(1) Option A (25 glee club members are randomly selected; 16 plan to go to a 4-year college.) would probably best represent the entire population of seniors.
(2) 416 seniors would be planning to attend a four-year university, by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
(1) Since Option A has a larger fraction ([tex]\frac{16}{25} > \frac{14}{25} > \frac{13}{25}[/tex]), it is probably the only one that best represents the majority of the people.
(2) As seen from Part (1),
Out of 650 seniors, around 416 will go to a 4-year college as, by unitary method:
For every 25 members, 16 plan to go to 4-year college
For every 650 members, [tex]\frac{16}{25}(650)=416[/tex] will plan to go to 4-year college.
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(COMPLETE QUESTION:
Lincoln High wants to estimate the number of seniors who plan to go to a 4-year college. 1) Which of the following surveys probably would best represent the entire population of seniors? a) 25 glee club members are randomly selected; 16 plan to go to a 4-year college. b) 25 honor roll students are randomly selected from the senior class; 14 plan to go to a 4-year college. c) 25 seniors are randomly selected; 13 plan to go to a 4-year college. 2) There are 650 seniors at Lincoln High. Using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.)
Jerry and Katy ask students how far they live from school. The graphs show the data each person has collected. Distance from School - Jerry's Study 0 1 2 3 4 5 6 7 8 9 10 11 Number of miles Number of students Distance from School - Katy's Study 210987OSTMNTO 3 0-2 3-5 6-8 9-11 Number of miles
Answer:
1. 13 As there are 13 points indicating there are 13 students 2. 39.
Step-by-step explanation:
Solve for x.
3(x + 5) = 30
Answer:
x=5
Step-by-step explanation:
3(5+5) = 30
3(10) = 30
<3
Alabama has about 2.51 million acres of cropland. Florida has about 1.15 times as much cropland as Alabama. How much cropland does Florida have?
Florida has ___ million acres of cropland.
Answer: 2,8865 million acres of cropland in florida
Step-by-step explanation: To solve this problem we can multiply Alabama's cropland of 2.51 million acres by 1.15 giving: 2.51 million ×1.15=2.8865 million acres of cropland in Florida.
I Hope this helps :)
Answer: Florida has 2.8865 million acres of cropland.
Step-by-step explanation:
We can first do the multiplication, 2.51 x 1.15, and then add 1,255 + 2,510 + 25,100 then we get the answer: 2.8865
Hope this helps :)
You have a coupon for your favorite clothing store for $20 off any purchase of more than $75. The store is
also running a 15%-off sale on its entire inventory. Let x be the original price,
f x( )
be the price with the $20
coupon applied, and
g x( )
be the price with the 15% discount applied.
(a) Write an expression for
f x( ) . (3 points)
(b) Write an expression for
g x( ) . (3 points)
(c) Write the expression
(f g x )( )
and explain what it represents? (3 points)
(d) Write the expression
(g f x )( )
and explain what it represents? (3 points)
(e) If the store allows you to apply both the 15% discount and the $20-off coupon, does it matter which
you apply first? How do you know? (3 points
The expressions of all the functions are;
1) f(x) = 0.75x
2)g(x) = 0.8x
3) (f o g)(x) = 0.6x
4) (g o f)(x) = 0.6x
How to create Algebraic Equations?
We are told that f(x) is the price with the $20 coupon applied, and
g(x) is the price with the 15% discount applied. Thus;
1) An expression for f(x) is;
f(x) = (1 - 0.25)x = 0.75x
f(x) = 0.75x
2) An expression for g(x) is;
g(x) = (1 - 0.2)x = 0.8x
g(x) = 0.8x
3) An expression for (f o g)(x) is;
(f o g)(x) = f(g(x)) = 0.75(0.8x) = 0.6x
(f o g)(x) = 0.6x
4) An expression for (g o f)(x) is;
(g o f)(x) = 0.8(0.75x) = 0.6x
(g o f)(x) = 0.6x
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Geela has 20 litres of yoghurt that she wants to put into pots containing 1-litres each.
How pots can she fill ?
We get that the number of pots that can be filled are 20 pots.
We are given that:
The total amount of yoghurt with Geela = 20 liters.
The amount of yoghurt in 1 pot = 1 liter
Now, we need to find the number of pots that can be filled.
So, we will do this by using division.
We get that:
Number of pots that can be filled. = 20 / 1
Number of pots that can be filled. = 20 pots
Therefore, we get that the number of pots that can be filled are 20 pots.
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find the 10th term of the geometric sequence 3, 15, 75…
Answer: 5859375
Step-by-step explanation:
3, 15, 75...
75/15=5
15/3=5
Every term multiplied by 5 is the next term. Hence, the equation for this sequence can be expressed as:
y=3*[tex]5^{x-1}[/tex] ==> y is the term when x is the term number and 3 is the first number in the sequence
Now let's solve for the 10th term:
y=3*[tex]5^{10-1}[/tex]
y=3*[tex]5^{9}[/tex]
y=3*1953125
y=5859375
21. thirty-one increased by fourteen
22. the difference of sixteen and nine 23. the sum of seven, four, and eighteen 24. three times forty
25. the quotient of eighty-one and three
26. four more than the product of seven and eight
27. the cost of three slices of pizza at $2 each
Copyright
28. the number of days in six weeks
Answer:
Hope this helps :)
21) 31 + 14
22) 16 - 9
23) 7 + 4 + 18
24) 3 × 40
25)
26) 81 ÷ 3 OR 81/3 (the fraction bar also means divide)
27) 3 × 2 = 6
28) 7 x 6 = 42 (7 days in a week times by 6 weeks equal 42 days)
I'm not sure how to do this and im super confused
Answer: The m<A = 55
Step-by-step explanation:
1. We know that m<A is likely congruent to m<B (know that m< means measure of angle) {Also noting congruent means same}
2. With that, we can tell that the given info is telling us that 124 is the total degree for m<D.
3. So, this tells us that 2x + x + 41.5 = 124 is the formula we will use.
3a. 3x + 41.5 = 124 (Simplify)
3b. 3x = 82.5 (Combine like Terms)
3c. x = 27.5 (Divide)
4. Now we know what x is, so finding m<A is easy, 2(27.5) equals to 55, meaning m<A is 55. For m<B, 27.5 + 41.5 equals to 69. To make sure 55 + 69 equals to 124
5. So:
m<A = 55
m<B = 69
m<D = 124
P/3 +9 = 11 what does P equal
Answer:
P=6
Because 6/3=2
And 2+9=11
Step-by-step explanation:
i'm having trouble figuring out this like entire problem :(
Using similar triangles, it is found that the measure of angle B is of 74º.
What are similar triangles?Similar triangles are triangles that have the same angle measures, and whose side lengths are proportional.
In this problem, the triangle ABC was translated, resulting in triangle A'B'C'. A translation does not change the measures of the angles, hence their angles are given as follows:
80º, 26º and B.
The sum of the internal angles of a triangle is of 180º, hence:
80 + 26 + B = 180
B = 74º.
The measure of angle B is of 74º.
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How many digits are there in one period?
three digits hope this helped
find the 97th term of the arithmetic sequence -16, 2, 20
Answer:
1080
Step-by-step explanation:
Answer:
97th term of arthmetic progression is
-16+ 96* 18
Step-by-step explanation:
In the segment below, QV = 23. QT = 8. TR = RS = SV.
Answer:
Step-by-step explanation:
What is the vertex of the quadratic function below?
y=x² +12%-7
O A. (-6,-43)
OB. (-6,-29)
O C. (6,3)
OD. (6,29)
Answer:
A
Step-by-step explanation:
assuming you meant y = x² + 12x - 7 , then
given a quadratic in standard form
y = ax² + bx + c (a ≠ 0 )
the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = x² + 12x - 7 ← is in standard form
with a = 1 , b = 12 , then x- coordinate of vertex is
x = - [tex]\frac{12}{2}[/tex] = - 6
substitute x = - 6 into the equation for corresponding y- coordinate
y = (- 6)² + 12(- 6) - 7
= 36 - 72 - 7
= - 43
vertex = (- 6, - 43 )
Element X decays radioactively with a half life of 14 minutes. If there are 160 grams
of Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 11 grams?
loudy
y = a(.5)^t/h
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &11\\ P=\textit{initial amount}\dotfill &160\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ 11=160\left( \frac{1}{2} \right)^{\frac{t}{14}}\implies \cfrac{11}{160}=\left( \cfrac{1}{2} \right)^{\frac{t}{14}}\implies \log\left( \cfrac{11}{160} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{t}{14}} \right][/tex]
[tex]\log\left( \cfrac{11}{160} \right)=\cfrac{t}{14}\log\left[ \left( \cfrac{1}{2} \right)\right]\implies \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)}=\cfrac{t}{14} \\\\\\ 14\left( \cfrac{\log\left( \frac{11}{160} \right)}{\log \left( \frac{1}{2} \right)} \right)=t\implies {\LARGE \begin{array}{llll} \stackrel{mins}{54.1}\approx t \end{array}}[/tex]
a rectangle has a perimeter of 40.0 cm. one side has a length of 14.0 cm. what is the length, in cm, of an adjacent side?
Based on the calculations, the length, in cm, of an adjacent side of this rectangle is equal to 6.0 centimeters.
Given the following data:
Perimeter of rectangle = 40.0 centimeters.
Length of rectangle = 14.0 centimeters.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Note: The length of an adjacent side refers to the the width of this rectangle.
Substituting the parameters into the formula, we have;
40.0 = 2(14.0 + W)
40.0 = 28.0 + 2W
2W = 40.0 - 28.0
2W = 12.0
W = 12.0/2
Width, W = 6.0 centimeters.
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An electrician charges $24 per hour and $36 for each hour of overtime. for a job, the electrician works 8 regular hours and overtime hours. he also charges $202 for materials. the total amount of the bill for the job is $538. how many overtime hours did the electrician work?
The number of overtime hours done by electrician, as found by unitary method, is 4.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
Given:
Charge per hour = $24Charge per overtime hour = $36Number of regular hours = 8Charge of materials = $202Total amount of bill = $538To find: Number of Overtime hours
FInding:
Let the number of overtime hours be 'x'.
By unitary method, Charge of 1 regular hour = $24
Charge of 8 regular hours = $24(8) = $192
Again, by unitary method, Charge of 1 overtime hour = $36
Charge of x overtime hours = $36(x)
Cost of Materials = $202
Now, total bill = sum of all the expenses
=> 538 = 192 + 36x + 202
=> 538 - 294 = 36x
=> 144 = 36x
=> 4 = x
Hence, the number of overtime hours as found by unitary method is 4.
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A college plans to interview 8 students for possible offer of graduate assistantships. The college has three assistantships available. How many groups of three can the college select?.
The number of groups of three that the college can select is 56.
Total number of students = 8
Number of assistantships available = 3
Groups of three can be selected by the college means that out of the eight students three need to be selected at random and this can be done in ⁸[tex]C_{3}[/tex] ways.
In this case, we use combination and not permutation because the order of selection of the students does not matter.
Now, we know
ⁿ[tex]C_{r}[/tex] = ( n! )/( r! (n-r )!)
Here, n = 8 and r = 3
⁸[tex]C_{3}[/tex] = ( 8! )/( 3! (8-3)! )
⁸[tex]C_{3}[/tex] = ( 8 × 7 × 6 × 5! )/ ( 3 × 2 × 1 × ( 5! ) )
⁸[tex]C_{3}[/tex] = ( 8 × 7 × 6 )/ ( 3 × 2 )
⁸[tex]C_{3}[/tex] = 56
The number of groups of three that the college can select is 56.
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Is the square root of two A rational number or an irrational number
Square root of Two is an irrational number. because we are unable to express it in the form a/b, where a and b are whole numbers and b is not zero.
What is an irrational number?Any real number that cannot be written as the quotient of two integers—that is, as p/q, where p and q are both integers—is an irrational number. For instance, the square root of 2 cannot be represented by an integer or a fraction.
Is an irrational number a true number?Because these numbers may be represented on a number line, they are real numbers rather than complex numbers.
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What is the equation of the line that passes through the point (4, 6) and has an
undefined slope?
what’s the equation
Answer:
x = 4
Step-by-step explanation:
You want the equation of the vertical line through (4, 6).
Undefined slopeSlope is the ratio of rise to run for a line. When the "run" is zero, that ratio becomes undefined. The "run" will be zero for any rise when the line is vertical.
EquationThe equation of such a line has the form ...
x = c . . . . . for some constant c
In order for this equation to be satisfied when (x, y) = (4, 6), the value of the constant must match the x-coordinate of the point.
The equation is x = 4.
Consider the functions f(x)=4^x and g(x)=x-3. The function y is defined as y=f(g(x)) state the equation for y.
Answer:
Step-by-step explanation:
To find y = f(g(x)) replace the x in f(x) by g(x):-
y = 4^(x - 3)
---> y = 4^x * 4^-3
---> y = (4)^x / 64
In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now?
-7 degrees
-21 degrees
7 degrees
21 degrees
Answer:
-21 degrees
Step-by-step explanation:
-14 - 7 = 21
The redwood tree in ronin's yard grows at a rate of 6 feet in 1 year. the redwood tree in camren's yard grows 3 feet in 1/3 year.
Answer:
thsnk
Step-by-step explanation:
The Springfield zoo is breeding gorillas. They have 3 gorillas which can mate and give birth. After the first year there are 7 gorillas. After the second year there are 11 gorillas. If the gorillas continue to increase at the same rate, how long will it take for the Springfield zoo to have 35 gorillas?
Using a linear function, it will take 8 years for the Springfield zoo to have 35 gorillas.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, the parameters are given as follows:
m = 4, b = 3.
Hence the number of gorillas after x years is given by:
G(x) = 3 + 4x.
It will have 35 gorillas when:
G(x) = 35.
Hence:
3 + 4x = 35.
4x = 32.
x = 32/4
x = 8.
It will take 8 years for the Springfield zoo to have 35 gorillas.
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Find the p-value for a left tailed hypothesis test with a test statistic of z = - 1.81. decide whetehr to reject
According to the given data The value of p is[tex]0.0351<0.1[/tex](alpha) so reject H₀
What does it mean to have a left-tailed hypothesis?A left-tailed test is used when the alternative hypothesis claims that the true value of the parameter suggested by the null hypothesis is lower than the null hypothesis implies. If the sample being tested is within the one-sided critical zone, the alternative hypothesis will be accepted rather than the null hypothesis.
Financial analysts employ the one-tailed test to confirm an investment or portfolio hypothesis.
If our statistical analysis finds that the significance level is smaller than the set cut-off value, we reject the null hypothesis and accept the alternative hypothesis (for example, either 0.05 or 0.01).
z = -1.81alpha
= 0.1p [tex]( z < -1.81 )p ( z < -1.81 )[/tex]
= 0.0351 ( from z table )P <
alpha, reject H₀
When the p-value is less than or equal to alpha, hypothesis H0 is rejected;
however,
if the p-value is greater than alpha, hypothesis H0 is not rejected.
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missy rode her bicycle 16 miles in 1 1 4 hours. what was her average speed in miles per hour? miles per hour step by step
Missy rode her bicycle 16 miles in 1 1 4 hours. Her average speed in miles per hour is 12.8 mph
What is average speed?Calculating average speed involves dividing the whole distance traveled by the total time it takes to cover that distance.
Speed is the rate of movement of anything at a specific time. Average speed refers to the average speed during the course of a journey. Typically, average speed refers to the speed of moving objects like cars, trains, and aircraft. It is frequently expressed in kilometers per hour (kph) or miles per hour (mph) (kph).
In many different disciplines, such as physics, astronomy, and transportation, average speed is employed.
As we know,
average speed is distance traveled divided by time taken
⇒ average speed = 16 miles × 5/4
⇒ average speed = 12.8 miles/hour
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Mikaela purchased a paddleboard originally priced at $799. If all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount that Mikaela spent on the paddleboard?
$537.33
$514.16
$342.77
$377.53
The total amount that Mikaela spent on the paddleboard is $514.16
What is the total amount that Mikaela spent on the paddleboard?The given parameters are:
Original cost = $799
Discount = 40%
State tax = 7.25%
The total amount that Mikaela spent on the paddleboard is calculated as
Amount = Original cost * (1 - Discount) * (1 + State tax)
This gives
Amount = 799 * (1 - 40%) * (1 + 7.25%)
Evaluate
Amount = 514.16
Hence, the total amount that Mikaela spent on the paddleboard is $514.16
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Answer:
(B) $514.16
Step-by-step explanation:
Correct on my quiz.
HELP ASAP I DON'T UNDERSTAND
Answer:
A
Step-by-step explanation:
x² + 7x + 12 = 0
consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term (+ 7)
the factors are + 3 and + 4 , since
3 × 4 = + 12 and 3 + 4 = + 7 , then
(x + 3)(x + 4) = 0
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x + 4 = 0 ⇒ x = - 4
Sharon packs apples into bags. if she packs 6 apples in each bag, she will have 3 apples left. if she packs 7 apples in a bag, she will be four apples short. how many bags does she have? how many apples does she have?
The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.
Let total number of bags = x
Let total number of apples Sharon has = y
If she packs 6 apples in each bag, she will have 3 apples left. So, mathematically we can write
6x + 3 = y equation 1
If she packs 7 apples in a bag, she will be four apples short. So, mathematically we can write
7x - 4 = y equation 2
On subtracting equation 1 from equation 2 , we get
x - 7 = 0
⇒ x = 7
Substitute x = 7 in equation 1 , we get
6 ( 7 ) + 3 = y
⇒ y = 45
The total number of bags Sharon have is 7 and the total number of apples Sharon have is 45.
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The length of each side is quadrupled. How many times larger is the new area when compared to the original?
2 times
8 times
4 times
16 times
16 times larger is the new area when compared to the original.
Given that, the length of each side of the square is quadrupled.
We need to find how many times larger is the new area when compared to the original.
What is the area of a square?A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. The formula to calculate the area of a square is a².
Let the length of each side of the square be x.
Then the length of each side of the new square will be 4x.
Now, the area of the original square = x²
The area of the new square = (4x)² = 16x²
So, the new square = 16 × the original square
Therefore, 16 times larger is the new area when compared to the original.
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