The number of shirts and pairs of pants Sylvia brought are 10 and 6, respectively
How to determine the system of equations?From the question, we have the following parameters that can be used in our computation:
x = the number of pants she packed y = the number of shirts she packedWhen the statements are interpreted, we have the system of equations to be
x + y = 16
y = 2x - 2
The solution of the equationIn (a), we have
x + y = 16
y = 2x - 2
This gives
x + 2x - 2 = 16
Evaluate the like terms
3x = 18
Divide
x = 6
Recall that
y = 2x - 2
So, we have
y = 2 x 6 - 2
y = 10
Hence, the number of shirts she packed is 10
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Select all terms equivalent to √24.
A: the area of a square with side length 24 units
B: the side length of a square with area 24 units
C: the positive number x, where x - x = 24
D: the positive number y, where y = 24-24
E: the edge length of a cube with volume 24 cubic units
F: the volume of a cube with edge length 24 units
Answers
Answer:
B, E
Step-by-step explanation:
Is DEF = ABC? If so, type the reason, if not type no.
Answers
Answer:
Yes
Step-by-step explanation:
All you need to do is figure out the missing angles. We know that the three angles in a triangle add up to 180 degrees.
For angle B in ABC, 180-52-39= 89. So angle B = 89 degrees.
For angle D in DEF, 180-39-89= 52. So angle D = 52 degrees.
Then see if the order of the angles match up.
DEF = 52 degrees, 89 degrees, 39 degrees
ABC = 52 degrees, 89 degrees, 39 degrees
The order of the same angles match, so triangle DEF and triangle ABC are equal.
Answer:
Yes, triangle DEF is similar to triangle ABC because their corresponding angles are the same size.
Step-by-step explanation:
Interior angles of a triangle sum to 180°.
⇒ ∠A + ∠B + ∠C = 180°
⇒ 52° + ∠B + 39° = 180°
⇒ ∠B = 89°
⇒ ∠D + ∠E + ∠F = 180°
⇒ ∠D + 89° + 39° = 180°
⇒ ∠D = 52°
Two triangles are similar if their corresponding angles are the same size.
If ΔDEF ~ ΔABC then:
∠D = ∠A∠E = ∠B∠F = ∠CFrom inspection of the given diagram:
∠D = 52° and ∠A = 52° so ∠D = ∠A∠E = 89° and ∠B = 89° so ∠E = ∠B∠F = 39° and ∠C = 39° so ∠F = ∠CTherefore, the triangles are similar because their corresponding angles are the same size.
A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p^= the proportion of residents who have been exposed in a random sample of 240.
The standard deviation of p^ is approximately...
Answers
The standard deviation of p^ is approximately 0.00012.
What do you mean by standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.
How to calculate standard deviation?The formula for standard deviation S.D is given below:
By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Calculation:
The formula for standard deviation S.D is given below:
Here,P = 3% = 0.03 and N = 240
∴ S.D = √0.03(1 - 0.03)/240
∴ S.D = 0.00012.
The standard deviation of p^ is approximately 0.00012.
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the height of a triangle is 2 more than twice the base. the area is 20 square feet. find the quadratic equation that represents this situation if the formula for the area of a triangle is A = 1/2 bh.Select one a. 2b^2 - b - 20 = 0b. b^2 + 2b= 0с. b^2 + b - 20 = 0d. b^2 + 2b + 20 = 0
Answers
On solving the provided question we can say - area = 1/2 x b x (2b+2), area = [tex]b^2 + b -20 {[/tex]
What is Triangle?A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees. A three-sided form is a triangle. Triangles are known by a variety of names. Triangle kinds are determined by the size of the angles and the length of the sides (angles). Depending on how long their sides are, triangles fall into one of three categories. Isosceles, equilateral, and uneven
Let 'b' be the base of the triangle, then
then height is - 2b + 2
area = 1/2 bxh
area = 1/2 x b x (2b+2)
area =
[tex]b^2 + b -20 {[/tex]
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6. Calculate the number that you need to add to each side of the equation w 2– 3w = 350 to create a perfect square trinomial. Add this number to each side of the equation. Show your work. (3 points)
7. Factor the trinomial. (3 points)
Answers
The number that we need to add is 1.5^2 = 2.25, we will get the perfect square trinomial:
(w - 1.5)^2 = 352.25
How to complete squares here?Remember that a perfect square trinomial is:
(a - b)^2 = a^2 - 2ab + b^2
Here we have the quadratic equation:
w^2 - 3w = 350
We can rewrite this as:
w^2 - 2*1.5*w = 350
Then what we need to add and subtract is 1.5^2, then we will get:
w^2 - 2*1.5*w = 350
w^2 - 2*1.5*w + 1.5^2 - 1,5^2 = 350
Grouping the first 3 terms we will get:
(w - 1.5)^2 - 1.5^2 = 350
(w - 1.5)^2 = 350 + 1.5^2
(w - 1.5)^2 = 352.25
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The farm's owner wants to increase the income from the sale of strawberries to at least $70,000 per year. What change would you suggest that would allow the farm's owner to meet this goal?
Answers
Answer:
Possible changes —
(i) Increase farmland
(ii) Sow healthy strawberry seeds
(iii) Choose a nutrient-rich, suitable plot of land
A basketball team has 12 players. For the last game of the season the coach will randomly select 5 players to start the game. The first player selected is the center, the second player selected is the power forward, the third player selected is the forward, the fourth player selected is the shooting guard, and the fifth player selected is the point guard. Determine the number of different ways the coach can pick up he line of the game
Answers
The number of different ways the coach can pick up the line of the game is 792 ways
Step-by-step explanation:
Let n- number of players, r-selection of players.
We can select them using Combination: nCr = 12C5
Combination formula nCr =[tex]\frac{n!r!}{ (n-r)!}[/tex] = 12C5 = [tex]\frac{12!5!}{(12-5)! }[/tex]
=[tex]\frac{12!5!}{ 7!}[/tex]
= 792ways
The number of different ways the coach can pick up the line of the game is 792 ways.
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The cash register receipts each day last week at a coffee shop were $1,846, $1,521, $1,439, $1,439, $1,851, $2,722, and $2,540. (a) Find the mean. (Round your answer to to the nearest cent.)
Answers
9. Mai rode on a train at a rate of speed of 70 miles per hour for 3 hours. Then she rode in a car at a rate
of speed of 50 miles per hour for 2 hours. What is the difference between the number of miles Mai
rode on the train and the number of miles she rode in the car?
a. 20
b.
60
c.
100
d. 110
Answers
The difference between the number of miles travelled on train and car is 110 miles
How to determine the difference between the number of milesFrom the question, we have the following parameters that can be used in our computation:
Distance 1 (train): 70 miles per hour for 3 hoursDistance 2 (car): 50 miles per hour for 2 hoursThe difference between the distance covered can be calculated as
Distance difference = The difference of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance difference = 70 * 3 - 50 * 2
Evaluate the products
Distance difference = 210 - 100
Evaluate the difference
Distance difference = 110 miles
Hence, the distance difference is 110 miles
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part 1: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight east, the other is traveling 384 mph straight west.
How long will it take before they are 6045 miles apart?
part 2: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight NORTH, the other is traveling 384 mph straight WEST.
How long will it take before they are 1997 miles apart?
Answers
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.
If the distance between them is 6045 miles. Then the time is calculated as,
T = 6045 / (384 + 422)
T = 6045 / 806
T = 7.5 hours
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.
If the distance between them is 1997 miles. Then the time is calculated as,
T = 1997 / (384 + 422)
T = 1997 / 806
T = 2.48 hours
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
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What is 1.8 rounded to the nearest tenth
Answers
Answer: 1.8 rounded to the nearest tenth will remain as 1.8 because 0.8 is 8 tenths
Answer:
Step-by-step explanation:
11.3
What is the missing number, what property did you use? –––=0×5
Answers
Answer:
0 is the answer
Step-by-step explanation:
0*5=0
0=0*5 ==> use Zero property of multiplication
This property states that any number multiplied by 0 equals 0.
determine the longest wavelength photon (in nm) which can remove an electron from mercury metal if the work function of the metal is 4.475 ev (1 ev
Answers
To determine the longest wavelength photon which can remove an electron from mercury metal, we need to use the equation:
wavelength = hc/work function
What are photons?Photons are just light particles. Photons are basic subatomic particles that convey the electromagnetic force (and so much more). The photon is the basic unit of electromagnetic radiation, or the "quantum."
What is wavelength?A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
To determine the longest wavelength photon which can remove an electron from mercury metal, you need to use the equation:
wavelength = hc/work function
where h is the Planck constant (6.626 x 10^-34 Js), c is the speed of light (2.998 x 10^8 m/s), and work function is the minimum energy needed to remove an electron from the metal, in this case 4.475 eV.
Plugging these values into the equation gives:
wavelength = (6.626 x 10^-34 Js)(2.998 x 10^8 m/s)/(4.475 x 1.602 x 10^-19 J/eV)
This simplifies to:
wavelength = 404.4 nm
So, the longest wavelength photon which can remove an electron from mercury metal is 404.4 nm.
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In an experiment studying the effects of alcohol on social anxiety, alcohol is the ______ variable. A.) independent. B.) confounding. C.) random. D.) dependent.
Answers
In an experiment studying the effects of alcohol on social anxiety, alcohol is the dependent variable. So, correct option is option D.
What is Dependent variable ?Variables: The goal of all research is to describe and explain global dispersion. Variance is just the difference. That is, the fluctuations that occur naturally in the world, or the changes that occur as a result of manipulation. A variable is the name given to the variance you want to describe. A variable is the result of a force or is itself a force that changes another variable. There are two types of variables.
DependentIndependentWhen researchers administer an active drug to one group of people and placebo or an inactive drug to another group of people, the independent variable is drug treatment. Each person's response to active drug or placebo is called the dependent variable.
In this case, an experiment examining the effects of alcohol on social anxiety. Alcohol is the dependent variable here.
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The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1,60),(2,240),(3,960),(4,3840)}
What is the function equation in sequence notation?
wt=
Answers
Answer:
The answer is in my screen shot:
Explanation:
It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.
Im stuck on finding G im wondering if someone can help me
Answers
Answer:
G=15-1.25×t
or,G=1.25(12-t)
Answer:
G= 15-t1.25
Step-by-step explanation: