By comparing the speeds of all the people, Bob picked apple the fastest.
What is speed?Speed is generally the change in distance per unit time. In this case instead of distance we can use the number of apples.
What is the formula of speed?For this question, speed of picking apples = no of apples / time (in minutes). For Bob, speed = 15/8 = 1.88 apples/minute
For Mary, speed = 16/16 = 1 apples/minute
For Suie, speed = 10/19 = 0.526 apples/minute
This shows that Bob picked apples the fastest.
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What is -1/4(-8.6) written as a decimal to the nearest hundredth
Answer:
2.15
Step-by-step explanation:
Factorise this expression please help!!
Answer:
(a + 9)(a + 5)
Step-by-step explanation:
a² + 14a + 45
consider the factors of the constant term (+ 45) which sum to give the coefficient of the a- term (+ 14)
the factors are + 9 and + 5 , since
+ 9 × + 5 = = + 45 and + 9 + 5 = + 14 , then
a² + 14a + 45 = (a + 9)(a + 5)
determine if each set of equations is parallel perpendicular or neither place then in the correct category.
A. Perpendicular
B. Neither
C. Parallel
D. Parallel
E. Parallel
F. Perpendicular
G. Neither
H. Neither
I. Neither
a circle with a circumference of 396 cm is centered at the vertex of an angle, and the angle's rays subtend an arc that is 276.1 cm long. what is the measure of this angle in degrees?
1.1 cm is the 1/360th of the circumference. The circle's circumference is 69.72% of the arc that the angle's rays subtend.
We must comprehend and use the relationships between arc length and circumference in this question. By using geometry, we can determine that a circle's central angle is 360 degrees, and that the circle arc is directly proportional to the central angle.
The angle's rays' subtend an arc that is 69.72% the diameter of the circle.
The circumference's length is multiplied by 1/360 to get the 1/360th of the circumference, and the resulting measurement is
s= 1/360 x 396
= 1.1
the circumference is 1.1 cm.
By dividing the subtended arc by the arc length, one may determine the arc that the angle's subtend rays :
n = 276.1/396 x 100%
n= 69.72%
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Use £1 = 9.60 francs and £1 = 240 pesetas to work out how much 1 franc is in
pesetas.
Answer:
1 franc = 25 pesetas---------------------------------
Given:
£1 = 9.60 francs and £1 = 240 pesetasIt gives us:
9.60 francs = 240 pesetasDivide both sides by 9.60 to find the rate:
1 franc = 240/9.60 pesetas1 franc = 25 pesetasA statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.
Test Scores
Student First Test Grade Second Test Grade
1 50 70
2 91 58
3 55 74
4 58 65
5 79 60
6 70 60
7 97 48
8 51 73
9 51 73
10 59 66
11 69 67
12 56 70
13 56 73
14 41 76
15 49 72
16 58 68
17 58 73
18 99 53
19 87 58
20 95 50
21 97 55
Using statistical software, estimate the parameters of the model
Second Test Grade=β0+β1(First Test Grade)+εiSecond Test Grade=β0+β1(First Test Grade)+εi.
Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.
Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
To estimate the parameters of the model, we can use the following steps:
Calculate the mean of the first test scores and the mean of the second test scores.
Calculate the difference between each student's first test score and the mean first test score, and the difference between each student's second test score and the mean second test score.
Multiply the differences from step 2 together for each student, and sum the results.
Divide the sum from step 3 by the sum of the squares of the differences from step 2. This will give us the value of β1.
Calculate β0 by substituting the values of β1 and the mean first and second test scores into the equation: Second Test Grade = β0 + β1(First Test Grade)
Using these steps, we can calculate the estimates of the parameters as follows:
Mean first test score = (50+91+55+58+79+70+97+51+51+59+69+56+56+41+49+58+58+99+87+95+97)/21 = 68.381
Mean second test score = (70+58+74+65+60+60+48+73+73+66+67+70+73+76+72+68+73+53+58+50+55)/21 = 64.762
Difference between student 1's first test score and mean first test score = 50 - 68.381 = -18.381
Difference between student 1's second test score and mean second test score = 70 - 64.762 = 5.238
Difference between student 2's first test score and mean first test score = 91 - 68.381 = 22.619
Difference between student 2's second test score and mean second test score = 58 - 64.762 = -6.762
Sum of multiplied differences = (-18.3815.238) + (22.619-6.762) + (-13.3818.238) + (-10.381-0.762) + (10.619*-6.238) + (2.619*-7.238) + (28.619*-16.762) + (-17.3819.238) + (-17.3819.238) + (-9.381*-0.762) + (0.619*-0.238) + (-2.3816.238) + (-2.3817.238) + (-27.38116.238) + (-18.3813.238) + (-10.381*-3.762) + (-10.3815.238) + (-10.3815.238) + (30.619*-11.762) + (18.619*-6.762) + (26.619*-14.762) + (28.619*-9.762) = -962.676
β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619)
Thus, Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
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Please help me solve this algebraic expression
Answer:
Step-by-step explanation:
4+5(7)
4+ 35
39
I got this answer by simply plugging in the number that was given because it said a =7 I plugged in 7 instead of using a. The same goes to b it said that b=4 so then i plugged in 4 instead of using b.
Write the range for the relation.
((-1, 1), (-2, 5), (-3, 7). (5, 8))
The range of a relation is the set of all possible values of the second element of the ordered pairs in the relation. In this case, the range of the relation is the set {1, 5, 7, 8}. This can be found by looking at the second element of each ordered pair in the relation and listing all the different values that appear.
need help struggling!
Answer:
Step-by-step explanation:
This is the same as before, two sides are the same length, so we know the angles are also the same. That is, D and C are equal
180= 106+2a
now algebra again
(180-106)/2 = a
74/2 = a
37 = a
Pleaseeee helppppp meeeeee
Answer:
C
Step-by-step explanation:
You can do trial and error since it is a multiple ans question
Answer:
c
Step-by-step explanation:
do trial and error it's right the answer is c
Ling bought d donut to hare with coworker. There were 6 donut in each box. Write an expreion that how how many boxe of donut Ling bought
The expression for the number of boxes of donuts bought by Ling is d/6.
We are given that -
Ling bought a ' d ' donut to share with a coworker.
There were 6 donuts in each box. This implies that 1 box contains 6 donuts.
Now, let us write the expression for the number of boxes of donuts bought by Ling as follows -
The number of boxes of donuts = the total number of donuts/donuts in 1 box.
Hence, the number of boxes of donuts = d/6
Thus, the expression for the number of boxes of donuts bought by Ling is d/6.
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Let P(t) denote the population of bacteria in a
Petri disht hours after bacteria are introduced to the environment
of the Petri dish. Suppose that the initial population of bacteria
is known to be 5000, and that the bacteria population doubles
every 6 hours. Assume that the population can grow indefinitely.
Give a formula for P(t).
well, if the population is doubling from whatever they happen to be, so that means the growth rate is 100%, so if they're hmmm "g", then later they become "2g", or doubled, and the later becomes "4g" and so on, so the rate is simply 100%, because "g" plus "g" is just 2g, and "2g" plus "2g" is just 4g and so on, anyhow
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=hours\\ c=period\to &6 \end{cases} \\\\\\ A=5000(1 + 1)^{\frac{t}{6}}\implies A=5000(2)^{\frac{t}{6}}\implies {\Large \begin{array}{llll} P(t)=5000(2)^{\frac{t}{6}} \end{array}}[/tex]
A teacher recorded unit 4 test scores from her class.
58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.
Find the percentile rank of a score of 71 on this street -
Victor is in the 60th percentile, what was his score?
The percentile score of 71 on test score is 27 and the score of victor is 71.
What is Statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given, the teacher recorded unit 4 test scores from class.
The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.
A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.
The percentile rank of a score of 71 on the test is find by formula
[tex]R_{100} =\frac{100(N < )+\frac{1}{2} }{N}[/tex]
=100×4+1/2(1)/15
=400+0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60th percentile.
60=Score/15
score=71
Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.
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if f(x)=-2x+5, find x so f(x)=3
Answer:
f(x)=-2x+5
f(x)=3
then,
f(x)=-2x+5
or, 3=-2x+5
or, 2x=5-3
or,2x=2
or, x=2÷2
x=1
so, the value of x is 1
Answer:
x=1
Step-by-step explanation:
3= -2x+5
-5. -5
-2= -2x
/-2. /-2
1=x
hopes this helps
I need help I don’t know how to do this question on ixl
Name the x- and y - intercepts for the equation:
5x - 3y = 15
Answer:
Red=X-Int: (3,0) Y-int: (0,-5)
Step-by-step explanation:
To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 5(0)-3y=15 you get this by plugging in the 0 for x and then you solve. 5 x 0 is 0 so you'd get -3y=15 divide -3 on both sides and get y=--5 meaning that is the y-intercept. You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 5x-3(0)=15. -3 x 0 is 0. So you'd have 5x=15 divide both sides by 5 and you'd get x=3 meaning that is the x intercept.
(Hopefully you were able to understand how I got the x and y intercepts for this equation)
a quadrilateral must be a parallelogram if one pair of opposite sides is a. congruent, only b. parallel, only c. congruent and parallel d. parallel and the other pair of opposite sides is
a quadrilateral must be a parallelogram if one pair of opposite sides is congruent and parallel
A quadrilateral with two sets of opposing parallel sides is referred to as a parallelogram.To be a parallelogram, one pair of opposite sides must be congruent and parallel. Congruent means that two sides have the same measurements or length while parallel means that two lines never intersect. For example, if one pair of opposite sides is congruent and parallel, and the other pair of opposite sides is parallel, then the quadrilateral is a parallelogram. This is because the two pairs of opposite sides form parallel lines and the respective pairs have the same length. Therefore, the answer is c. congruent and parallel.
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20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
Keith's equivalent rate with simple compounding is 0.0998 or 9.98%.
The Correct option is (B).
What is Compound Interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
Keith is offered an interest rate of 8.27% for a loan.
Now, using the following formula:
r = ([tex]e^{(i/n)[/tex] - 1) x n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
We have, i = 8.27%
Also assume that the number of compounding periods per year is 12, since many loans are compounded monthly.
Then,
r = ([tex]e^{(0.0827/12[/tex]) - 1) x 12
= (1.0082 - 1) x 12
= 0.0082 x 12
= 0.0984 or 9.84%
Hence, The equivalent rate is 0.0984 or 9.84%.
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From the observation deck of a skyscraper, Shaniece measures a 48^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1121 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
By using trigonometry it can be calculated that-
Horizontal distance from the base of the skyscraper out to the ship is 1009.91 feet
What is trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\\[/tex]
Trigonometry is a very important tool in mathematics.
Trigonometry is used here
Here, a diagram has been attached
Let AB be the skyscraper and C is the position of the boat
Let the horizontal distance from the base of the skyscraper be x feet
Angle of depression = 48°
Height of the observation deck = 1121 feet
[tex]tan 48 = \frac{1121}{x}\\1.11 = \frac{1121}{x}\\x = \frac{1121}{1.11}\\[/tex]
x = 1009.91 feet
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Answer: 1009.35
Step-by-step explanation:
solve please
A
B
c
d
Answer:
the answer is A
Hope this helps
What’s the surface area of this prism ?
The surface area of the triangular prism is 191 cm².
What is a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.
We know the surface area of a triangular prism is (S₁ + S₂ + S₃)/l + bh.
The given triangular prism has a surface area from the given diagram we determine, 3(D×A) + 2(B×C) [area of rectangles and triangles],
= 3(8×4) + 2(10×6).
= 3(24) + 2(60).
= 71 + 120.
= 191 cm².
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6. The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x)
The function that is gotten after transformation is; f(x - 1) = -2x - 4
How to Interpret the Graph Transformation?We are told that the parent function is f(x).
Now, after transformation, the function becomes;
f(x) = f(x - 1)
Now, the solid line graph has;
y-intercept = -2
x intercept = 1
Slope = -2/1 = -2
Thus, equation is;
f(x) = -2x - 2
Thus, for f(x - 1), what it means is that we will plug in (x - 1) for x in the parent function to get;
f'(x - 1) = -2(x - 1) - 2
= -2x -2 - 2
= -2x - 4
The graph that represents the function after transformation is as attached.
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Complete question is;
The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x - 1)?
Paul’s car is 17 ft long. He is making a Mindel of his car this 1/6 the actual size. What is the length of the model
Answer:2.8333…
Step-by-step explanation:
you just have to divide
Find equivalent expressions of 3 2x−9−4x 11 5x−x. choose three expressions.
Answer:
[tex]-(220x^2-5x+9)[/tex]
Step-by-step explanation:
[tex]3*2x-9-4x*11*5x-x\\\\-4*11*5xx+3*2x-x-9\\\\-4*11*5xx+6x-x-9\\\\-220x^2 +6x-x-9\\\\-44 5x^2 +6x-x-9\\\\-220x^2+6x-x-9\\\\-220x^2 +(6x-x)-9\\\\-220x^2+5x-9\\\\(-(220x^2-5x+9))[/tex]
Factor -1 out of -220x^2 +5x-9
A. 2.9 inches
B. 40 inches
C. 3.2 inches
D. 2.1 inches
The required measure of length of the box is 2.9 inches. Option A is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
according to the question,
h = 3l - 2.5
w = 3/4l
The volume of the box,
40 = l × w × h
40 = l × 3/4l × [3l-2.5]
40 = 3/4l²[3l - 2.5]
40 = 9/4l³ - 7.5/4l²
9/4l³ - 7.5/4l² - 40 = 0
t = 2.91932
t ≈ 2.9 inches
Thus, the length of the box must be at least 2.9 inches. Option A is the right answer.
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5c=13
what does equal?
help please
The equal gives the solution for the variable 'c' in the given equation. I.e., c = 2.6.
What is a solution for an equation?A solution is the only value that satisfies the equation. It is also said to be the root of the equation.
Calculation:The given equation is
5c = 13
To solve the equation, divide both sides of the equation by 5.
So, we get
5c/5 = 13/5
⇒ c = 13/5
On converting the fraction into a decimal, we get c = 2.6.
To find whether the solution is correct or wrong, just substitute the value into the equation. If we get L.H.S = R.H.S, then that solution is the valid or correct one.
Substituting the value in L.H.S of the given equation, we get
5c = 5(2.6)
On multiplying,
5c = 13.0 ≈ 13
⇒ L.H.S = R.H.S
Hence, the solution is valid. The value of c is 2.6.
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Estimation Gabe goes to the mall. If k is the number of items he bought, the
expression 12.92k + 27 gives the amount he spent in dollars at one store. Then he
spent 20 dollars at another store. Find the expression which represents the amount
Gabe spent at the mall. Then estimate how much Gabe spent if he bought 2 items.
The total spent at the mall by Gabe is $72.84 and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
12.92 k + 27, where k is the number of items bought,
Calculate the expression which represents the amount Gabe spent at the mall as shown below,
Total amount = Amount spent in one store + Amount spent in the second store
Total amount = 12.92 k + 27 + 20
Calculate the estimate of Gabe spent by putting k = 2,
Total spent in mall = 12.92 × 2 + 27 + 20
Total spent in mall = 25.84 + 47
Total spent in mall = $72.84
Therefore, the total spent at the mall by Gabe is $72.84, and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
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determine the probability of drawing either a queen or a heart? write your answer as a reduced fraction.
The probability that the card drawn is either a queen or a heart is 4/13
According to the given information
Consider the random experiment of picking one card from a deck of 52 cards that has been expertly shuffled, as well as the subsequent occurrences.
A queen is the card that was drawn.
H: the heart card was shown.
The chance that "the card drawn is a queen" is P(Q) = 4/52 = 1/13 because there are four queens.
The probability that the card selected will be a heart is P(H) = 13/52, or 1/4, because there are 13 hearts in the deck. Because the queen of hearts is one of the deck's cards, events Q and H are inclusive events. P(Q and H) = 1/52 is the likelihood that "the card picked is a queen and a heart (the queen of hearts)".
Four queens and thirteen hearts are included in the chance that "the card picked is a queen or a heart," but we do not want to count the queen of hearts twice. There are so 16 different methods to depict a queen.
The probability that the card drawn is either a queen or a heart
P(Q or H) = P(Q) + P(H) - P(Q and H)
= [tex]\frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
= [tex]\frac{16}{52}[/tex]
= [tex]\frac{4}{13}[/tex]
The probability that the card drawn is either a queen or a heart is 4/13
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A hotel ha food proviioned for 30 day to erve 80
people. If 40 more men join the hotel, the ame proviion
would have lat for how many day?
By using the formula, days = (original number of people / new number of people) * original number of days, the same food would last for 20 days.
What is number?A number is a mathematical concept that refers to a quantity or value that can be represented by a symbol. Numbers can be used to represent quantities in various contexts, such as counting, measuring, and quantifying.
What is irrational numbers?Irrational numbers are numbers that cannot be expressed as the ratio of two integers (e.g. pi, the square root of 2).
days = (original number of people / new number of people) * original number of days
In this case, we can plug in the values as follows:
days = (80 / (80 + 40)) * 30
days = (80 / 120) * 30
days = 2/3 * 30
days = 20
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Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?.
The correct option A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
Explain the term even integer?Odd numbers cannot be divided by two exactly, whereas even numbers were integers that can be divided by two exactly. Even number examples include 2, 6, 10, 20, 50, etc.The statement made by Xavier that the product of two odd integers always results in an even integer should be noticed.
For the given case, conjecture that the sum of two odd integers is always an even integer is -
Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.To know more about the even integer, here
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The complete question is-
Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?
Select option;
A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
B: Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.
C: Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.
D: Every time you add two odd numbers, the sum is an even number.