Answer:
Step-by-step explanation: I think its the second one
Which point is on the line that passes through point h and is perpendicular to line fg? (–6, 10) (–2, –12) (0, –2) (4, 2)
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).
You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points.
The slope of the perpendicular lines is negative reciprocals.
So if FG is 3/4, it would be -4/3.
The slope is calculated as m = (y2-y1)/(x2-x1).
So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3
m= (10-(-6)/(-6-6) (-6-6)
m = 16/-12
m= -4/3
As a result, the ultimate answer to this question is A) (-6, 10)
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Answer:
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is
Step-by-step explanation:
The point is on the line that passes through point h and is perpendicular to line fg is (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is
Find the equation of a line perpendicular to 4x + 3y = -24 that passes through
the point (-8, 3).
The equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
4x + 3y = -24 and point (-8, 3).
Calculate the slope,
3y = -4x - 24
y = -4 / 3 x - 8
so, m = -4 / 3
The slope of the perpendicular line, M = - 1 / m
M = - 1 / -4 / 3 = 3 / 4
Calculate the equation of the line as shown below,
y - 3 = 3 / 4 [x - (-8)]
y - 3 = 3 / 4 [x + 8]
4y - 12 = 3x + 24
4y = 3x + 36
Therefore, the equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.
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Jeremy has 50 ft of fencing to enclose a rectangular-pen for his dog. He plans on using a side of his house for one side of the pen. What dimensions will produce an enclosed area of 288 ft?
The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.
What is the dimension of length and width?We know that,
P = l + 2w
50 = l + 2w
50 - 2w = l
A = l x w
288 = (50 - 2w)w
288 = 50w -2w²
2w² - 50w + 288
By dividing throughout by 2
w² - 25w + 144
This is in quadratic equation form.
By applying quadratic formula,
w = (-(-25) ± [tex]\sqrt{(-25)^{2}-4*1*144[/tex]) / 2
w = (-(-25) ± 7)/2
w1 = (-(-25) + 7)/2
w1 = (25 + 7) / 2
w1 = 16
w2 = (-(-25) - 7)/2
w2 = (25 - 7) / 2
w2 = 9
By substituting the values in eq1,
A = l x w
if w = 16
288 = l x 16
l = 288/16
l = 18
if w = 9
288 = l x 9
l = 288/9
l = 32
The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.
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In order for a school to allow a vending machine to be placed next to the cafeteria, 65% of the school’s population must ask for it. If 340 of the school’s 650 students have requested the vending machines, how many more are needed to get the vending machines?
Show your work!
Using percentages, we know that 83 students more are needed to vote for the vending machine.
What is the percentage?Additionally, "pct," "pct," and occasionally "pc" are used. A % is a number without dimensions and without a standard measurement.
For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).
So, 65% of the school population is:
650/100 * 65
422.5
Rounding off: 423
Students voted for vending machines is 340.
A number of more votes/asks for the vending machine will be:
423 - 340
83
Therefore, using percentages, we know that 83 students more are needed to vote for the vending machine.
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A survey is given to children and adults about their favorite meal of the day.
*Breakfast is preferred by one and half times more children than adults.
*Children and adults both had 24 respondents for dinner.
*There were 62 adults who responded lunch, twice as great as the number of children who responded lunch. The results are shown in the table.
Which category has an error in the table?
Breakfast
Lunch
Adults
Children
Table below:
The category has an error in the table is A. breakfast.
How to illustrate the survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted by phone, mail, or the internet, as well as on street corners or in shopping malls.
Historically, survey research has included large amounts of population-based data collection.
The primary goal of this type of survey research was to quickly obtain information describing the characteristics of a large sample of individuals of interest.
The category has an error in the table is breakfast. In this case, the children should be 45 and not 30.
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In 2012, there are approximately 275 students in the Delaware High School band. In 2018, that number increased to 305. Find the annual rate of change from 2012 to 2018 in the number of students.
Using exponential function, the annual rate of change in the school is 1.74%
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function)
In this problem, the annual rate of change can be calculated as
A = P(1 + r)ˣ
r = ratex = timeLet's substitute the values into the equation and solve;
305 = 275(1 + r)⁶
r = 0.0174
r = 0.0174 * 100
r = 1.74%
The annual rate of change is 1.74%
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Which of the correlation values represent a perfect linear relationship between x and y?
a. 0.5
b. 1
c. 100
d. -1
e. 0
The correlation values 1 and -1 represent a perfect linear relationship between the two variables x and y.
Step to Step explanation:
To represent perfect linear relationship between two variables the correlation values should be 1 and -1.When correlation value is equal to 1 it represent the positive linear relationship between two variables x and y.Slope of the correlation value positive 1 indicates the increasing slope.When correlation value is equal to -1 it represent the negative linear relationship between two variables x and y.Slope of the correlation value negative 1 indicates the decreasing slope.Therefore, the perfect linear relationship between two variables x and y is given correlation value 1 and -1.
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two dice are tossed. what is the probability that their sum will be 6, given that exactly one face shows 2? (round your answer to three decimal places.)
The probability that their sum will be 6 is 1/6.
What is probability?
The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.
Here are all rolls of the dice, the sample space,
which contains 36 elements:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
If one face shows a 2, then there are 6 possible faces on the other die.
Only one of those is a 4 which would make the sum of 6.
Hence, the probability that their sum will be 6 is 1/6.
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PLEASE ANSWER ASAP! Choose ALL equations that would create a parallel line to y=78x+9
The equation of the parallel to y = 7/8x + 9 will be y = 7/8x+11, 7x - 8y = 3, and (y-6) = 7/8(x-1).
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is y = 7/8x+9. For the equation to be parallel the slope of the line must be the same.
The equations having the same slope of the line as that of y = 7/8x + 9 are,
y = 7/8x+11,
7x - 8y = 3,
(y-6) = 7/8(x-1)
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At the beginning of spring, Allison planted a small sunflower in her backyard. When it was first planted, the sunflower was 15 inches tall. The sunflower then began to grow at a rate of 2 inches per week. How tall would the sunflower be after 9 weeks? How tall would the sunflower be after w weeks?
Answer:
Hope this helps you out
Step-by-step explanation:
After 9 weeks, the sunflower would be 39 inches tall.
After w weeks, the sunflower would be 15 + (2 * w) inches tall.
A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup (in cm) that will use the smallest amount of paper. (round your answers to two decimal places. ).
The height and radius of the cup that will use the smallest amount of paper are 3.86 cm and 2.72 cm. The result is obtained by using the first derivative .
How to find the dimension of a cone?To find the height and radius of a cone for the smallest surface area, we can use the first derivative dS/dh. We then equate it to 0 for the maximum value.
The volume of a cone-shaped paper drinking cup is 30 cm³. Find the height and radius for the smallest amount of paper!
The radius of the cone can be expressed as
V = 1/3 (πr²h)
30 = 1/3 (πr²h)
90 = πr²h
r² = 90/πh
The surface area of the cone can be expressed as
S = πrs
[tex]S = \pi r \times \sqrt{h^{2} + r^{2}}[/tex]
[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{{h^{2} + \frac{90}{\pi h}[/tex]
[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{\frac{(\pi h^{3} + 90)}{\pi h}[/tex]
[tex]S = \sqrt{90} \times \sqrt{\frac{(\pi h^{3} + 90)}{h^{2}}[/tex]
[tex]S = \sqrt{90} \times \sqrt{\pi h + \frac{90}{h^{2}} }[/tex]
The 1st derivative is
[tex]\frac{dS}{dh} = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]
[tex]0 = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]
The height for the smallest amount of paper is
π - 180/h³ = 0
π = 180/h³
h³ = 180/π
h³ = 57.32
h = 3.86 cm
The radius for the smallest amount of paper is
r² = 90/πh
r² = 90/π(3.86)
r² = 7.42
r = 2.72 cm
Hence, the dimension of the cone-shaped paper drinking cup for the smallest amount of paper is
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hippocrates magazine states that 35 percent of all americans take multiple vitamins regularly. suppose a researcher surveyed 750 people to test this claim and found that 296 did regularly take a multiple vitamin. is this sufficient evidence to conclude that the actual percentage is different from 35% at the 5% significance level? select the [p-value, decision to reject (rh0) or failure to reject (frh0
The solution to this problem is , we reject null hypothesis R H0 at p value =0.005 .
What is significance level ?The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.
Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.
Persons surveyed = 750
Of those survived no of persons who took multiple vitamin = 296
Sample proportion = p =0.395
q =1-p = 0.605
[tex]H_{0}\\[/tex] : p= 0.35
[tex]H_{A}[/tex] : p ≠ 0.35
(Two tailed test)
Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]
=>0.0174
p difference = 0.045
Test statistic = 0.045/0.0174
=>2.58
p value = 0.005 for right tailed
Reject H0:
Therefore , we reject R H0 at p value =0.005 .
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6x+2=4x+3
Please help asap I been doing the work for so long and can’t get a final answer
Answer x=1/2
Step-by-step explanation:
6x+2=4x+3
2x+2=3
2x=1
x=1/2
Answer:
x= 1/2
Step-by-step explanation:
x=1/2
6x+2=4x+3
-4x -4x
2x+2=3
-2 -2
2x=1
/2 /2
x=1/2
Cai is ordering a taxi from an online taxi service. He has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far he travels. He wrote an equation to represent his total cost, y=1. 3x+2y=1. 3x+2, where yy represents the total cost in dollars and cents, and xx represents the number of miles he travels. What could the number 1. 3 represent in the equation?.
The equation of cost of taxi payed by cal is,
y=1. 3x+2
here , y --> total cost of taxi
x --> distance travelled by him
Cofficient of x i.e., 1.3 represents the cost/rate of taxi per mile .
We have given a equation of total cost pay by Cal on ordering a taxi from online taxi service. The equation is
y = 1.3x+2
where, y represents the total cost in dollars
x represents the number of miles he travels ; 2 is fixed charge
Since, x represents the number of miles he travels then the cofficient of x is representing the taxi rate or cost per mile . So, that when we multiply 1.3 with number of miles he travel(i.e x ) we get the total cost on travelling x distance.
After adding the total cost of travelling with fixed charge of taxi we get total cost of journey.
Hence, 1.3 represents the cost per mile.
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a 20 foot ladder is placed 5 feet from the base of a building. how high on the building will the ladder reach?
As calculated with the help of Pythagorean theorem, The ladder will reach 19.36 feet high on the building.
What is Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle. The square whose side is the hypotenuse, or the side across from the right angle, has an area equal to the sum of the areas of the squares on its other two sides. The Pythagorean equation, which connects the lengths of the sides B, P, and the hypotenuse H, can be used to express this theorem.
H² = B² + P²
As given in the question,
the length of the ladder is 20 ft. which will work as a hypotenuse of a right angled triangle,
The base is 5 ft.
we need to find the perpendicular line to the base.
Applying Pythagorean theorem.
H² = B² + P²
20² = 5² + P²
400 = 25 + P²
400 - 25 = P²
P = 19.36 ft.
Therefore, the ladder will go 19.36 ft. high on the building.
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I need help with quadrilateral proofs
The completed two-column table to prove that ABCD is a rectangle is presented as follows;
Step Statement [tex]{}[/tex] Reason
1 [tex]{}[/tex] ΔABD ≅ ΔDCA Given
[tex]{}[/tex] [tex]\overline{AD}[/tex] ≅ [tex]\overline{BC}[/tex]
2. [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex] Reflexive property
3. [tex]\overline{CA}[/tex] ≅ [tex]\overline{CA}[/tex] [tex]{}[/tex] Reflexive property
4. [tex]{}[/tex] ∠CAD ≅ ∠BDA CPCTC
5. [tex]{}[/tex] [tex]\overline{AE}[/tex] ≅ [tex]\overline{ED}[/tex] Side length of isosceles triangle ΔAED
6. [tex]{}[/tex] [tex]\overline{AB}[/tex] ≅ [tex]\overline{ED}[/tex] CPCTC
7. [tex]{}[/tex] ΔABD ≅ ΔBCD SSS
8. ΔDCA ≅ ΔABC [tex]{}[/tex] SSS
9. ∠B ≅ ∠C ≅ ∠D ≅ ∠A [tex]{}[/tex] CPCTC
10. [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A [tex]{}[/tex] Definition of congruency
11. [tex]{}[/tex] ∠B + ∠C + ∠D + ∠A = 360° [tex]{}[/tex] Angles in quadrilateral
12. [tex]{}[/tex] 4·∠B = 360° Substitution property
13. [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A = 90° Substitution property
14. [tex]{}[/tex]ABCD is a rectangle Definition of a rectangle
What is a rectangle?A rectangle is a quadrilateral that has four interior angles that are right angles (90°) each and in which the length of the adjacent sides are different.
The details of the reasons used to prove that ABCD is a rectangle are presented as follows;
Reflexive property
The reflexive property of congruency states that a part is congruent to itself
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent
Isosceles triangle
An isosceles triangle is a triangle with a pair of congruent sides and a pair of congruent base angles
SSS
The Side-Side-Side (SSS) congruency postulate states that two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle
Definition of congruency
A geometric shape is congruent to another geometric figure if they have the same measurement
Angles in a quadrilateral
The sum of the interior angles in a quadrilateral is 360°
Substitution property
The substitution property of equality states that if a = b then b can substitute a in equations and expressions, without changing their value
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Identify the measure of angle x:
Answer:
79°
Step-by-step explanation:
All three of the angles form a straight line = 180°
28 + x + 73 = 180
x = 79°
Answer:x=79
Step-by-step explanation:
what does the central limit theorem say about the shape of the distribution of the sample means? the distribution will be approximately normal regardless of sample size. the distribution will be normal when all sample means within 2 standard deviations of the actual mean are considered. the distribution will be approximately normal when the standard deviation of the sample means is the same as the population standard deviation. the distribution will be approximately normal when the sample size is large. the distribution will be approximately normal when the sample size is small.
Thus, the distribution will be approximately normal when the sample size is large.
What is central limit theory ?According to the central limit theorem, even if a population isn't normally distributed, if you take sufficiently big samples from it, the sample means will be.
Here,
the central limit theorem say about the shape of the distribution of the sample means because
If the sample size is big, the solution will be when the distribution is roughly normal.
thus, the distribution will be approximately normal when the sample size is large.
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Which of the statements are true about the function f given by f(x) = 100 • e^-x
Select all that apply. s
A. The y-intercept of the graph off is at (0, 100).
B. The values f increase when x increases.
C. The value of f when x = -1 is a little less than 40.
D. The value of f when x = 5 is less than 1.
E. The value of f is never 0.
Answer:
A. The y-intercept of the graph of f is at (0, 100).
D. The value of f when x = 5 is less than 1.
E. The value of f is never 0.
The first two statements are not true because the function f is defined by the equation f(x) = 100 • e^-x, where e^-x is the base of the natural logarithm (commonly known as "e") raised to the power of -x. Since e is always greater than 1, the value of e^-x will always be between 0 and 1, so the function f will always decrease as x increases. This means that statements B and C are not true.
Step-by-step explanation:
What is an equation of the line that passes through the point (6,1)(6,1) and is perpendicular to the line 2x+3y=182x+3y=18?.
The equation of a line passes through (6,1) is 3x - 2y = 16.
Here we have to find the equation of a line.
Data given:
Point = (6,1)
The equation of another line is 2x + 3y = 18
From the given equation we can find the slope;
So we have
3y = -2x + 18
y = -2/3x + 18/3
So the slope is -2/3
As the line is perpendicular, so the slope of the line perpendicular to it will be 3/2
The general formula of the line is:
(y - y1) = m(x-x1)
(x1, y1) is the point
The point is (6,1 ) and the slope is 3/2
Now put that in the equation we get:
(y - 1) = 3/2(x - 6)
2y - 2 = 3x - 18
3x - 2y = 16
Therefore the equation is 3x - 2y = 16.
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How do you prove SAS congruence rule?
The prove the SAS congruence rule, two sides and one angles between the includes sides of the triangle and the two sides and one angles between the includes sides of the another triangle should be equal
The SAS congruence rule is used to prove the congruence of the one triangle angle and another triangle.
SAS congruence rule stands for the side-angle-side congruence rule of triangles.
Side-angle-side rule of congruence states that if two sides and one angles between the includes sides of the triangle is equal to the two sides and one angles between the includes sides of the another triangle, then the both the triangles are congruent
Therefore, to prove the SAS congruence rule two sides and one angle of both triangle should be equal
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6. Tom's cousin, George, is three times as old as Tom. In 15
years, Tom will be two-thirds as old as his cousin, George.
How old is each of them in 15 years?
The answer to this Question based on ages is 20 years and 30 years
What is age?
The age is measure of how old the person is. It also gives us idea about how many years before he was born This data is used at various places in application forms medical form etc
Let age of Tom be x and age of George be y
given 1st condition george is 3 times as old as Tom
hence we can write y = 3x
After 15 years age of tom = x + 15 and age of George be y + 15
according to 2nd condition
x + 15 = 2/3(y + 15)
3x + 45 = 2y + 30
2y - 3x = 15
put y = 3x here
2(3x) - 3x = 15
3x = 15
x = 5
and y = 3(5)
y = 15
present age of tom = 5 years and after 15 years he will be 20 years old
present age of george = 15 tears and after 15 years he will be 30 years old
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write the function in terms of unit step functions. find the laplace transform of the given function. f(s)
The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x
Rewrite f in terms of the unit step function:
[tex]f(t) \left \{ {{y=5} for 0\leq t \leq 7\atop {x=-3}} \rightfor t\leq 7[/tex]
⇒ f(t) = 5{u(t) -u(t -7) - 3u (t -7)}
= 5u(t) - 8u (t-7)
Recall the time-shifting property of the Laplace transform:
L I u(t - c)f(t -c) I
= e⁻ᵃˣ L[f(t)]
and the Laplace transform of a constant function,
L(K) = [tex]\frac{k}{a}[/tex]
So we have
L{f(t)} = 5u(t) - 8u (t-7)
= 5 L[1] - 8e⁻⁷ˣ
= 5 - 8e⁻⁷ˣ/ x
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A football field i 300 ft long. A loth moving very quickly travel 60 ft every 5 min. Baed on thi ratio how many minute would it take the length of a football field
Using simple unitary method, the time taken to take the length of the football field is 25min.
What do you mean by number system?The system for naming or representing numbers is known as the number system or numeral system. We are aware that a number is a mathematical value that aids in the measurement and counting of items as well as in several mathematical operations.
What do you mean by unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Loth travels 60 ft in 5 min.
Loth travels 1 ft in 5/60 min.
Loth travels 300 ft in 5/60 * 300 min.
=1/12 * 30
=25min
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4. Jennifer has a lemonade stand. She charges $1.25 for a glass of lemonade. It costs her $0.60 to make each glass of lemonade plus $15 a day for other expenses. Write an equation (do not solve) to determine how many glasses of lemonade, 1, Jennifer needs to sell each day in order to break even?
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the number of glasses of lemonade Jennifer needs to sell each day
Total charge for x glasses = 1.25x
It costs her $0.60 to make each glass of lemonade:
=> For x glasses, cost = 0.6x
Per day cost = 0.6x + 15
In order to break even,
Total charge for x glasses = Per day cost
1.25x = 0.6x + 15
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Please help!!! i need this done by tonight!! 50 points!!
The equation of best fit is y = (-22/5)x + 10.
What is an equation of a line?
The equation of a line is given by:
y = mx + c where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The following coordinates are given:
Pick two coordinates.
(0, 10) and (25, -100)
The equation of best fit.
y = mx + c
Now,
m = (-100 - 10) / (25 - 0)
m = -110 / 25
m = -22/5
Now,
(0, 10) = (x, y)
10 = (-22/5) x 0 + c
c = 10
Now,
y = mx + c
y = (-22/5)x + 10
Thus,
Using the coordinates the equation of best fit is y = (-22/5)x + 10.
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At a bowling alley, the cost of shoe rental is $2. 55 and the cost per game is $3. 75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?.
The recursive equation for f( n ) is f( n-1 ) + 3.75
Any term of a sequence in terms of its preceding terms is a recursive equation. The equation can be defined as a mathematical statement made up of expressions. For example, b (n ) = 2b ( n-1 ) + 4 is a recursive equation.
As per the question,
The cost of shoe rental ( c ) = 2.55The cost per game ( g ) = 3.75number of games = nThe total cost of shoe rental = f ( n ) The recursive equation for f ( n ) = ?As we know,
⇒ f ( n ) = total cost
= g × n + c
f ( n ) = 3.75 ( n ) + 2.55
Replace n with n - 1,
⇒ f ( n - 1 ) = 3.75 ( n - 1 ) + 2.55
⇒ f ( n - 1 ) = 3.75 n - 3.75 + 2.55
⇒ f ( n - 1 ) = 3.75 n + 2.55 - 3.75
⇒ f ( n - 1 ) = f ( n ) - 3.75
⇒ f ( n ) = f ( n - 1 ) + 3.75
Therefore, f( n-1 ) + 3.75 is the recursive equation for f ( n ).
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Sam and Julia are running a lemonade stand. Sam is selling regular lemonade for $0.50 per cup, while Julia is selling pink lemonade for $0.75 per cup. In total, they sell 140 cups of lemonade and make $90. Define x = number of regular lemonade cups that Sam sells Define y = number of pink lemonade cups that Julia sells (a) Write a system of equations that represents this situation. (b) Find how many cups of regular lemonade that Sam sold. Response area (c) Find how many cups of pink lemonade that Julia sold. Response area
a) The system of equations that represents this situation is given as follows:
x + y = 140.0.5x + 0.75y = 90.b) The number of cups of regular lemonade sold is given as follows: 60.
c) The number of cups of pink lemonade sold is given as follows: 80.
How to obtain the amounts?The amounts are obtained with a system of equations, in which the variables are as defined in the problem.
Variable x: number of regular lemonade cups.Variable y: number of pink lemonade cups.They sell 140 cups, hence:
x + y = 140.
y = 140 - x.
They earn a total of $90, hence, considering the amount earned per cup:
0.5x + 0.75y = 90.
Replacing the first equation into the second, the variable x is obtained as follows:
0.5x + 0.75(140 - x) = 90.
0.25x = 15
x = 15/0.25
x = 60.
Then the variable y has a value of:
y = 140 - x = 140 - 60 = 80.
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the international air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. the maximum possible rating is 10. suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the miami international airport. the ratings obtained from the sample of business travelers follow.
A confidence interval estimate of the population mean rating for Miami is:
Confidence interval:
(Mean - E) ≤ μ ≤ (mean + E)
(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)
6.8622 ≤μ≤ 8.1778
Now, According to the question:
Given the data:
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Assume a confidence interval of 95%
Using calculator :
The mean of the distribution (m) = 7.52
Standard deviation (s) = 2.314
Sample size),
Obtaining the t score ;
Degree of freedom (df) = (n-1) = 50 - 1 = 49
t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)
Margin of Error :
2.01 * s/√n = 2.01 * 2.314/7.0710678
Margin of Error (E) = 0.6578
Confidence interval:
(Mean - E) ≤ μ ≤ (mean + E)
(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)
6.8622 ≤μ≤ 8.1778
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The complete question is this:
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.
2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9
6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9
7 10 7 9 9 9 9
Required:
Develop a confidence interval estimate of the population mean rating for Miami.
Can you guys work your mathical math ASAP
Answer:
216.025 I think
Answer: S=237.5 in
Step-by-step explanation:
S=2(5)(6,5)+2(6.5)(7.5)+2(5)(7.5)
S=6,5(10)+97.5+7.5(10)
S=65+97.5+75
S=237,5 in