The real engine is 65.25 feet long
How to determine the length?The scale is given as:
Scale = 87 feet to 1 foot
The scale length is given as
Scale length = 9 inches
Convert inches to feet
Scale length = 9/12 feet
The actual length is then calculated as:
Actual = 87 * 9/12 feet
Evaluate
Actual = 65.25 feet
Hence, the real engine is 65.25 feet long
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which of the following functions is graphed below?
The function that's illustrated in the graph is function D.
How to explain the function?First, you look at the left side of the graph. You can tell by the shape that it is an x³ function.
Also, the filled-in circle means inclusive. so we know that when x is less than or equal to a number.
The answer that illustrates the information explained is D.
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Answer:
B.
Step-by-step explanation:
An open circle means to exclude the point.
A closed circle means to include the point.
In this graph we see a part of a parabola with an open circle above. The parabola starts at x = 1, but does not include x = 1, and the x values of the parabola increase.
A parabola has an x squared in the equation.
The solution has to have an equation with an x² as its greatest exponent, and also must include x > 1.
The lower part of the graph is a third degree polynomial, so it must have an x cube term, x³. Also, the greatest x value for the x³ function is x = 1, but x = 1 is included. Then all x values tot he left of x = 1 are also included, so for the cubic polynomial, the domain (x values) must be x ≤ 1.
The answer is B.
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The linear function y = 3 · w - 1 represents the number of sea shells found in each week.
The speed of the driven gear is 180 rounds per minute.
How to use direct and inverse relationships to analyze situations
In the first problem we have an example of linear progression, in which the number of sea shells is increased linearly every week. After a quick analysis, we conclude that the linear function y = 3 · w - 1, a kind of direct relationship.
In the second problem, we must an inverse relationship to determine the speed of the driven gear. Please notice that the speed of the gear is inversely proportional to the number of teeths. Then, we proceed to calculate the speed:
[tex]\frac{v_{1}}{v_{2}} = \frac{N_{2}}{N_{1}}[/tex]
If we know that [tex]v_{2} = 60\,rpm[/tex], [tex]N_{2} = 60[/tex] and [tex]N_{1} = 20[/tex], then the speed of the driven gear is:
[tex]v_{1} = v_{2}\times \frac{N_{2}}{N_{1}}[/tex]
[tex]v_{1} = 60\,rpm \times \frac{60}{20}[/tex]
[tex]v_{1} = 180\,rpm[/tex]
The speed of the driven gear is 180 rounds per minute.
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A sports store sells 70 pairs of running shoes per
day for $40.00 each. The owner estimates that
for each $3.00 increase in price, 3 fewer sales
are made each day. What price should be charged
to maximize profit?
Answer:
$55
Step-by-step explanation:
so, we know that each day the store will currently sell $2800 worth of shoes.
we want to know the maximum of the expression (40+3x)(70-3x), expanding we get 2800 - 9x^2 + 90x,
the maximum of this would be x = 5, so the price they should charge is 55
Use the data in the table to describe how the population in a town is changing. Then identify a function that
models the data. Use your function to predict the population after 6 years.
Population in a Town
Year
0
1
2
3
Population
600
1200
2400
4800
O There is a constant ratio 2
y = 600(2)*
38,400
O There is a constant ratio 2
y = 600 + 2x
5412
O There is a constant ratio 4
y = 600(2x)
7200
www
There is a constant ratio 4
y = 600 + 2x
664
D
The data given illustrates that there's a constant ratio of 2 and y = 600(2)^x; 38400
How to compute the ratio?The ratio based on the information given will be:
= 1200/600
= 2
Therefore, the constant ratio is 2.
In 6 years, the population will be:
= 600 × 2^6
= 600 × 64
= 38400
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A university freshman class has 9900 students 4554 of thoses students are majoring in computer science what percentage of the class is computer science majors
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
What percentage of the class is computer science majors?Percentage is simply number or ratio expressed as a fraction of 100.
It is expressed as;
Percentage = ( Part / Whole ) × 100%
Given the data in the question;
Total number of students or Whole = 9900Number of students majoring in computer science or Part = 4554Percentage of the class majoring in computer science = ?We substitute the given values into the above equation.
Percentage = ( Part / Whole ) × 100%
Percentage = ( 4554 / 9900 ) × 100%
Percentage = ( 0.46 ) × 100%
Percentage = 46%
Given the total number of students in the university freshman class and the number of students majoring in computer science, the percentage of the class majoring in computer science is 46%.
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I am odd I am less than 40 both of my digits are perfect squares t-u=0
Answer:
19 or 14
Step-by-step explanation:
Since the number is odd you can disqualify all even numbers up to 40 including 0.
Next since this number has 2 digits you can take out all 1 digit numbers.
After that, find perfect squares that also are 1 digit each.
Lastly merge the combination of the numbers as each digit on each sides in such a way that the result is less than 40.
Why we need the least common denominator to add or subtract ration?
Answer:
It is necesary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator
Step-by-step explanation:
Each container must hold exactly 1 litre of water Each container must have a minimum surface area
The containers must be spheres of radius = 6.2cm
How to minimize the surface area for the containers?
We know that the shape that minimizes the area for a fixed volume is the sphere.
Here, we want to get spheres of a volume of 1 liter. Where:
1 L = 1000 cm³
And remember that the volume of a sphere of radius R is:
[tex]V = \frac{4}{3}*3.14*R^3[/tex]
Then we must solve:
[tex]V = \frac{4}{3}*3.14*R^3 = 1000cm^3\\\\R =\sqrt[3]{ (1000cm^3*\frac{3}{4*3.14} )} = 6.2cm[/tex]
The containers must be spheres of radius = 6.2cm
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1 On a trip, a family drove 270 kilometers in 3 hours. a Find how many kilometers were traveled in one hour. Express this as a rate per hour. it rate
Answer:
90 kilo per hour
Step-by-step explanation:
hope that helps!!
Determine which equation is belongs to the graph of the limacon curve below.
[-5,5] by [-5,5]
a.
r = 1 + 3 sin theta
c.
r = 1 + 3 cos theta
b.
r = 2 + 2 sin theta
d.
r = 3 + sin theta
Option a. The equation that is used to show the graph of the limacon is given as r = 1 + 3 sin theta.
How to solve for the equationWe have these ppoints [-5,5] by [-5,5]
The limacoin is used to represent a shape that may appear like that of a snail.
This is written in the form of
r = a ± b sin θ
and
r = a ± b cos θ
Given that we have the ± sign, the curve that is at the top of the horizontal; line is the + sign and the one below is the -
If a/b < 1 then a circle is within the circle that was formed as a graph.
Hence from the description that we have given here, the graph has the forms of
r = a + b sin θ
This is the equation that can be used to suit the form r = 1 + 3 sin theta
Hence option a is right.
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If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?
hi
f(x) = x² -2x
g(x) = 6x+4
(f+g) (x) = x²-2x +6x+4 = x²+4x +4 = (x+2)² = (x+2) (x+2)
(f+g) (x) = 0 means = (x+2) (x+2) = 0
so x+2 = 0
x = -2
(f+g) (x) = 0 for x = -2
In order to solve the following system of equations by addition, which of the
following could you do before adding the equations so that one variable will
be eliminated when you add them?
4x - 2y = 7
3.x - 3y = 15
Answer:
Multiply the top equation by -3 and the bottom equation by 2
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}4x-2y=7\\3x-3y=15 \end{cases}[/tex]
To solve the given system of equations by addition, make one of the variables in both equations sum to zero. To do this, the chosen variable must have the same coefficient, but it should be negative in one equation and positive in the other, so that when the two equations are added together, the variable is eliminated.
To eliminate the variable y:
Multiply the top equation by -3 to make the coefficient of the y variable 6:
[tex]\implies -3(4x-2y=7) \implies -12x+6y=-21[/tex]
Multiply the bottom equation by 2 to make the coefficient of the y variable -6:
[tex]\implies 2(3x-3y=15) \implies 6x-6y=30[/tex]
Add the two equations together to eliminate y:
[tex]\begin{array}{l r r}& -12x+6y= &-21\\+ & 6x-6y= & 30\\\cline{1-3}& -6x\phantom{))))))} = & 9\end{array}[/tex]
Solve for x:
[tex]\implies -6x=9[/tex]
[tex]\implies x=-\dfrac{9}{6}=-\dfrac{3}{2}[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies 3\left(-\dfrac{3}{2}\right)-3y=15[/tex]
[tex]\implies -\dfrac{9}{2}-3y=15[/tex]
[tex]\implies -3y=\dfrac{39}{2}[/tex]
[tex]\implies y=-\dfrac{39}{2 \cdot 3}[/tex]
[tex]\implies y=-\dfrac{13}{2}[/tex]
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You have a credit card that charges an interest rate of 16.15% compounded monthly. The table below shows your activity for the month of April. Date Activity Amount Balance April 1 Beginning Balance 1,000.00 April 5 Purchase 29.10 1,029.10 April 12 Payment −225.00 804.10 April 15 Purchase 97.25 901.35 April 23 Purchase 19.00 920.35 April 26 Purchase 28.40 948.75 April 30 Ending Balance 948.75 What is the average daily balance for this account? $ What is the finance charge for the month of April? $
1. The average daily balance for this credit card account is $187.74.
2. The finance charge for the month of April is $249.22.
How is the average daily balance calculated?The average daily balance for April is the total of the balance for every day in the billing cycle divided by the number of days in the billing cycle.
A billing cycle for a credit card account is usually one month.
Data and Calculations:Interest rate = 16.15% compounded monthly
Date Activity Amount Balance
April 1 Beginning Balance $1,000.00
April 5 Purchase 29.10 1,029.10
April 12 Payment −225.00 804.10
April 15 Purchase 97.25 901.35
April 23 Purchase 19.00 920.35
April 26 Purchase 28.40 948.75
April 30 Ending Balance 948.75
Total $5,632.05
Average daily balance = $187.735 ($5,632.05/30 days)
Daily interest rate = 0.04425 (16.15%/365)
Finance charge = $249.22 ($187.74 x 0.04425 30 days)
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The sides of a rectangle are enlarged by a scale factor of 2. Write
down the scale factor that the area is enlarged by.
Answer:
4
Step-by-step explanation:
both sides are multiplied by 2 which means its the original area*2*2 which means it's the original area*4
Factor the expression 3x^(2)+10x+8
Hello,
If we want to factor the expression, we have to solve
3x² + 10x + 8 = 0
a = 3 ; b = 10 ; c = 8
∆ = b² - 4ac = 10² - 4 × 3 × 8 = 4 > 0
x1 = (-b - √∆)/2a = (-10 - 2)/6 = -12/6 = -2
x2 = (-b + √∆)/2a = (-10 + 2)/6 = -8/6 = -4/3
Factor :
a (x - x1)(x - x2)
= 3(x + 2)(x + 4/3)
= (x + 2)(3x + 4)
Does this represent a proportional relationship
Answer:
D.
Step-by-step explanation:
the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.
The probability that a student has a Visa card (event V) is .76. The probability that a student has a Master card (event M) is .16. The probability that a student had both is .04.
Answer:
The Probability of both happening is 0.304.
Step-by-step explanation:
P(A) × P(B)
= 0.76 × 0.4
= 0.304
Can you help with this question? I'm not sure if the black highlighted choice is right
Answer:
See below
Step-by-step explanation:
Remember... when you square a negative number, you get a positive result
AND you cannot divide by zero AND you cannot have the sqrt of a negative number so:
-2 > x > 2 (looks like 'D' but there is a negative sign missing)
Find the value of t; log3y=2 and log3ty=6
Answer: [tex]10^4[/tex]
Step-by-step explanation:
Assuming we are using the common log (base 10),
[tex]\log 3ty=6\\\\\log 3y +\log t=6\\\\2+\log t =6\\\\\log t=4\\\\t=10^4[/tex]
Explain how to draw a line segments that measures 2 7/16 inches. d
Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart
Step-by-step explanation: On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches
Micheal solved this inequality as shown: step 1: -6(x + 3) + 10 < -2 step 2: -6x - 18 + 10 < -2 step 3: -6x - 8 < -2 step 4: -6x < 6 step 5: x > -1. what property justifies the work shown between step 3 and 4?
================================================
Explanation:
These are the steps to focus on
step 3: -6x - 8 < -2
step 4: -6x < 6
The move from the third step to the fourth step has us adding 8 to both sides. Therefore, we use the addition property of inequality.
That property has four forms
If [tex]a > b[/tex] then [tex]a + c > b+c[/tex]If [tex]a < b[/tex] then [tex]a+c < b+c[/tex]If [tex]a \ge b[/tex] then [tex]a + c \ge b+c[/tex]If [tex]a \le b[/tex] then [tex]a+c \le b+c[/tex]It's similar to the idea of starting with a = b, then adding c to both sides to get a+c = b+c
We add the same thing to both sides to keep things balanced.
in circle V, r=14. What is the area of circle V
Answer:
[tex]\pi[/tex][tex]14^{2}[/tex] or [tex]\pi 196\\[/tex]
Step-by-step explanation:
The circle V has the radius of 14 (r=14)
The formula of area is (A=[tex]\pi r^{2}[/tex])
So we insert the value of (r=14)
[tex]A=\pi 14^2[/tex]
[tex]A=\pi 196[/tex]
And that's the answer, The exact value is 615.752...
Answer: 196 pi
Step-by-step explanation:
Ramon is six years younger than 4 times his brothers age. Oh f his brother is 5 year old, how old is Ramon
Answer:
14
Step-by-step explanation:
The equation would be R = 5(4) - 6. Multiply 5 by 4 to get 20, then subtract 6 to get 14.
Find the interquartile of the data set that consists of 8,18,4,2,3,7,11,13,5,1 answers 11,8,6,3
Answer:
I.Q.R = 11 - 3
I.Q.R = 9
the interquartile range = 9
Circles A circular device has a diameter of 4.5 inches. What is the radius of the device? Choose one 2 points O2.25 inches O4.5 inches O 4.5 inches O 2.25 inches 10 CO D
Answer: 2.25 inches
Step-by-step explanation:
The radius of a circle is half the diameter.
find the outer perimeter of this figure
Answer:
41.12 ft
Step-by-step explanation:
10 + 6 = 16
2 x pi x r = 25.12
16 + 25.12 = 41.12
Answer:
Step-by-step explanation:
find the outer perimeter of this figure
we find the perimeter of the semicircleThe perimeter of circle formula = 2πr unitsr = diameter : 2 = 8 : 2 = 4
2π4 =
8π=
8 × 3.14 = 25.12 ft
find figure perimeter
25.12 + 6 + 10 =
41.12 ft
Pizza prices by city (Data in Pizza prices) The company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:
The answers to the questions are
a. No they are not the same
b. The presence of outliers are known to affect the market.
How to solve the box plot
For these areas we have
Q1 = 2.7 Q3 = 3 median = 2.8 out;ier 2.
Q1 = 2.5 Q3 = 2.7 median = 2.6 out;ier 3.1.
Q1 = 2.5 Q3 = 2.75 median = 2.65 out;ier 1.6
Q1 = 2.4 Q3 = 2.6 median = 2.5
We can see that the median prices in the markets are nearly similar except for the one that is conatined in the first market.
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What is the value of c in the equation below?
22²=a=c
Answer:
484
Step-by-step explanation:
because a=22² , which is equal to 484
because a=22² , which is equal to 484, but a=c hence C is equal to 484
The graph of f(x) = x3 − 7x − 6 is shown.
Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6?
x = −6
x = −2, −1
x = −2, −1, 3
x = −6, −2, −1, 3
In accordance with the graph of the cubic function, the roots are - 2, - 1, 3.
What are the roots of a cubic equation according to a graph?
In this question we have a graph of a cubic equation, the roots are the points of the curve that pass through the x-axis. Cubic equations have at least a real root and at most three. In accordance with the graph of the cubic equation, the roots are - 2, - 1, 3.
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find the value of x and y