[tex](2x+1)(x-2) = 0[/tex]
Multiplying the factors we obtain:
[tex]2x\cdot x+2x\cdot (-2)+1\cdot x+1\cdot (-2)=0[/tex]
[tex]2x^2-4x+x-2=0[/tex]
[tex]2x^2-3x-2=0[/tex]
The general form of quadratic equation is:
[tex]ax^2+bx+c=0[/tex]
Therefore,
[tex]a=2[/tex]
[tex]b=-3[/tex]
[tex]c=-2[/tex]
The correct answer is the first one.
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. (Round your answers to 4 decimal places where possible)
Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is orange or yellow.
Compute the probability that three randomly selected peanut M&M's are all red.
If you randomly select two peanut M&M's, compute that probability that neither of them are red.
If you randomly select two peanut M&M's, compute that probability that at least one of them is red.
Answer:
Step-by-step explanation:
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.
Colour Brown Yellow Red Blue Orange Green total
Prob 0.12 0.15 0.12 0.23 0.23 0.15 1
The probability that a randomly selected peanut M&M is not yellow
=[tex]1-P(Yellow) = 0.85[/tex]
the probability that a randomly selected peanut M&M is orange or yellow.
= [tex]0.23+0.15=0.38[/tex]
the probability that three randomly selected peanut M&M's are all red.
= [tex](0.12)^3 = 0.001728[/tex]
(assuming large number of peanuts and thus independent )
If you randomly select two peanut M&M's, compute that probability that neither of them are red.
= [tex](1-0.12)^2\\= 0.7744[/tex]
If you randomly select two peanut M&M's, compute that probability that at least one of them is red
=[tex]1-P(both non red)\\= 1-0.88^2\\= 0.2256[/tex]
about 30% of the population is left-handed. If two people are random selected what is the probability that both are left handed? What is the probability that at least one is right handed?
Answer:
0.91
Step-by-step explanation:
1 - P(both left handed)
1 - 0.3² = 0.91
College basketball team has won 14 games and lost 6 games. If they continue to win at this rate, how many games would the team win in a 50 game schedule?
Answer:
42 games
Step-by-step explanation:
If the college basketball team has won 14 games and lost 6 games,
The Probability of recording a win is given as:
Probability(of a win)[tex]=\frac{Number of Outcomes }{Total Number o trials}[/tex]=[tex]\frac{14}{20}[/tex]
In experimental probability, this can also be taken as the Relative Frequency of a win.
Therefore: Number of Expected Wins
=Relative Frequency of a win X Total Number of Trials
[tex]\frac{14}{20}X60=42[/tex]
The team would expect to win 42 games in a 60 game schedule
Final answer:
The team would win 35 games in a 50 game schedule.
Explanation:
To find out how many games the team would win in a 50 game schedule, we can use a proportion. The team has won 14 out of 20 games so far, which can be written as 14/20. We can set up a proportion with x representing the number of games the team would win in a 50 game schedule:
14/20 = x/50
Now we can cross-multiply and solve for x:
20x = 14 * 50
20x = 700
x = 700/20
x = 35
So, if they continue to win at this rate, the team would win 35 games in a 50 game schedule.
In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban population moves into the city. In 2015, there were 10,000,000 residents in the city and 800,000 in the suburbs. Set up a difference equation that describes this situation, where Subscript[x, 0] is the initial population in 2015. Then estimate the populations in the city and in the suburbs two years later, in 2017.
Answer:
City @ 2017 = 8,920,800
Suburbs @ 2017 = 1, 897, 200
Step-by-step explanation:
Solution:
- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:
0.94*p_c + 0.04*p_s = p_c'
0.06*p_c + 0.96*p_s = p_s'
- Assuming 6% moved while remaining 94% remained settled at the time of migrations.
- The matrix representation is as follows:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right][/tex]
- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1[/tex]
- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:
[tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1[/tex]
- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.
[tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o[/tex]
- Where,
[tex]x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right][/tex]
- The population in 2017 x_2 would be:
[tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right][/tex]
The estimated populations in 2017 are approximately 9,792,000 for the city and 807,360 for the suburbs
To set up the difference equation for this situation, let's denote the city population in a given year as [tex]\( C_n \)[/tex] and the suburban population as [tex]\( S_n \),[/tex] where [tex]\( n \)[/tex] represents the number of years since 2015. The initial populations in 2015 are given as [tex]\( C_0 = 10,000,000 \)[/tex] and[tex]\( S_0 = 800,000 \)[/tex].
Each year, 6% of the city's population moves to the suburbs, which can be represented as [tex]\( 0.06C_n \)[/tex]. Similarly, 4% of the suburban population moves into the city, which is [tex]\( 0.04S_n \).[/tex]
The difference equations describing the change in population each year are:
[tex]\[ C_{n+1} = C_n - 0.06C_n + 0.04S_n \][/tex]
[tex]\[ S_{n+1} = S_n + 0.06C_n - 0.04S_n \][/tex]
Now, let's calculate the populations for 2016 (one year after 2015,[tex]\( n = 1 \))[/tex]:
[tex]\[ C_1 = C_0 - 0.06C_0 + 0.04S_0 \][/tex]
[tex]\[ S_1 = S_0 + 0.06C_0 - 0.04S_0 \][/tex]
Plugging in the initial values:
[tex]\[ C_1 = 10,000,000 - 0.06 \times 10,000,000 + 0.04 \times 800,000 \][/tex]
[tex]\[ S_1 = 800,000 + 0.06 \times 10,000,000 - 0.04 \times 800,000 \][/tex]
Calculating the values:
[tex]\[ C_1 = 10,000,000 - 600,000 + 32,000 \][/tex]
[tex]\[ S_1 = 800,000 + 600,000 - 32,000 \][/tex]
[tex]\[ C_1 = 9,432,000 \][/tex]
[tex]\[ S_1 = 1,368,000 \][/tex]
Next, we calculate the populations for 2017 [tex](\( n = 2 \)):[/tex]
[tex]\[ C_2 = C_1 - 0.06C_1 + 0.04S_1 \][/tex]
[tex]\[ S_2 = S_1 + 0.06C_1 - 0.04S_1 \][/tex]
Using the populations from 2016:
[tex]\[ C_2 = 9,432,000 - 0.06 \times 9,432,000 + 0.04 \times 1,368,000 \][/tex]
[tex]\[ S_2 = 1,368,000 + 0.06 \times 9,432,000 - 0.04 \times 1,368,000 \][/tex]
Calculating the values:
[tex]\[ C_2 = 9,432,000 - 565,920 + 54,720 \][/tex]
[tex]\[ S_2 = 1,368,000 + 565,920 - 54,720 \][/tex]
[tex]\[ C_2 = 9,792,000 \][/tex]
[tex]\[ S_2 = 807,360 \][/tex]
Two ships leave a harbor together, traveling on courses that have an angle of 135°40' between them. If they each travel 402 miles how far apart are they?
Final answer:
The distance between two ships leaving a harbor can be calculated using vector addition and the cosine law formula, resulting in an approximate distance of 565 miles.
Explanation:
The distance between the two ships can be calculated using vector addition.
To find the distance apart, we can add the vectors representing the paths of the two ships. Using the cosine law formula, we calculate the magnitude of the resultant vector to be approximately 565 miles.
please find the factors to this equation
Answer:(x,-14) (x+6)
Step-by-step explanation:
I think correct me if I am wrong.
Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.
Answer: the price of a bag of popcorn is $5.3
Step-by-step explanation:
Let x represent the price of one drink.
Let y represent the price of one bag of popcorn.
Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. This is expressed as
4x + 9y = 65.25- - - - - - - - - - - - - - -1
Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn.
This is expressed as
8x + 3y = 51.75- - - - - - - - - - - - - - -2
Multiplying equation 1 by 8 and equation 2 by 4, it becomes
32x + 72y = 522
32x + 12y = 207
Subtracting, it becomes
60y = 315
y = 315/60
y = 5.25
HELP PLS 20 POINTS! I WILL MARK BRAINLIEST
Answer:
I believe it is 2 for $5.08
Step-by-step explanation:
1.27 times 2 is 2.54
2.54 times 5 is 12.70
Answer:
D 2(1/2) for $6.25
Step-by-step explanation:
a. 5.08/2=2.54
b.12.7/5=2.54
c.1.27/0.5=2.54
d.6.25/2.5=2.5
help me, someone, I really need it
Answer:
Point B
Step-by-step explanation:
Because the x coordinate is -2
Move two to the left.
The y-coordinate is 2
After we are at -2 for x, then move up to reach the y=2 line. \
Then that will be your point.
Answer:
it would be point b
Josiah has 3 packs of toy animals.Each pack has the same number of animals.Josiah gives 6 animals to his sister stephanie.Then josiah has 9 animals left.How many animals were in each park?
Answer:
there are 5 animals in each pack.
Step-by-step explanation:
if you add 9+6= 15 then divide 15 by 3 you will get 5 as your answer
Answer: there were 5 animals in each pack.
Step-by-step explanation:
Let x represent the number of toy animals in each pack.
Josiah has 3 packs of toy animals. Each pack has the same number of animals. This means that the number of animals in the 3 packs is
3x
Josiah gives 6 animals to his sister stephanie. This is expressed as 3x - 6. If she has 9 left, it means that
3x - 6 = 9
3x = 9 + 6
3x = 15
x = 15/3
x = 5
two integers whose product is 90 and whose sum is 21
Answer:
6 and 15
Step-by-step explanation:
Answer:
6 and 15
Step-by-step explanation:
the factors of 90 are:
1 90
2 45
3 30
5 18
6 15
9 10
find the factors that =21
6+15=21 and 6 x 15=21
Two trains leave the station at the same time. One is traveling east at rate of 78mph. The other is traveling west at rate of 72 mph. How long to they have to travel until they are 1,162.5 miles apart?
Answer:
The time the both trains have to travel for making a distance of 1162.5 miles apart T = 7.75 hour
Step-by-step explanation:
Speed of the first train = 78 [tex]\frac{mi}{h}[/tex]
Speed of the second train = 72 [tex]\frac{mi}{h}[/tex]
Suppose the both trains have to travel for time = T hour
The distance traveled by first train ( [tex]D_{1}[/tex] ) = Speed × time
⇒ [tex]D_{1}[/tex] = 78 × T --------- (1)
The distance traveled by second train ( [tex]D_{2}[/tex] ) = 72 × T --------- (2)
Total distance D = [tex]D_{1}[/tex] + [tex]D_{2}[/tex]
⇒ D = 78 × T + 72 × T
⇒ 1162.5 = 150 T
⇒ T = 7.75 hour
This is the time the both trains have to travel for making a distance of 1162.5 miles apart.
A wooden structure has the shape of a right triangle with a base of 12 feet and a height of 8 feet. It is supported by a wire stretched from point C to the ground at point D such that the support wire is perpendicular to the top of the structure, AC.
(1) how far away from point b should point d be placed? give an exact answer in feet and inches.
(2) to the nearest tenth of a foot what is the length of the support wire?
Answer:
(1)5 ft 4 in
(2)9.6 ft
Step-by-step explanation:
We are given that
AB=12 ft
BC=8 ft
All right triangles are similar
(1)Let BD=x
Triangle ABC and DBC are similar
When two triangle are similar then , the ratio of their corresponding sides are equal.
[tex]\frac{12}{8}=\frac{8}{x}[/tex]
[tex]x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft[/tex]
[tex]x=\frac{64}{12}\times 12=64 inches[/tex]=5 ft 4in
1 feet=12 inches
(2)In triangle DBC
[tex]CD^2=BC^2+DB^2[/tex]
Using Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(perpendicular\;side)^2[/tex]
[tex]CD^2=(8)^2+(5.3)^2[/tex]
[tex]CD=\sqrt{64+28.09)}=9.6 feet[/tex]
Hence, the length of support wire=9.6 feet
The distance from point B that point D should be placed in the triangle is 5 feet 4 inches.
How to solve the triangle?The distance from point B that point D should be placed in the triangle will be calculated thus:
Let the distance be represented by x
12/8 = 8/x
x = (8 × 8) / 12
x = 5 ft 4 in
The length of the support wire will be calculated thus:
CD² = 8² + 5.3²
CD² = 64 + 28.09
CD² = 92.09
CD = ✓92.09
CD = 9.6 feet
Therefore, the length of the support wire is 9.6 feet.
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A square kitchen floor has an area of 500 square feet. Estimate the length one wall to the nearest tenth of a foot. Someone please help me with this question. I'm really stumped XD
Before polling the students in Scion School of Business, a researcher divides all the current students into groups based on their class standing, such as freshman, sophomores, and so on. Then, she randomly draws a sample of 50 students from each of these groups to create a representative sample of the entire student body in the school. Which of the following sampling methods is the researcher practicing? 1. stratified random sampling 2. simple random sampling 3. cluster sampling 4. systematic random sampling 5. snowball sampling
Answer:
1. Stratified Random Sampling
Step-by-step explanation:
Sampling is a technique of drawing small number of representative units from population.
Stratified Random Sampling is when population is divided into : heterogenous (different) groups, homogeneous (identical) within themselves - known as Strata.
Process of drawing Sample from each such strata group is called Stratified Random Sampling. This sampling makes sample better representative of various groups in population. Eg : Dividing population in strata based on gender , religion etc & then drawing sample from each strata.
Researcher dividing students into - freshman, sophomores & other groups ; then drawing sample from each group is an example of Stratified Sampling. It creates representative sample of each student body in school .
The researcher is practicing stratified random sampling by dividing the students into groups based on their class standing and randomly selecting a sample from each group.
Explanation:The researcher is practicing stratified random sampling.
In stratified random sampling, the population is divided into homogeneous groups called strata. The researcher then randomly selects a sample from each stratum to create a representative sample of the entire population.
In this case, the researcher divided the students into groups based on their class standing and randomly selected 50 students from each group.
This ensures that the sample includes students from all class standings and accurately represents the entire student body of the Scion School of Business.
Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
Answer:
5f+3g=5.70
2f+10g=3.60
Step-by-step explanation:
Cost of 1 piece of fudge =f
Cost of 1 piece of bubble gum =g
If Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70.
Chase's Cost:
For 5 pieces of Fudge, his cost is 5f
For 3 pieces of bubble gum, his cost is 3g
His Total, 5f+3g=$5.70
Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60.
Sara's Cost:
For 2 pieces of fudge, her cost is 2f
For 10 pieces of bubble gum, her cost is 10g
Her Total, 2f+10g=$3.60
The system of equation that could be used to determine the cost of 1 piece of budge and bubblegum is then:
5f+3g=$5.70
2f+10g=$3.60
Write declaration statements to declare and initialize two variables: one is an integer variable named age, initialized to 18, and the other variable, named weight, is initialized to 114.5.
Answer:
int age;
age=18;
float weight;
weight=114.5F;
Step-by-step explanation:
int age; \\ it is declared as integer because 18 is an integer value
age=18; \\ initialized as 18 is stored in the variable 'age'
float weight; \\ weight is declared as float because it's value is floating or decimal value which cannot be declared as integer value
weight=114.5F; \\ F shows that it's single floating type value of 32 bits, if F is not written then it means it double floating type value which is 64 bits long
In order to declare and initialize two variables, one as an integer named 'age' initialized to '18' and the other named 'weight' initialized to '114.5', you'd write 'int age = 18;' and 'double weight = 114.5;' respectively.
Explanation:To declare and initialize two variables in a programming language such as Java or C++, you would use the following syntax:
int age = 18;
double weight = 114.5;
The keyword 'int' declares an integer variable, and 'double' declares a variable for floating-point numbers. After the variable name, an equals sign ('=') is used to assign or initialize the variable to a specific value.
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Find the value of c that makes each trinomial a perfect square.
x^2-13x+c
Answer:
169/4
Step-by-step explanation:
x² - 13x + c
x² -2(x)(13/2) +(13/2)²
(13/2)² = 169/4 or 42 ¼
Which statement is true about the circumference of a circle? The circumference is equal to the radius of the circle. The circumference is equal to the diameter of the circle. The circumference is found by multiplying Pi by the radius. The circumference is found by multiplying Pi by the diameter.
Solution:
The circumference of a circle is given as:
[tex]\text{circumference } = 2 \pi r[/tex]
Where,
"r" is the radius of circle
We know that,
[tex]diameter = 2 \times radius\\\\d = 2 \times r\\\\d = 2r[/tex]
Thus the circumference can also written as:
[tex]\text{circumference } = 2 \pi r\\\\\text{circumference } = \pi \times d[/tex]
Thus, the circumference is found by multiplying Pi by the diameter is correct statement
The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.
What is the Circumference of a Circle?A circle's circumference is it's perimeter.Given the diameter of the circle, d, the formula for finding the circumference of the circle is: πd.π is called pi.Therefore, the true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.
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PLZ HURRY IT'S URGENT!!
What is the slope of the line that passes through the points (3, –1) and (–2, –5)? −54
−45
45
54
Option C: [tex]\frac{4}{5}[/tex] is the slope of the line
Explanation:
The line passes through the points [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]
We need to find the slope of the line.
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]
Let us substitute the points in the formula
Thus, we have,
[tex]m=\frac{-5-(-1)}{-2-3}[/tex]
Simplifying, we get,
[tex]m=\frac{-5+1}{-2-3}[/tex]
Adding the numerator and denominator, we have,
[tex]m=\frac{-4}{-5}[/tex]
Cancelling the negative terms, we get,
[tex]m=\frac{4}{5}[/tex]
Thus, the slope of the line is [tex]m=\frac{4}{5}[/tex]
Therefore, Option C is the correct answer.
The 32 species that make up the dolphin family are closely related to whales and in fact include the animal known as the killer whale, which can grow to be 30 feet long and is famous for its aggressive hunting pods.
(A) include the animal known as the killer whale,which can grow to be 30 feet long and is
(B) include the animal known as the killer whale,growing as big as 30 feet long and
(C) include the animal known as the killer whale,growing up to 30 feet long and being
(D) includes the animal known as the killer whale,which can grow as big as 30 feet long and is
(E) includes the animal known as the killer whale,which can grow to be 30 feet long and it is
Answer:
A
Step-by-step explanation:
- Generally, the agent of a COMMA + VERBing modifier must be the nearest preceding SUBJECT.
- B and C: The 32 species...include the animal known as the killer whale, growing
- Here, COMMA + growing seems to refer to the 32 species -- the nearest preceding subject -- implying that the SPECIES are GROWING.
Not the intended meaning.
- The intended meaning of the original sentence is that THE KILLER WHALE can GROW.
Eliminate B and C.
- In D and E, includes (singular) does not agree with the 32 species (plural).
Eliminate D and E.
- the correct answer is A
The correct answer is option (A). include the animal known as the killer whale,which can grow to be 30 feet long
To determine this, we need to ensure the sentence maintains proper subject-verb agreement and logical consistency. The primary subject is 'The 32 species that make up the dolphin family,' which is plural.
Therefore, the verb 'include' is correct, rather than 'includes' which would be for a singular subject.
Additionally, 'which can grow to be 30 feet long and is' clearly and correctly describes the killer whale.
The correct answer to this question is (A) include the animal known as the killer whale, which can grow to be 30 feet long and is.
The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm. Determine the volume of the box retaining the proper number of significant figures in your answer
Answer:
The Volume of the Shoebox is therefore 5884.7[tex]cm^3[/tex]
Step-by-step explanation:
The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm.
We want to determine the volume of the box.
The Shoebox is in the shape of a Cuboid and;
Volume of a Cuboid=Length X breadth X height
Volume of the Shoebox= 11.4.X 17.8 X 29 =5884.68[tex]cm^3[/tex]
=5884.7[tex]cm^3[/tex] (correct to 1 decimal place)
The volume of the box is 5884.68 cubic cm.
Important information:
Dimensions of the box are 11.4 cm, 17.8 cm, and 29 cm.We need to find the volume of the box.
Volume of cuboid:The volume of a cuboid is:
[tex]V=l\times b\times h[/tex]
Where [tex]l[/tex] is length, [tex]b[/tex] is breadth and [tex]h[/tex] is height.
The volume of the box is:
[tex]V=11.4\times 17.8\times 29[/tex]
[tex]V=5884.68[/tex]
Therefore, the volume of the box is 5884.68 cubic cm.
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Can someone answer the blank ones please!!!
The equation is [tex]155p+225f=5050[/tex].
If p = 17, f = 13. This value is a reasonable value in this context.
If f = 28, p = -10. This value is not reasonable in this context.
Step-by-step explanation:
Step 1:
[tex]155p+225f=5050[/tex],
where p is the part-time memberships and f is the number of full-time memberships.
Kiri needs to make $5,050 a month from this rented space.
Each part-time membership costs $155 and each full-time membership costs $225.
Step 2:
We need to calculate the value of f when p = 17,
Substituting the value, p = 17 in the equation, we get;
[tex]125(17)+225f=5050[/tex], [tex]225f=5050-125(17),[/tex]
[tex]225f=2925, f = \frac{2925}{225}, f =13.[/tex]
The value of f = 13 and p = 17. This is a reasonable value in this context.
Step 3:
We need to calculate the value of p when f = 28,
Substituting the value, f = 28 in the equation, we get;
[tex]125p+225(28)=5050[/tex], [tex]125p=5050-225(28)[/tex]
[tex]125p=-1250, p = \frac{-1250}{125}, p=-10.[/tex]
The value of f = 28 and p = -10. This is not a reasonable value in this context. as the values of f and p cannot be negative for this given equation.
For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00. What are the values for the sample mean and standard deviation?
Final answer:
The sample mean (μ) and standard deviation (σ) are calculated using the provided z-scores and corresponding sample values, resulting in a mean of 30 and a standard deviation of 10.
Explanation:
To solve for the sample mean and standard deviation using the given z-scores and sample values, we can employ the formula for calculating a z-score:
z = (X - μ) / σ
where X is the sample value, μ is the mean, and σ is the standard deviation. For X = 45 with a z-score of 1.50, the equation is:
1.50 = (45 - μ) / σ
For X = 40 with a z-score of 1.00, the equation becomes:
1.00 = (40 - μ) / σ
By solving these two equations simultaneously, we can find the values of μ and σ.
From the first equation, we have:
1.50σ = 45 - μ
From the second equation, we have:
1.00σ = 40 - μ
If we multiply the second equation by 1.5, it becomes:
1.50σ = 60 - 1.5μ
We can set the expressions for 1.50σ equal to each other:
45 - μ = 60 - 1.5μ
Solving for μ gives us the sample mean:
μ = 60 - 45 = 15 / (1.5 - 1) = 15 / 0.5 = 30
To find the standard deviation σ, we substitute μ = 30 into one of the original equations:
1.50σ = 45 - 30 = 15
Therefore, σ = 15 / 1.50 = 10
So, the sample mean (μ) is 30 and the sample standard deviation (σ) is 10.
Final answer:
The sample mean (μ) is 30 and the standard deviation (σ) is 10.
Explanation:
The question is asking to find the sample mean and standard deviation based on given z-scores for specific values in a normal distribution.
To find these parameters, we'll use the formula for calculating a z-score:
z = (X - μ) / σ, where z is the z-score, X is the value, μ is the mean, and σ is the standard deviation.
For X = 45 and z = 1.5, the equation becomes 1.5 = (45 - μ) / σ. For X = 40 and z = 1.0, the equation is 1.0 = (40 - μ) / σ.These two equations can be solved simultaneously to find the values of μ and σ.
Steps for solving them are:
Rewrite the equations:Therefore, the sample mean (μ) is 30 and the standard deviation (σ) is 10.
To the right are the outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event. a. Among three children, there are exactly 2 boys. b. Among three children, there are exactly 3 boys. c. Among three children, there is exactly 1 boy.
Answer:
The probabilities are 3/8, 1/8 and 3/8 respectively
Step-by-step explanation:
The sample space for the provided case can be written as:
S= {(bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg)}
Here, boy child is denoted by "b" and girl child by "g".
Total number of outcomes are 8.
Number of outcomes that show exactly boys = 3.
Number of outcomes that show exactly 3 boys = 1
Number of outcomes that show exactly 1 boy = 3.
Thus, the required probabilities can be calculated as:
(a)
[tex]\\P( Exactly 2 boys) =\frac{3}{8}[/tex]
(b)
[tex]P( Exactly 3 boys) =\frac{1}{8}[/tex]
(c)
[tex]P(Exactly 1 boy)= \frac{3}{8}[/tex]
Thus, the required probabilities are 3/8, 1/8 and 3/8 respectively.
This is a problem in Mathematics, specifically probability, at the High School level. The student is asked to calculate the probability of certain gender distributions among three children. The outcomes are determined and the respective probabilities calculated: the probability for exactly 2 boys and 1 boy is found to be 3/8 each, while for exactly 3 boys it's 1/8.
Explanation:This question pertains to the understanding of probability in a specific scenario: calculating the likelihood of certain outcomes when a couple has three children. Given that each child can be a boy or a girl (2 possibilities), and there are three children, there are 2^3 or 8 total possible outcomes.
a. To find the probability of having exactly 2 boys, we count the outcomes where that is the case: BBG, BGB, GBB. This is three outcomes, so the probability is 3/8.
b. There is only one outcome where all three children are boys (BBB), therefore the probability of exactly 3 boys is 1/8.
c. The outcomes with exactly 1 boy are BGG, GBG, GGB. This gives us three outcomes, hence the probability is also 3/8.
Learn more about Probability here:https://brainly.com/question/22962752
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Determine if the numerical value describes a population parameter or a sample statistic. 74% of all instructors at your school teach 2 or more classes.
Answer:
Population parameter
Step-by-step explanation:
We are given the following in the question:
74% of all instructors at your school teach 2 or more classes.
Parameter and statistic:
Parameter is the value that describes a population.Population is the collection of all the possible observations of an event.Statistic is the quantitative value that describes a sample.A sample is a part of a population and is always smaller than a population.Population:
all instructors at your school
Parameter:
74% of all the instructors at your school teach 2 or more classes
Thus, 74% describes the population that takes two or more classes.
Hence, it is a population parameter.
Noah bought a new car costing 25350. He made a 20% down payment on the car and financed the remaining cost of the car for 5 years at 6.5%. How much interest did Noah pay on his car loan?
Answer: Noah paid $6591 on his car loan.
Step-by-step explanation:
The amount of money paid as down payment for the car is
20/100 × 25350 = 5070
Therefore, the amount paid to finance the remaining cost of the car is
25350 - 5070 = $20280
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
From the information given,
P = 20280
R = 6.5%
T = 5 years
I = (20280 × 6.5 × 5)/100 = $6591
Answer:its $6591
Step-by-step explanation:
The amount of money paid as down payment for the car is
20/100 × 25350 = 5070
Therefore, the amount paid to finance the remaining cost of the car is
25350 - 5070 = $20280
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
From the information given,
P = 20280
R = 6.5%
T = 5 years
I = (20280 × 6.5 × 5)/100 = $6591
There are a dozen eggs in a basket. 4 are white. The rest are brown. Tell what fraction of the eggs are brown. The write the fraction in simplest form.
Out of a dozen eggs, with 4 being white, the fraction that represents the brown eggs is 8/12. Simplified, this fraction is 2/3.
Explanation:The question is asking us to find what fraction of the eggs are brown if there are 4 white eggs out of a dozen in a basket. Since there are 12 eggs in a dozen, and we know 4 are white, we can subtract the 4 white eggs from the total to find out how many are brown.
12 eggs (total) - 4 white eggs = 8 brown eggs.
Therefore, the fraction of the basket that contains brown eggs is 8/12. To simplify this fraction, we look for the greatest common divisor of both the numerator (8) and the denominator (12), which is 4. Dividing both by 4, we get:
8 ÷ 4 = 2
12 ÷ 4 = 3
So the fraction of the eggs that are brown in simplest form is 2/3.
A piano tuner charged a flat rate of $25 plus $12 per hour to tune a piano. Which expression represents how much the piano tuner earns tuning a piano for h hours?
Answer:
T = 25 + 12 * h
Step-by-step explanation:
To find the rate of the tuner it is necessary to go to an equation:
First would be the full rate that has a value of 25. And for every hour that is 12.
That is to say:
T = 25 + 12 * h
h being the hours it takes to tune the piano. And this equation would reprehend what the piano tuner
A rectangular prism with the surface area of 336 and width of 4 is similar to a rectangular prism with the width of 6, what is the surface area of the larger prism
Answer:
The larger surface area would be 756 [tex]Unit^2[/tex]
Step-by-step explanation:
Given the surface area of rectangular prism is 336 [tex]Unit^2[/tex] when its width is 4 [tex]Unit[/tex].
We need to compute the surface area when its width is 6 [tex]Unit[/tex].
Also, it was given that prisms are similar to each other.
Let us assume the [tex]l[/tex] is length [tex]b[/tex] is width and [tex]h[/tex] is the height of the prism.
So, the surface area would be
[tex]S=2(lb)+2(bh)+2(hl)[/tex]
[tex]336=2(4l)+2(4h)+2(hl)[/tex] Equation (1)
Now, the new width is 6 [tex]Unit[/tex]. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.
We can write
[tex]b'=1.5\times b=1.5\times 4=6\\l'=1.5\times l\\h'=1.5\times h[/tex]
So, the new surface area would be
[tex]S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5\times l\times 1.5\times 4)+2(1.5\times4 \times 1.5\times h)+2(1.5\times h\times 1.5\times l)\\S'=2.25\times 2(l4)+2.25\times 2(h)+2.5\times 2(hl)[/tex]
[tex]S'=2.25[2(4l)+2(4h)+2(hl)][/tex]
From Equation (1) we can plug [tex]336=2(4l)+2(4h)+2(hl)[/tex]
[tex]S'=2.25\times 336=756\ Unit^2[/tex]
So, the larger surface area would be 756 [tex]Unit^2[/tex]