Answer:
A. {2,3,5,7,11,13}
Step-by-step explanation:
Since, prime numbers are the whole numbers which have only two multiple which are 1 and itself.
Thus, the prime numbers are,
2, 3, 5, 7, 11, 13, 17, 19, 23, ..................
Note : 1 is not a prime number because it has only one multiple i.e. 1.
or it does not satisfy the definition of prime number.
Thus, the prime numbers that are less than 15,
2, 3, 5, 7, 11, 13
Which are the elements of the set S,
Hence, S = { 2, 3, 5, 7, 11, 13 }
OPTION A is correct.
The heights of 18-year-old men are approximately normally distributed with mean 68 inches and standard deviation 3 inches. What is the probability that the height of an 18-year-old man selected at random is between 64 inches and 66 inches
Sari is factoring the polynomial 2x2 + 5x + 3. What is the missing number in her factorization?
2x2 + 5x + 3
Answer:
the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Step-by-step explanation:
We need to factor the polynomial [tex]2x^{2}+5x+3[/tex]
Break the expression into groups,
[tex]=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c[/tex]
[tex]x^2=xx[/tex]
then
[tex]2x^2+2x=2xx+2x[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x[/tex]
[tex]=2x\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
[tex]=2x\left(x+1\right)+3\left(x+1\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
[tex]=\left(x+1\right)\left(2x+3\right)[/tex]
Hence, the factor of polynomial [tex]2x^{2}+5x+3[/tex] is [tex]=\left(x+1\right)\left(2x+3\right)[/tex]
A salesperson earns $300.50 per week plus 7% of her weekly sales. Which of the following describes the sales necessary for the salesperson to earn at least $900.85 in one week?
A. x is greater then or equal to 900.85
B. x is greater then or equal to 8576.43
C. x is greater then or equal to 600.35
D. x is greater then or equal to 17162.14
salesperson earns $300.50 per week plus 7% of her weekly sales .To have the sales necessary for the salesperson to earn at least $900.85 in one week we can form an inequality equation. Let x denote his weekly sales.
300.50+7% x ≥ 900.85
Subtracting 300.50 both sides:
7%x≥ 600.35
0.07x ≥ 600.35
Dividing both sides by 0.07
x≥8576.428
Option B . x is greater then or equal to 8576.43 is the right answer.
what is the nth term of 3 8 15 24 35
. Identify the converse of the conditional statement. Determine the truth values of the original conditional and its converse. If an angle is a right angle, then its measure is 90.
A.
If the measure of an angle is 90, then it is a right angle.
Original: true
Converse: true
B.
If an angle is not a right angle, then its measure is not 90.
Original: true
Converse: true
C.
If an angle is not a right angle, then its measure is 90.
Original: true
Converse: false
D.
If the measure of an angle is 90, then i ...?
use the substitution method to solve the system of equations . choose the correct ordered pair. 2x = 3y = 29, x=4
Answer:
4, 7
Step-by-step explanation:
Myra's stamp collection consisted of 120 stamps in october by the following march her collection had grown to 138 by how much did her collection increase between october and march
i know this is really late but this is for anyone else that wants to know the answer
138 -120 = 18 18/120 X 100 = 15%
Consider the function f(x) = ax+3 over x-b.
Find a and b given that y=f(x) has asymptotes with equations x = -1 and y = 2.
The value of 'a' is determined from the horizontal asymptote y=2, which gives a=2. The value of 'b' is derived from the vertical asymptote x=-1, leading to b=1. Hence, the function with the given asymptotes is f(x) = 2x+3 over x-1.
To find the values of a and b for the function f(x) = ax+3 over x-b, given the horizontal and vertical asymptotes, we need to consider the general behavior of rational functions. A vertical asymptote occurs where the denominator of a rational function is zero, while a horizontal asymptote is determined by the relationship between the degrees of the numerator and the denominator.
Since the vertical asymptote is x = -1, we know that the denominator of the function must be zero when x = -1. Thus, we can determine that b = 1, since the denominator is x - b and -1 - b = 0.
The horizontal asymptote is given by y = 2. This indicates the value that the function approaches as x goes to infinity. For the function f(x) = ax+3 over x-b, the degrees of the numerator and denominator are both one. Therefore, the horizontal asymptote is determined by the ratio of the leading coefficients of the numerator and the denominator, which means a / 1 = 2, so a = 2.
Therefore, the values of a and b are 2 and 1, respectively.
Ron bought 2 dvds for 12.95 each. he spent $25. did he spend more on dvds or magazines
evaluate the expression 5/12-4/9
A box has a length of 5 cm, a width of 10 cm, and a height of 2 cm. The volume of the box is
Answer:
100 cm3
Step-by-step explanation:
To find the solution to this problem, we have to use the formula for volume, which is Length x Width x Height. So, we have to do 5cm x 10cm x 2cm, which is 100. Finally, we have to square the centimeters, which gives us
100 cm3
Hope this helped!
11x-1+5x+5+3x+5=180
geometry solve for x
What is the relationship between Sample Size and the width of the Confidence Interval? Please explain further as to why
A bank requires a four-digit access code for each account. The access code is generated using the digits 0–9, and the digits can be repeated. What is the probability of an access code “1234”?
Answer:
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
Step-by-step explanation:
" The probability of an event is defined as the ratio of total number of favourable outcomes to the total number of possible outcomes ".
A bank requires a four-digit access code for each account. The access code is generated using the digits 0–9, and the digits can be repeated.
The total number of outcomes possible are 10×10×10×10=10000
since the first place any of the 10 digits are possible, similarly for the second, third and fourth place.
Also each code is a unique representation in itself.
Hence the code "1234" is unique.
Hence, the probability of an access code “1234”= [tex]\dfrac{1}{10000}[/tex]
The average distance between the variable scores and the mean in a set of data is the __________.
a. range
b. standard deviation
c. mean
d. median user: all of the following are limitations of statistics except that it __________.
a. provides limited information
b. cannot be influenced by inaccurate assumptions
c. promotes limitations in perceptions
d. can be misrepresented
The B. standard deviation is the measure that represents the average distance between the variable scores and the mean in a dataset. Statistics can indeed be b. cannot be influenced by inaccurate assumptions
The average distance between the variable scores and the mean in a set of data is the standard deviation. The standard deviation quantifies the variation or dispersion from the average of a dataset. It provides insight into how spread out the data points are relative to the mean. A low standard deviation suggests that the data points tend to cluster near the mean, whereas a high standard deviation indicates a wider spread of data points.
As for the limitations of statistics, they do not include that statistics cannot be influenced by inaccurate assumptions. In fact, statistics can be greatly influenced by assumptions, and care must be taken to ensure that the data and the assumptions upon which the analyses are based are accurate. Otherwise, the conclusions drawn from statistical analyses may be misleading.
I am part of a whole. i am greater than three fourths,but less than nine tenths. i am a decimal with a 3 in my hundredths place. what number am i?______________
If a rectangle JKLM, JK is equal to 12 feet, and LN is equal to 6.5 feet, find KM
Answer:
13 feet
Step-by-step explanation:
KM=LJ
LJ =LN+LN
=6.5×2
=13 feet
Lois has 36 colored pencils. They are either green or red. For every green pencil, Lois has 3 red pencils. How many red pencils does Lois have?
Answer:
12
Step-by-step explanation: 36/3=12
Tabitha bought peppers that cost $0.79 per pounds. she paid $3.95 for the peppers. how many pounds of peppers did she buy? show your work
Tabitha bought 5 pounds of peppers for $3.95 at a rate of $0.79 per pound by dividing the total cost by the price per pound.
Explanation:The student asked how many pounds of peppers Tabitha bought if she paid $3.95 for them at a cost of $0.79 per pound.
To answer this, we need to divide the total cost by the price per pound.
So, we calculate $3.95 / $0.79 per pound to get the total pounds of peppers.
Here's how the calculation is done step-by-step:
Write down the total amount spent on peppers: $3.95.Write down the cost per pound of peppers: $0.79.Divide the total cost by the cost per pound to find the quantity purchased: $3.95 / $0.79 = 5 pounds.Therefore, Tabitha bought 5 pounds of peppers.
An automobile travels 34.o mpg of gasoline . how many kilometers does it travel per liter of gasoline ? use these equalities : 1 mile=1.61 kilometers ; 1 gallon = 3.79 liters
omar is 3 times as old as jason.
henry is 5 years older than jason.
if their total age is 80 years old,how much older is omar than henry?
Simplify 6a+8b-a-3b plz
A. A band leaves a free T-Shirt under every 6th seat at a concert. They leave a free backstage pass under every 4th Street.
Which of these seat numbers get a free T-SHirt? Which Get a backstage pass? Which get both? Explain Your reasoning
If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (c * d ) (x)?
A ) 4x3 + 18x2 – 10x
B ) x2 + 9x – 2
C ) 16x2 + 4x – 6
D ) 4x2 + 20x – 2
Five different written driving tests are administered by the Motor Vehicle Department. One of these five tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
The probability that exactly two of the five applicants will take the same test is approximately 0.384.
To solve the problem of finding the probability that exactly two of the five applicants for a driver's license will take the same written driving test, we can use the principles of combinatorial probability.
Identify the Total Number of Tests:
The Motor Vehicle Department administers 5 different tests.Identify the Total Number of Applicants:
There is a group of 5 applicants (2 women and 3 men).Understand the Requirement:
We need to find the probability that exactly 2 out of the 5 applicants take the same test, and the remaining 3 take different tests.Select the Applicants Who Share the Same Test:
Choose 2 out of the 5 applicants to take the same test. This can be done in:
[tex]\binom{5}{2} = 10 \text{ ways}[/tex]
Choose the Test for the Selected Applicants:
Any of the 5 tests can be taken by the 2 selected applicants. Thus, we have 5 choices for the test.Assign Tests to the Remaining Applicants:
The remaining 3 applicants must take different tests. Since one test is already taken by the 2 applicants, there are 4 tests left available for the other 3.
We need to choose 3 tests from the remaining 4, which can be selected in:
[tex]\binom{4}{3} = 4 \text{ ways}[/tex]
The arrangement of these selected tests among the 3 remaining applicants can happen in:
[tex]3! = 6 \text{ ways}[/tex]
Calculate the Total Ways to Arrange Tests:
The total ways to assign tests involving both the shared test and unique tests is calculated as:
[tex]10 \times 5 \times 4 \times 6 = 1200 \text{ ways}[/tex]
Total Possible Assignments Without Restrictions:
Without any restriction, each of the 5 applicants could take any of the 5 tests, leading to:
[tex]5^5 = 3125 \text{ total combinations}[/tex]
Calculate the Probability:
The probability that exactly two applicants take the same test is then:
[tex]P(X=2) = \frac{1200}{3125} \approx 0.384[/tex]
Smith high school offers a baseball camp that is 75$ for 4 days of camp and a basketball camp for that 100$ for 5 days of camp.which is a a better deal and by how much?
What is the surface area of this design?
Answer:
256
Step-by-step explanation:
Answer:
Surface Area of Design = 256 in.²
Step-by-step explanation:
Given: a Shape which is made by placing two cuboid on one another.
To find: Surface area of shape.
Figure is attached.
Surface Area of Design
= Lateral Surface Area of Base Cuboid + Lateral Surface area of Top Cuboid + Area of rectangle CDLJ + Area of rectangle EFNM + Area of rectangle ABHG
Dimensions of Base Cuboid:
Length, CJ = 8 in.
Width, CD = LJ = MN = 5 in.
Height, AD = 4 in.
Dimensions of Top cuboid:
Length, HI = BI - BH = 8 - 4 = 4in.
Width, GH = KI = MN = 5 in.
Height, FH = JN - JI = 8 - 4 = 4 in.
Length of rectangle ABHG, AB = 5 in.
Width of rectangle ABHG , BH = 4 in.
Length of rectangle DCJL, DC = 5 in.
Width of rectangle DCJL , CJ = 8 in.
Length of rectangle EFNM, EF = 5 in.
Width of rectangle EFNM , FN = 4 in.
Lateral Surface Area of Base Cuboid = 2 × Height ( length + Width )
= 2 × 4 ( 8 + 5 )
= 8 ( 13 )
= 104 in²
Lateral Surface Area of Top Cuboid = 2 × Height ( length + Width )
= 2 × 4 ( 5 + 4 )
= 8 ( 9 )
= 72 in²
Area of rectangle DCJL = length × breadth
= 5 × 8
= 40 in.²
Area of rectangle ABHG = length × breadth
= 5 × 4
= 20 in.²
Area of rectangle EFNM = length × breadth
= 5 × 4
= 20 in.²
⇒ Surface Area of Design = 104 in.² + 72 in.² + 40 in.² + 20 in.² + 20 in.²
= 256 in.²
Therefore, Surface Area of Design = 256 in.²
Compensation for 195x5
Two factors of 24 add up to 14 what are they
12 and 2 Are the answers.
find a polynomial function of degree 4 with -1 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1.
f(x)=? ...?