Answer:
a) d(x)=[tex]\sqrt{17x^{2} -12x+5}[/tex]
b)d'(x)=[tex]\frac{17x-6}{\sqrt{17x^{2} -12x+5} }[/tex]
c)The critical point is x=[tex]\frac{6}{17}[/tex]
d)Closest point is ([tex]\frac{6}{17}[/tex],[tex]\frac{7}{17}[/tex]
Step-by-step explanation:
We are given the line
[tex]y=4x-1[/tex]
Let a point Q([tex]x,y[/tex]) lie on the line.
Point P is given as P(2,0)
By distance formula, we have the distance D between any two points
A([tex]x_{1},y_{1}[/tex]) and B([tex]x_{2},y_{2}[/tex]) as
D=[tex]\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_2)^2}[/tex]
Thus,
d(x)=[tex]\sqrt{(x-2)^2+(y-0)^2}[/tex]
But we have, [tex]y=4x-1[/tex]
So,
d(x)=[tex]\sqrt{(x-2)^2+(4x-1)^2}[/tex]
Expanding,
d(x)=[tex]\sqrt{17x^2-12x+5}[/tex] - - - (a)
Now,
d'(x)= [tex]\frac{\frac{d}{dx} (17x^2-12x+5)}{2(\sqrt{17x^2-12x+5}) }[/tex]
i.e.
d'(x)=[tex]\frac{17x-6}{\sqrt{17x^{2} -12x+5} }[/tex] - - - (b)
Now, the critical point is where d'(x)=0
⇒ [tex]\frac{17x-6}{\sqrt{17x^{2} -12x+5} }[/tex] =0
⇒[tex]x=\frac{6}{17}[/tex] - - - (c)
Now,
The closest point on the given line to point P is the one for which d(x) is minimum i.e. d'(x)=0
⇒[tex]x=\frac{6}{17}[/tex]
as [tex]y=4x-1[/tex]
⇒y=[tex]\frac{7}{17}[/tex]
So, closest point is ([tex]\frac{6}{17},\frac{7}{17}[/tex]) - - -(d)
:
Which represents the explicit formula for the arithmetic sequence an=15+5(n−1) in function form?
A
f(n)=5n+15
B
f(n)=n+20
C
f(n)=5n+10
D
f(n)=n+10
For this case we have the following arithmetic sequence:
[tex]a_ {n} = 15 + 5 (n-1)[/tex]
To write in function form, we apply distributive property to the terms within parentheses:
[tex]f (n) = 15 + 5n-5[/tex]
Different signs are subtracted and the major sign is placed.
We simplify:
[tex]f (n) = 5n + 10[/tex]
Answer:
[tex]f (n) = 5n + 10[/tex]
Option C
The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10.
Explanation:The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10 (Option C).
The arithmetic sequence is represented as an=15+5(n−1). This equation can be further simplified to an=15+5n-5, which eventually gives us an=5n+10. So the explicit formula for this arithmetic sequence in function form is option C, which is f(n)=5n+10. This function f(n), directly gives us the nth term of the arithmetic sequence.
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Select the correct choices that belong in the blank for the system of equations shown below.
24x - 39 = 165
-6x +13y = -51
In order to solve this system by elimination, Stacy ____________ by ______. Then, when she adds the equations together, the x terms will cancel.
Question 4 options:
multiplies the second equation; 4
multiplies the first equation; 4
multiplies the second equation; -4
Answer:
The answer to your question is Stacy multiplies the second equation by 4.
Step-by-step explanation:
24x - 39y = 165 (I)
- 6x + 13y = -51 (II)
Multiply the second equation by 4
24x - 39 y = 165
-24x + 52y = -204
Simplify
0 + 13y = 39
y = 39/ 13
y = 3
Find "x" value 24x - 39(3) = 165
24x - 117 = 165
24x = 165 + 117
24x = 282
x = 282 / 24
x = 47/4
A school population consists of 33 seventh-, 47 eighth-, and 37 ninth-grade students. If we select one child at random from the total group of students, what is the probability that the child is in the ninth-grade
Answer:
Step-by-step explanation:
Total number of students: 33 +47 +37 = 117 students
Students in 9th class = 37
So probabilty of selecting a 9th class student from a class of 117 students is:
=>(Total student in 9th class)/(Total student in the sample)
=>37/117 =>Ans
To find the probability of selecting a ninth-grade student from a school population, divide the number of ninth-grade students by the total population.
Explanation:To find the probability that a randomly selected student is in the ninth-grade, we need to calculate the fraction of ninth-grade students out of the total population of students. Here's how:
Add up the number of seventh, eighth, and ninth-grade students: 33 + 47 + 37 = 117.Divide the number of ninth-grade students by the total population: 37 / 117 = 0.316 (rounded to three decimal places).The probability that the randomly selected student is in the ninth-grade is approximately 0.316, or 31.6%.
Susan wants to make pumpkin bread and zucchini bread for the school bake sale. She has 15 eggs and 16 cups of flour in her pantry. Her recipe for one loaf of pumpkin bread uses 2 eggs and 3 cups of flour. Her recipe for one loaf of zucchini bread uses 3 eggs and 4 cups of flour. She plans to sell pumpkin bread loaves for $5 each and zucchini bread loaves for $4 each. Susan wants to maximize the money raised at the bake sale. Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.What is the objective function for the problem?
A. P = 15x + 16y
B. P = 5x + 7y
C. P = 5x + 4y
D. P = 4x + 5y
Answer:
Option C.
Step-by-step explanation:
Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.
Pumpkin bread zucchini bread Total
Eggs 2 3 15
Flour(cups) 3 4 16
Selling price $5 $4
Susan wants to maximize the money raised at the bake sale.
Objective function :
[tex]P=5x+4y[/tex]
Subject to constraints:
[tex]2x+3y\leq 15[/tex]
[tex]3x+4y\leq 16[/tex]
[tex]x,y \geq 0[/tex]
Since the objective function is P = 5x + 4y, therefore the correct option is C.
Answer:
c
Step-by-step explanation:
i got it correct on edgenunity
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. (Assume the car travels the same distance for each one gallon of gas)
The number of miles traveled varies directly with the number of gallons of gas you use.
a. Write an equation that relates miles traveled to gallons of gas used. (Use any variable you like in the equation.
b. How far can you drive with 3.7 gallons of gas? (Make sure to show the calculations you did to determine this answer)
Answer:
Step-by-step explanation:
Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that
1 gallon of gas would be used to drive 392/14 = 28 miles
a) The number of miles traveled varies directly with the number of gallons of gas used.
Let x =number of gallons of gas you use.
Let y = the number of miles travelled.
Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,
y = kx
If 28 miles will require 1 gallon of gas, it means
28 = 1×k
k = 28
So y = 28x
b) we want to determine how far you can drive with 3.7 gallons of gas.
x = 3.7
y = 28x = 28×3.7
y = 103.6 miles
9/20
Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
nd
01
ations
02
O cannot be determined
are
00
e
100%
Answer:
No real roots
Step-by-step explanation:
The given quadratic equation is
[tex] {x}^{2} + 5x + 7 = 0[/tex]
Comparing this to the general quadratic equation:
[tex]a {x}^{2} + bx + c = 0[/tex]
We have a=1, b=5 and c=7
Recall that the discriminant is
[tex]D = {b}^{2} - 4ac[/tex]
We plug in the values to get:
[tex]D = {5}^{2} - 4(1)(7)[/tex]
[tex]D =25- 28 = - 3[/tex]
Since the discriminant is less than zero, the given equation has no real roots
I made a distribution of 15 apartment rents in my neighborhood. One apartment had a higher rent than all the others, and this outlier caused the mean rent to be higher than the median rent. Does this make sense because the outlier with a large value increases the mean, but does not affect the median?
Answer:
Yes this makes sense
Step-by-step explanation:
When their is one outlier it makes the average spike which can present misleading data while with median the outlier is left relatively unaffected.
Answer:
Yes this makes sense.
Step-by-step explanation:
The given dataset consists of 15 apartment rents. A data value which is an outlier (much larger than the rest) will increase the overall mean value of the population but it may not affect the median. Let us take an example of 15 sample rent value in ascending order,
100,120,130,140,150,170,175,185,190,200,220,250,280,290,1000
Here , mean rent will become high due to the single high rent datapoint(1000) but the median won't be impacted.
A rectangular swimming pool has a perimeter of 96 ft. The area of the pool is 504 ft2. Which system of equations models this situation correctly, where l is the length of the pool in feet and w is the width of the pool in feet?
Answer:
2l + 2w = 96 ..... eqn1
lw = 504 ...... eqn2
Step-by-step explanation:
To model this case where we have two unknowns l and w, we need two equations.
Firstly, the perimeter of a rectangle is given by
2l + 2w = p
Where l,w and p are length, width and perimeter of the rectangle respectively.
Hence,
2l + 2w = 96 ... eqn1
Secondly, the area of a rectangle is given by
Length × width = Area
Hence,
l × w = 504
lw = 504 ... eqn2
With these two equations the solutions to the length and width of the rectangular pool can be derived.
Answer:
D. 2l+2w=96
lw=504
Step-by-step explanation:
Edge 2020 (got 100%)
Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard deviation of 0.11 oz. Find the probability that a single can of Coke has at least 12.19 oz.
Answer:
0.0421
Step-by-step explanation:
Mean(μ) = 12.00 oz
Standard deviation (σ) = 0.11 oz
Z = (x - μ)/σ
Z = (12.19 - 12.00) / 0.11
Z= 0.19/0.11
Z = 1.727
From the normal distribution table, Z = 1.727 = 0.4579
Φ(Z) = 0.4579
Recall that if Z is positive
Pr(x>a) = 0.5 - Φ(Z)
Pr(x > 12.19) = 0.5 - 0.4579
= 0.0421
Jake is building a fence around his property. He wants the perimeter to be no more than 100 feet. He also wants the length to be at least 10 feet longer than the width. If he builds his fence according to these limits, which would be the maximum possible width of the fence?
The maximum possible width of the fence is 7.5 feet.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Let's start by assigning variables to the length and width of the fence.
Let x be the width of the fence in feet, then the length of the fence is x + 10 feet
(since the length is at least 10 feet longer than the width).
Now,
The perimeter of the fence is the sum of the lengths of all its sides.
Since the fence has four sides of equal length,
The perimeter is 4 times the length of one side.
So,
The equation for the perimeter, P, in terms of x.
P = 4(x + x + 10)
= 8x + 40
Now,
We know that Jake wants the perimeter to be no more than 100 feet,
So we can write an inequality:
8x + 40 ≤ 100
Solving for x:
8x ≤ 60
x ≤ 7.5
Therefore,
The maximum possible width of the fence is 7.5 feet.
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Final answer:
To find the maximum width for Jake's fence with the given constraints, set up inequalities with the perimeter and length requirements. Solving for the width, we find that the maximum possible width Jake can use is 20 feet.
Explanation:
Jake is constructing a fence around his property and wishes for the perimeter to not exceed 100 feet, while the length must be at least 10 feet longer than the width. Let's denote the width of the property as w and the length as l. According to the constraints:
The perimeter (2w + 2l) ≤ 100 feet
The length (l) ≥ w + 10 feet
Using these inequalities, we have:
2w + 2(w + 10) ≤ 100
2w + 2w + 20 ≤ 100
4w ≤ 80
w ≤ 20
The maximum possible width is therefore 20 feet.
A Biology student who created a regression model to use a bird's height when perched for predicting its wingspan made these two statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation.
a. An R2 of 93% shows that this linear model is appropriate.
b. A bird 10 inches tall will have a wingspan of 17 inches.
A) Choose the correct choice below.
A. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.
B. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A scattered residuals plot is the indicator of an appropriate model.
C. R2 is an indication of the strength of the model, not the appropriateness of the model. A scattered residuals plot is the indicator of an appropriate model.
D. R2 is an indication of the strength of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.
B) Choose the correct choice below.
A. Regression models give predictions, not actual values. The student should have said, "The model predicts that a bird 10 inches tall is expected to have a wingspan of 17 inches."
B. Regression models give averages, not actual values. The student should have said, "A bird 10 inches tall will, on average, have a wingspan of 17 inches."
C. Regression models give probabilities, not actual values. The student should have said, "A bird 10 inches tall will probably have a wingspan of 17 inches."
D. Regression models give actual values, but the student should have said, "The model states that a bird 10 inches tall will have a wingspan of 17 inches."
Answer:
a) C
b) A
Step-by-step explanation:
The wingspan is the dependent variable while the bird height is the independent variable.
a) Since R2 is the dependent variable, it can be expressed by the independent variable. An R2 of 93% represents 93% of the variation in the wingspan which can be explained by using the birds height. This means that the appropriateness of the model should not be determined by R2 but by using a scatter plot.
b) The model predicts the value of wingspan using the value of bird height. We cannot say that the bird 10 inches tall has a wingspan if 17 inches instead, we say that the wingspan of the bird which is 10 inches tall is 17 inches.
It is therefore possible that the wing span is not exactly 17 inches
Final answer:
The R2 value does not indicate the appropriateness of the model, and regression models provide predictions, not actual values.
Explanation:
A. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.
A bird 10 inches tall will have a wingspan of 17 inches.
A. Regression models give predictions, not actual values. The student should have said, "The model predicts that a bird 10 inches tall is expected to have a wingspan of 17 inches."
A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September.
A) The sample size was 4.
B) The sample size was 100.
C) The sample size was 400.
D) The sample size was 1.
Answer:
B) The sample size was 100
Step-by-step explanation:
Number of sample size in January = 100
Number of sample size in March = 100
Number of sample size in June = 100
Number of sample size in September = 100
The average sample size for the study = (100 +100+100+100)/4
= 400/4
= 100
So the average sample size for the study is 100 women between 18 to 21 years.
use the intermediate value theorem to determine, if possible, whether g(x)=2x^3+3x^2-3x+4 has a real zero between -2 and -1
Answer:
Step-by-step explanation:
g(-2)=2(-2)^3+3(-2)^2-3(-2)+4=-16+12+6+4=6
g(-1)=2(-1)^3+3(-1)^2-3(-1)+4=-2+3+3+4=8
it does not change sign ,so there is no real zero between -2 and -1.
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y equals start fraction one over two end fraction x plus four question mark?
Answer:
[tex]y = \frac{1}{2}x - 2[/tex]
Step-by-step explanation:
Given lines,
y = 2x - 5,
y = -x + 1
Subtracting these two equations,
0 = 3x - 6
[tex]\implies 3x = 6[/tex]
[tex]\implies x = \frac{6}{3}=2[/tex]
By first equation,
[tex]y=2(2) -5=4-5 = -1[/tex]
Thus, point of intersecting would be (2, -1).
Now, the equation of a line is y = mx + c,
Where,
m = slope of the line,
So, the slope of the line [tex]y=\frac{1}{2}x+4[/tex] is 1/2.
∵ two parallel lines have same slope.
Hence,
Equation of the parallel line passes through (2, -1),
[tex]y+1=\frac{1}{2}(x-2)[/tex]
[tex]y+1=\frac{1}{2}x - 1[/tex]
[tex]y = \frac{1}{2}x - 2[/tex]
The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours. The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 hours. If both outlets are used at the same time, approximately what is the number of hours required to fill the pool?
(A) 0.22
(B) 0.31
(C) 2.50
(D) 3.21
(E) 4.56
Answer: (D) 3.21
Step-by-step explanation:
Let [tex]t_A=[/tex] Time taken by one outlet to fill the pool.
[tex]t_B=[/tex]Time taken by second outlet to fill the pool.
Given : The time taken by one outlet to fill the entire pool : [tex]t_A=[/tex] 9 hours
The time taken by second outlet to fill the entire pool : [tex]t_B=[/tex] 5 hours
Now , if both outlets are used at the same time, approximately what is the number of hours required to fill the pool (T) , then the time required to fill the pool will be :_
[tex]\dfrac{1}{T}=\dfrac{1}{t_A}+\dfrac{1}{t_B}\\\\\Rightarrow =\dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{9+5}{(9)(5)}=\dfrac{14}{45}\\\\\Rightarrow\ T=\dfrac{45}{14}=3.21428571429\approx3.21[/tex]
Hence, the approximate time taken by both outlets to fill the pool together = 3.21 hours.
Thus , the correct option is (D) 3.21
The question is about rate, time and work. Using the given rates of the outlets, we determine the combined rate. We then use the time = work/rate formula to calculate the time it would take for both outlets to fill the pool, which comes out to approximately 3.21 hours.
Explanation:This question is a typical problem in rate time and work, which is a common topic in mathematics especially algebra. The problem talks about two outlets with different rates filling a pool.
Let's consider the rate of the first outlet as 1/9 pool/hour and the second outlet as 1/5 pool/hour. If both outlets are working at the same time, their rates would add up. Hence, the combined rate would be 1/9 + 1/5 = 14/45 pool/hour.
To find how long it would take for both outlets to fill the pool, we use the equation time = work/rate. Plugging in our values, we get time = 1 pool / 14/45 pool/hour. Therefore, the time is amounts to approximately 3.21 hours.
Therefore, "the correct answer is (D) 3.21".
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A survey conducted five years ago by the health center at a university showed that 18% of the students smoked at the time. This year a new survey was conducted on a random sample of 200 students from this university, and it was found that 50 of them smoke. We want to find if these data provide convincing evidence to suggest that the percentage of students who smoke has changed over the last five years. What are the test statistic (Z) and p-value of the test?
Answer:
test statistic (Z) is 2.5767 and p-value of the test is .009975
Step-by-step explanation:
[tex]H_{0}[/tex]: percentage of students who smoke did not change
[tex]H_{a}[/tex]: percentage of students who smoke has changed
z-statistic for the sample proportion can be calculated as follows:
z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where
p(s) is the sample proportion of smoking students ([tex]\frac{50}{200}[/tex] =0.25)p is the proportion of smoking students in the survey conducted five years ago (18% or 0.18)N is the sample size (200)Then, z=[tex]\frac{0.25-0.18}{\sqrt{\frac{0.18*0.82}{200} } }[/tex] ≈ 2.5767
What is being surveyed is if the percentage of students who smoke has changed over the last five years, therefore we need to seek two tailed p-value, which is .009975.
This p value is significant at 99% confidence level. Since .009975 <α/2=0.005, there is significant evidence that the percentage of students who smoke has changed over the last five years
Go tigers tail is around 30% of its total length the total length of one Bengal tiger is 96 cm around how long is the tiger?
Final answer:
To determine the length of a Bengal tiger's tail, which is 30% of its total length of 96 cm, we calculate 30% of 96 to get a tail length of approximately 28.8 cm.
Explanation:
The question asks us to calculate the length of a Bengal tiger's tail given that it is 30% of its total length. If the total length of the tiger is 96 cm, we can find the length of the tail by calculating 30% of 96 cm.
To find 30% of 96, we convert the percentage into a decimal by dividing by 100 and then multiply by the total length:
30% = 30/100 = 0.3
0.3 x 96 cm = 28.8 cm
Therefore, the length of the Bengal tiger's tail is approximately 28.8 cm.
Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 120 pounds of blended coffee beans selling for $5.17 per pound. She plans to do this by blending together a high quality beans costing $6.50 per pound and a cheaper bean at $2.50 per pound. To the nearest pound, find how much high quality coffee bean and how much cheaper coffee bean she should blend.
a.She should blend _____________lbs of high quality beans.
b.she should blend______________lbs of cheaper beans.
Answer:
a) 80 ibs
b) 40 ibs
Step-by-step explanation:
Let X be the pound of the high quality bean at $6.50
(120-x) will be the pound of the cheaper bean at $2.50
6.5x + 2.5(120 - x) = 5.17(120)
6.5x + 300 - 2.5x = 620.4
Collect like terms
6.5x - 2.5x = 620.4 - 300
4x = 320.4
x = 320.4/4
x= 80.1
x = 80 ibs(to the nearest pounds)
For the cheaper bean we have 120 -x
= 120 - 80
= 40 ibs
Sarah would blend 80 ibs of quality bean and 40 ibs of cheaper bean
Sarah should blend 80 pounds of high quality beans and 40 pounds of cheaper beans to achieve her target blend of 120 pounds at $5.17 per pound.
Sarah Meeham needs to blend high quality and cheaper coffee beans to create a blend selling for $5.17 per pound, using a total of 120 pounds. Let x be the pounds of high-quality beans and 120 - x be the pounds of cheaper beans. Setting up the equation for the total cost of the blend, we have:
6.50x + 2.50(120 - x) = 5.17 \\times 120
Solving for x, we get:
6.50x + 300 - 2.50x = 620.4
4x = 320.4
x = 80.1
To the nearest pound, Sarah should blend 80 pounds of high quality beans and 120 - 80 = 40 pounds of cheaper beans.
Find the quadratic function y=ax^2 + bx + c whose graph passes through the given points. (-3,37), (2,-8), (-1,13)
The quadratic function is [tex]y=1x^{2} + (-8)x + 4[/tex]
Step-by-step explanation:
The quadratic function given is [tex]ax^{2} + bx + c=y[/tex]
and same quadratic function is passes through (-3,37), (2,-8), (-1,13)
Replacing points one by one
we get,
For (-3,37) :
[tex]a(-3)^{2} + b(-3) + c=37[/tex]
[tex]9a + -3b + c=37[/tex] = equation 1
For (2,-8) :
[tex]a(2)^{2} + b(2) + c=(-8)[/tex]
[tex]4a + 2b + c=(-8)[/tex] = equation 2
For (-1,13)
[tex]a(-1)^{2} + b(-1) + c=(13)[/tex]
[tex]a + -1b + c=13[/tex] = equation 3
Solving the linear equation to get values of a,b,c
Subtract equation 2 with equation 3
we get,[tex](4a + 2b + c)-(a + -1b + c)=(-8)-13[/tex]
[tex](3a + 3b )=(-21)[/tex]
[tex](a + b )=(-7)[/tex] = equation 4
Now, Subtract equation 1 with equation 2
we get,[tex](9a + -3b + c)-(4a + 2b + c)=(37)-(-8)[/tex]
[tex](5a - 5b )=(45)[/tex]
[tex](a - b )=(9)[/tex] = equation 5
Now, Add equation 4 with equation 5
we get,[tex](a + b)+(a - b)=(-7)+(9)[/tex]
[tex](2a - 0b )=(2)[/tex]
[tex](a)=1[/tex]
Replacing value of a in equation 5
[tex](a - b )=(9)[/tex]
[tex](1 - b )=(9)[/tex]
[tex](b)=(-8)[/tex]
Replacing value of a and b in equation 1
[tex]9a + -3b + c=37[/tex]
[tex]9(1) + -3(-8) + c=37[/tex]
[tex]9 + 24 + c=37[/tex]
[tex] c=4[/tex]
Thus,
The quadratic function [tex]y=1x^{2} + (-8)x + 4[/tex]
A book sold 34,100 copies in the first month the release suppose this represents 7.9% of the number of copies sold to date how many copies have you sold to date
Answer:
431,646
Step-by-step explanation:
The problem statement tells us ...
34,100 = 0.079 × (sold to date)
Dividing by 0.079, we get ...
34,100/0.079 = (sold to date) ≈ 431,646
About 431,646 copies have been sold to date.
The total number of books sold to date is approximately 431,646. This was determined by using the percentage of the total sales represented by the first month's sales (7.9%) and the number of books sold in the first month (34,100 copies).
To solve this problem, we need to understand that the 34,100 books sold in the first month represent 7.9% of the total number of copies sold to date. In mathematics, percentage is a way of expressing a number as a fraction of 100. Here, we need to find the whole, where 7.9% is equivalent to 34,100 copies.
To do this, we use this formula:
Total Copies Sold = Number of Copies Sold / Percentage sold (in decimal form)So, the calculation would be:
Total Copies Sold = 34100 / 0.079The result we get from the calculator is approximately 431,646 copies. This means, approximately 431,646 copies were sold to date.
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Problem Page A jet travels 3310 miles against a jetstream in 5 hours and 3810 miles with the jetstream in the same amount of time. What is the rate of the jet in still air and what is the rate of the jetstream?
Answer:
jet in still air: 712 mi/hjetstream rate: 50 mi/hStep-by-step explanation:
The relation between speed, time, and distance is ...
speed = distance/time
Against the wind, the speed is ...
(3310 mi)/(5 h) = 662 mi/h
With the wind, the speed is ...
(3810 mi)/(5 h) = 762 mi/h
The jet stream adds to the speed in one direction, and subtracts in the other direction, so the difference in travel speeds is twice the speed of the jet stream:
(762 mi/h -662 mi/h)/2 = jet stream speed = 50 mi/h
__
The speed of the plane is the average of the two speeds, or the sum of jet stream speed and the lower speed, or the difference of the higher speed and the jet stream speed. Any of these calculations will give the plane's speed in still air:
(762+662)/2 = 662 +50 = 762 -50 = 712 . . . mi/h
What is the area of the figure?
Answer:
96 m²
Step-by-step explanation:
The figure is a trapezoid with bases of length 10 m and 22 m, and height 6 m. Putting these numbers into the formula for area of a trapezoid gives ...
A = (1/2)(b1 +b2)h
= (1/2)(10 m +22 m)(6 m) = 96 m²
The area of the figure is 96 m².
What is the measurement of BC?
Answer:
4.45
Step-by-step explanation:
cos(70)= BC/13
BC=13*cos(70)
BC= 4.45 cm
A person earns $25000 per month and pays 9000 income tax per year. The government increased income tax by 0.5% per month and his monthly earning was increased $11000. How much more income tax will he pay per month.
Answer:
The person will pay $ 510 more as income tax per month .
Step-by-step explanation:
Given as :
The monthly income of person = $ 25000
The amount paid as income tax per year =$ 9000
So,The amount paid as income tax per month =$ [tex]\frac{9000}{12}[/tex] = $750
Or, x% is the income tax of the monthly income
I.e x % of 25000 = 750
∴ x % = [tex]\frac{750}{25000}[/tex]
Or, x = [tex]\frac{750}{25000}[/tex] × 100
I.e x = 3 %
Now, since the income tax is increase by 0.5 % per month
So, x' = 3 % + 0.5 % = 3.5 %
And The monthly income increase by $ 11000
I.e New monthly income = $ 25000 + $ 11000 = $ 36000
Now, The income tax which the person pay now is 3.5 % of $ 36000
i.e The income tax which the person pay now = 0.035×36000 = 1260 per month
so, The income tax which the person pay now as per year = 1260 × 12 = $ 15,120
∴ The increase income tax per month = $ 1260 - $ 750 = $ 510
Hence The person will pay $ 510 more as income tax per month . Answer
Final answer:
To calculate the additional income tax the person will pay per month, we add the tax increase due to the salary increase to the original increased tax after the 0.5% hike. The total increased monthly tax payment amounts to $930.
Explanation:
The question is asking how much more income tax a person will pay per month after their salary is increased and the government increased income tax by 0.5%. To find the additional income tax that a person will pay, we need to consider the initial monthly income, the new monthly income, the old annual tax amount, and the increased tax rate.
Originally, the person earned $25,000 per month and paid $9,000 in income tax yearly. With the 0.5% monthly increase in tax, we first need to calculate the monthly increase based on the initial salary. The monthly increase is 0.5% of $25,000, which is $125. Therefore, the new monthly tax without accounting for the salary increase is the old monthly tax plus the $125 increase.
The monthly tax paid before the income increase was $9,000 / 12 months = $750 per month. After the 0.5% monthly increase, the tax becomes $750 + $125 = $875 per month. But the person's monthly earnings were increased by $11,000, resulting in a new monthly income of $25,000 + $11,000 = $36,000.
To calculate how much more in income tax the person will pay on the additional $11,000 monthly earnings at the increased rate: 0.5% of $11,000 is $55. So the additional tax per month is $55. Therefore, the total increased monthly tax is $875 + $55 = $930.
Find an explicit rule for the nth term of the sequence.
7, -7, 7, -7, ... (5 points)
Select one:
a. an = 7 • (-1)n-1
b. an = 7 • (-1)n
c. an = 7 • 1n-1
d. an = 7 • 1n+1
Answer:
(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Step-by-step explanation:
Here, the given sequence is 7, -7, 7, -7, ...
The first term = 7, Second term = -7, Third term =-7 and so on..
Now check the given sequence for each given formula, we get:
(1) [tex]a_n = 7 \times (-1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1-1}\\[/tex]
[tex]= 7 \times (-1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (-1)^{2-1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_2 = -7[/tex]
Hence, the given formula satisfies the given sequence.
(2) [tex]a_n = 7 \times (-1)^{n}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (-1)^{1}\\[/tex]
[tex]= 7 \times (-1)^1 = 7 \times (-1) = -7 \implies a_1 = -7[/tex]
But, First term = 7
Hence, the given formula DO NOT satisfy the given sequence.
(3) [tex]a_n = 7 \times (1)^{n-1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1-1}\\[/tex]
[tex]= 7 \times (1)^0 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2-1}\\[/tex]
[tex]= 7 \times (1)^1 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
(4) [tex]a_n = 7 \times (1)^{n+1}\\[/tex]
Now, for n = 1 : [tex]a_1 = 7 \times (1)^{1+1}\\[/tex]
[tex]= 7 \times (1)^2 = 7 \times 1 = 7 \implies a_1 = 7[/tex]
Similarly, for, n = 2: [tex]a_2 = 7 \times (1)^{2+1}\\[/tex]
[tex]= 7 \times (1)^3 = 7 \times (1) = 7 \implies a_2 = 7[/tex]
But, Second term = -7
Hence, the given formula DO NOT satisfy the given sequence.
So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7 \times (-1)^{n-1}\\[/tex].
Answer:
an=7•(-1)^n-1
Step-by-step explanation:
Help with this question please answer it
correctly and show work please and I am gonna Mark you as a brainliest
Answer:
15.5 yards
They will be picked up at an elevation of 15.5 yards
Step-by-step explanation:
Here we are going to make the ski slope of the mountain as the hypotenuse of a right-angled triangle where the top of the slope and bottom of the slope are two ends of the hypotenuse.
We first have to find the height of the top of the mountain with respect to the bottom.
Here we have been given heights with respect to sea level above and below.
Clearly, sum of the distances above and below sea level will be total elevation with respect to the bottom.
h1 - Height of summit above sea level
h2 - Height of bottom below sea level
Hb - Elevation of top w.r.t bottom
Hb = h1 + h2
Hb = [tex]17\frac{3}{4}+13\frac{1}{4}[/tex]
Hb = 31 yards
Now, the ski lift is picking them up in the middle of the slope (hypotenuse of the triangle).
By midpoint theorem line segment parallel to base joins the midpoints of the other 2 sides.
Thus the elevation will clearly be half of total elevation.
Height at which they are picked up is Hb/2
Therefore,
They will be picked up at an elevation of 15.5 yards
What is the slope of a line that is perpendicular to the line whose equation is y=4x+1?
The slope of a line perpendicular to the line with equation y=4x+1 is -1/4. This is found by taking the negative reciprocal of the original line's slope, which is 4.
Explanation:The slope of a line that is perpendicular to a given line can be determined by taking the negative reciprocal of the slope of the given line.
Given the equation y=4x+1, we can see that the slope (m) is 4.
Therefore, a line that is perpendicular to this line would have a slope that is the negative reciprocal of 4, which is -1/4.
The concept of perpendicular lines in coordinate geometry implies that two lines are perpendicular if the product of their slopes is -1.
Our given line has a positive slope, hence the slope of its perpendicular counterpart must be negative. A positive slope indicates that the line moves up as we move from left to right, whereas a negative slope indicates that the line moves down.
To test the effect of music on productivity, a group of assembly line workers are given portable mp3 players to play whatever music they choose while working for one month. For another month, they work without music. The order of the two treatments for each worker is determined randomly. This is
(a) an observational study.
(b) a completely randomized experiment.
(c) a block design.
(d) a matched pairs experiment.
(e) impossible to classify unless more details of the study are provided.
Answer:
(d) a matched pairs experiment.
Step-by-step explanation:
The correct answer is option D that is d) a matched pairs experiment.
A matched pair experiment is special case of randomize block design. This experiment can be used when the statement has two treatment conditions and subjects are grouped into pair based on some treatment. For each pair, random treatments are assigned to the subjects. It is an improvement over complete randomized design.
This is an experiment because a treatment (the MP3 players) was assigned to different members of the sample(the assembly line workers) randomly.
This study is a d) matched pairs experiment where assembly line workers are given portable mp3 players to play their chosen music while working for one month and then work without music for another month, with the order determined randomly.
Explanation:This study is a matched pairs experiment because each worker serves as their own control by experiencing both treatments, with the order of treatments determined randomly. In a matched pairs experiment, participants are paired up based on similar characteristics, and each pair is randomly assigned to different treatments. Here, the workers are matched based on their own preferences for the music they choose.
The workers are given portable mp3 players and can choose their own music, which serves as the treatment variable. The productivity of the workers is measured in two different months, one with music and one without music. By comparing the workers' productivity in the two months, the study aims to determine the effect of music on productivity.
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Alex and bob are playing 5 chess games. Alex is 3 times more likely to win than bob. What is the probability that both of them will win at least 2 games?
To find the probability of both Alex and Bob winning at least 2 games during their 5 games chess play, principles of geometric probability and the Multiplication rule are used. The equation _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))] is formed considering Alex is 3 times more likely to win than Bob.
Explanation:Calculating Probability of Games
In this scenario, Alex and Bob are playing 5 games with Alex being 3 times more likely to win than Bob. The primary question is to find the probability for both of them winning at least 2 games.
We would utilize the principles of geometric probability to solve this. Geometric probability treats each game as a Bernoulli trial, a game of win or lose. Moreover, we operate with the Multiplication rule in finding the probability of both events, Alex and Bob winning 2 games, happening.
Firstly, we define the probability of Alex winning as p, therefore, the probability of Bob winning is p/3. Bob and Alex must win 2 games each, leaving one game open to any outcome. Since the games are independent, the Multiplication rule applies. Therefore, the probability is calculated by multiplying probabilities for each win and possible combinations of five games taken two at a time. In other words, the equation will look like _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))].
The resulting value will be the probability for both of them winning at least 2 games.
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What is the value of x, given that AE || BD
Answer:
x = 7.8
Step-by-step explanation:
If AE is parallel to BD, then you can use the theorem called ratio of sides of parallel line.
AC/AB = EC/ED
x+11/x = 12/5
x=7.8
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the unknown sides will be equal to 7.857 units.
What are Similar Figures?
Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".
For the two similar triangles, ΔAEC and ΔBDC, the ratio of the sides will be,
11/7 = (11+x)/(5+7)
11/7 = (11+x)/12
(11×12)/7 = 11+x
18.857 - 11 = x
x = 7.857
Hence, the length of the unknown sides will be equal to 7.857 units.
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