Let 'y' be the weight of the airplane corresponding to when the amount of fuel is 'x'.
Given that the airplane weighs 2104 when fuel is 16 gallons, this can be represented as the ordered pair,
[tex](16,2104)[/tex]Also, given that the airplane weighs 2312 when fuel is 48 gallons.The corresponding ordered pair will be,
[tex](48,2312)[/tex]It is mentioned that there is a linear relationship between the amount of fuel (x), and the weight of airplane (y).
Consider that the equation of a straight line passing through two given points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x_2-x_1)[/tex]As per the given problem,
[tex]\begin{gathered} (x_1,y_1)=(16,2104) \\ (x_2,y_2)=(48,2312) \end{gathered}[/tex]Substitute the values,
[tex]\begin{gathered} y-2104_{}=\frac{2312-2104}{48-16}\cdot(x-16) \\ y-2104_{}=\frac{13}{2}\cdot(x-16) \\ y-2104=\frac{13}{2}x-104 \\ y=\frac{13}{2}x-104+2104 \\ y=\frac{13}{2}x+2000 \end{gathered}[/tex]At the instant when the fuel is 66 gallons,
[tex]x=66[/tex]The corresponding weight of airplane is calculated as,
[tex]\begin{gathered} y=\frac{13}{2}(66)+2000 \\ y=429+2000 \\ y=2429 \end{gathered}[/tex]Thus, the airplane weighs 2429 if it is carrying 66 gallons of fuel.
Evaluae the expression jv+b
jv + b
where b = 8, v = 4 and j = -6
Therefore
jv + b = (-6)(4) + 8 = -24 + 8 = -16
A patient that you are tending to cannot exceed 500 Cal per meal. You notice that on the label the meal has 21grams of fat, 68 grams of carbohydrates, and 40 grams of protein. On average fat has 9 Cal/g, carbohydrates have4 Cal/g, and protein has 4 Cal/g.a) How much energy would the patient consume if they would eat the whole meal?b) What is the unit symbol of the answer?c) Are they within the 500 Cal limit? Input Y for yes and N for no
To determine the total amount of calories consumed in that meal, we have to multiply the number of grams of each type of nutrient by the energy provided by each gram of that nutrient.
We are given that 1 gram of fat has 9 calories, therefore, 21 grams of fat have:
[tex]9\times21\text{ calories=189 calories}[/tex]1 gram of carbohydrates gives 4 calories of energy, therefore, 68 grams have
[tex]68\times4\text{ calories= }272\text{ calories.}[/tex]1 gram of protein has 4 calories, therefore, 40 grams of protein has:
[tex]40\times4\text{ calories=160 calories.}[/tex]The mean has a total of:
[tex](189+272+160)\text{ calories=621 calories.}[/tex]Answer:
A) 621 Cal.
B) Cal.
C) N.
A small business owner is determining her profit for one month. Her expenses were$230.21 for utilities, $2,679.82 for rent, and $3,975.00 for employee salaries. Shehad $11,449.27 in sales for the month. What is her profit?a. $4,550.00b. $4,564.24C. $4,794.45d. $5,034.66
Answer:
B) $4,564.24
Explanation:
We are given the following information:
Expenses:
Utilities = $230.21
Rent = $2,679.82
Employee Salaries = $3,975.00
Sales = $11,449.27
The profit is obtained by the difference between Sales and Expenses as shown below:
[tex]\begin{gathered} Profit=Sales-Expenses \\ Profit=11,449.27-(230.21+2,679.82+3,975.00) \\ Profit=11,449.27-6885.03 \\ Profit=4564.24 \\ \\ \therefore Profit=\text{\$}4564.24\text{ } \end{gathered}[/tex]Therefore, the correct option is B
Graph the given functions, fand g, in the same rectangular coordinate system Select integers for x, starting with-2 and ending with 2, and describe how the graph of g is related to the graph off.f(x)=x?_g(x)=x² - 3
Given
The functions,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]To complete the ordered pairs for f(x)=x².
Explanation:
It is given that,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]That implies, for x=-2,
[tex]\begin{gathered} f(-2)=(-2)^2 \\ =4 \end{gathered}[/tex]Also, for x=-1.
[tex]\begin{gathered} f(-1)=(-1)^2 \\ =1 \end{gathered}[/tex]For x=0,
[tex]\begin{gathered} f(0)=0^2 \\ =0 \end{gathered}[/tex]For x=1,
[tex]\begin{gathered} f(1)=1^2 \\ =1 \end{gathered}[/tex]For x=2,
[tex]\begin{gathered} f(2)=2^2 \\ =4 \end{gathered}[/tex]Hence, the ordered pairs are,
[tex]\left(-2,4\right),(-1,1),(0,0),(1,1),(1,4).[/tex]Use the following sample Epworth Sleepiness Scores for the problems below;6, 4, 3, 5, 4, 2, 4, 5, 4, 6, 1, 4, 5, 2Sample variance=Sample Standard Deviation=
Given:
The data are,
[tex]6,4,3,5,4,2,4,5,4,6,1,4,5,2[/tex]To find:
Sample variance and the Sample Standard Deviation
Explanation:
Using the formula,
Is the vertex of the quadratic function below a maximum or minimum?
A quadratic equation is of the form below:
[tex]ax^2+bx+c=y[/tex]The vertex of the quadratic equation is the value of y where the curve cut the y-axis.
To find the vertex, we would first first find the x-coordinate of the equation using
[tex]x=-\frac{b}{2a}[/tex]To find the vertex, we would substitute for x in the equation to get y.
Given the quadratic function below
[tex]f(x)=-3x^2-4x+7[/tex]It can be observed that
[tex]a=-3;b=-4,c=7[/tex]The x-coordinate of the vertex is as shown below:
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=\frac{--4}{2(-3)} \\ x=\frac{4}{-6} \\ x=-\frac{2}{3} \end{gathered}[/tex]The vertex would be
[tex]\begin{gathered} f(-\frac{2}{3})=-3(-\frac{2}{3})^2-4(-\frac{2}{3})+7 \\ f(-\frac{2}{3})=-3(\frac{4}{9})+\frac{8}{3}+7 \\ f(-\frac{2}{3})=-\frac{4}{3}+\frac{8}{3}+7 \\ f(-\frac{2}{3})=\frac{-4+8}{3}+7 \\ f(-\frac{2}{3})=\frac{4}{3}+7 \\ f(-\frac{2}{3})=1\frac{1}{3}+7=8\frac{1}{3}=\frac{25}{3} \end{gathered}[/tex]Hence, the vertex of the quadratic function is (-2/3,25/3)
It should be noted that when a is positive, the quadratic graph opens upward and the vertex is minimum but when a is negative, the quadratic curve opens downward, and the vertex would be maximum
The graph of the quafratic function given is shown below
It can be observed that the vertex is maximum
which is the graph of f(x) and the translation g(x)=f(x+1)
SOLUTION
Step 1 ;
In this question, we are meant to examine the graph of the function,
[tex]f\text{ ( x ) = 3 sin ( }\frac{1}{2}\text{ x )}[/tex]We also to know the sketch of the graph of f ( x ) and
the translation y ( x ) = f ( x + 1 )
Step 2 :
The graph is as shown below:
CONCLUSION: OPTION A IS VERY CORRECT.
What is the equation of a line that passes through the point (8, -4) and is parrallel to the line 6x + 2y = 9
Answer:
the answer Is y= -3x +20.
Identify whether the problem is "Sum of Two Cubes" or "Difference of Cubes". Then, factor the problem.x^3 - 8
We have in this case the difference of Perfect Cubes since we have:
[tex]x^3-8=x^3-2^3[/tex]We know that this case can be factored as follows:
[tex]a^3-b^3=(a-b)\cdot(a^2+ab+b^2)[/tex]If we have that:
a = x
b = 2
Then, we have:
[tex](x-2)\cdot(x^2_{}+2x+2^2)=(x-2)\cdot(x^2+2x+4)[/tex]Therefore, the factored form of the perfect cube (for difference) is:
[tex]undefined[/tex]If O is an angle in standard position and its terminal side passes through the point(-15,-8), find the exact value of tan 0 in simplest radical form.
The definition of the tangent function for a angle in standard form is given by:
[tex]\tan \theta=\frac{y}{x}[/tex]where x and y are the coordinates of the terminal point (x,y).
Then in this case we have:
[tex]\tan \theta=\frac{8}{15}[/tex]Can someone help me I’ve been stuck on this for like hours now
We are given the inequality p>4
We want to find any numbers greater than 4
Any negative numbers are less than 4
1, or any numbers starting with 3 are less than 4
4 is equal to 4
Numbers greater than 4
4.001
4.01
4.1
5
7
9
12
an architect designed a mountain lodge with special viewing windows on the top floor. how many square yards of glass will it take to make in large window?
Explanation
to find the area of the glass, we can divide the shape into 2 more known shapes, a triangle and a rectangle
so
total area= area of the rectangle(green)+area of the triangle(yellow)
the area of a rectagle is given by:
[tex]\text{Area}_{rectangle}=base\cdot heigth[/tex]and for the triangle, the area is
[tex]\text{Area}_{triangle}=\frac{1}{2}base\cdot height[/tex]then replace
[tex]\begin{gathered} \text{total area=(2 yd }\cdot1\text{ yd)+}\frac{\text{(2 yd }\cdot\text{ 2 yd)}}{2} \\ \text{total area=2 yd}^2+2yd^2 \\ \text{total area=}4yd^2 \end{gathered}[/tex]so, the answer is
[tex]4yd^2[/tex]I hope this helps you
4. The perimeter of a rug is 16 feet. Rosiedecides she needs a rug that is 3 times larger forher foyer. What is the perimeter of the rug sheneeds to buy for the foyer?A. 48 feetB. 144 feetC. 5.3 feetD. 32 feet
The given perimeter is 16
To make 3 times larger rug
we need to multiply the current perimeter by 3
so the answer is
[tex]16\times3=48[/tex]the new perimeter is 48 .
Can you please help me with the following equation
a(1.50) + b(0.50) = $7.00
Answer:
I am sure there can be more than one way to solve the equation, but the answer that I got first is...
3(1.50) + 5(0.50) = $7.00
a = 3 and b = 5
Step-by-step explanation:
When you solve the equation by plugging 3 as a and 5 as b, the equation balances out to be 7 = $7, making the equation true.
Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)
Marko originally filled out 8 more applications than Henry. Then each boy filled out 3 additional applications, bringing the total to 28. How many applications did each boy originally fill out?Let m= number of applications Marko originally filled outLet h= number of applications Henry originally filled outWhat equation can we make to represent the relationship between the number of applications Marko and Henry originally filled out? AnswerUse your relationship from the question above to create an equation representing the number of applications after completing 3 more each: AnswerThe equation we can use to find the number of applications Henry and Marko each completed is :AnswerThe number of applications Marko originally filled out is AnswerThe number of applications Henry originally filled out is Answer
We have the next information
m= number of applicantios Marko originally filled out
h= number of applications Henry originally filled out
We know that Marko originally filled out 8 more applications than Henry
m=h+8
Then each filled out 3 additional applications
m+h+6=28
Already we have a system of equations of two variables
For the question What equation can we make to represent the relationship between the number of applications Marko and Henry originally filled out.
m=h+8
Use your relationship from the equation above to create an equation representing the number of applications after completing 3 more each
(h+8)+h+6=28
The equation we can use to find the number of applications Henry and Marko each completed is
2h+14=28
We can solve the equation above
2h=28-14
2h=14
h=14/2
h=7
m=h+8=15
The number of applications Marko originally filled out is 15
The number of applications Henry originally filled out is 7
For a function f(x), you know that f(3) = -8 and f(4) = 3. One zero of f(x) would be located between x= and x=
Problem Statement
The question tells us that f(3) = -8 and f(4) = 3 and we are asked to find where one of the zeros of the function.
Solution
The function f(x) moves from negative to positive when moves from x = 3 to x = 4. This means that the value of f(x) must cross the x-axis between these two values of x.
Answer
Thus, one zero of the function lies between X = 3 and X = 4
What is the spread of the data? 17 18 19 20 21 22 23 24 25 26 Age of female U.S. Olympic swimmers (years) O A. 21 to 25 years B. 15 to 30 years C. 18 to 25 years O D. 18 to 21 years
The spread of data is the difference between the maximum value and the minimum value.
Minimum value = 18
Maximum value = 25
Correct option: C . 18 to 25 years
As the Earth revolves around the sun, it travels at a speed of approximately 18 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will the Earth travel in 15 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Speed:
Distance traveled in 15 seconds
The speed in kilometers per second is 28.8 kilometers per second
The distance traveled in 15 seconds is 432 kilometers
Converting speed to kilometers per second and distanceFrom the question, we are to convert the speed to kilometers per second
From the given information,
The speed of the Earth is approximately 18 miles per second
Now, we will convert 18 miles to kilometers
Also, from the given information,
We are to assume that 1 mile is equal to 1.6 kilometers
If 1 mile = 1.6 kilometers
Then,
18 miles = 18 × 1.6 kilometers
= 28.8 kilometers
Thus,
The speed is 28.8 kilometers per second
To determine how many kilometers the Earth would travel in 15 seconds
The distance the Earth will travel in 15 seconds = 15 × 28.8
The distance the Earth will travel in 15 seconds = 432 kilometers
Hence, the distance is 432 kilometers
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Find the two dimensional diagonal. Round to the nearest tenth.
Given the value of b and c, we want to get the value of a
The three sides represent the sides of a right triangle
By the use of Pythagoras' theorem, we can get the value of a
From the diagram, the disgonal represents the hypotenuse of the right triangle
According to Pythagoras' theorem, the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
[tex]\begin{gathered} c^2=a^2+b^2 \\ 6^2=3^2+a^2 \\ 36=9+a^2 \\ a^2\text{ =36-9} \\ a^2\text{ = 27} \\ \text{a = }\sqrt[]{27} \\ a\text{ = 5.2 units} \end{gathered}[/tex]Anylu drew a picture of her bedroom using the scale 1in=2ft. In her drawing the length of her bedroom was 3 1/2 ftand the width of her room was 3 1/8 in. What are the actual dimensions of her room?Ready? Enter your answer here.
Answer: 7 ft x 6.25 ft
Explanation:
To answer this question we need to make use of the scale:
[tex]1in=2ft[/tex]This means that 1 inch of her drawing represents 2 feets in real life.
To convert from the measurements of her drawing to the actual measurements of her room we need to take the quantity in inches and multily it by 2 and now they become feet.
Length of the room
In her drawing: 3 1/2 in
In real life:
[tex]3\frac{1}{2}(2)=3.5(2)=7ft[/tex]Width of the room: 3 1/8 in
In real life:
[tex]3\frac{1}{8}(2)=3.125(2)=6.25ft[/tex]The dimensions of the room are: 7 ft x 6.25 ft
Question 1 Given a mean of 25 and a standard deviation of 2.5, what is the z-score of a data value X = 29? -1.06 1.6 ООО -1.6 1.06
The information we have is:
Mean:
[tex]\mu=25[/tex]Standard deviation:
[tex]\sigma=2.5[/tex]Value of x:
[tex]x=29[/tex]--------------------------------------------------------
To solve this problem, we need to use the z-score formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substituting our values:
[tex]z=\frac{29-25}{2.5}[/tex]We need to solve the subtraction first:
[tex]z=\frac{4}{2.5}[/tex]Finally, solve the division to find the z-score:
[tex]z=1.6[/tex]the z-score is 1.6
Answer: 1.6
cellusTranslate the triangle.Then enter the new coordinates.A -1,61B(0,4)A'([?], [])B'([],[])C'([],[])C (-6,1)< 10.2 >IEnter
The coordinates of the images are;
[tex]undefined[/tex]Here, we want to translate the given triangle
The translation is in the units of (10,2)
What this mean is that we are going to make a translation of 10 in the x-axis direction and 2 units in the y-axis direction
Hence, we are having a unit of 10 rightwards (positive x-axia) and 2 unit of 2 units upwards (vertically on the y-axis)
So what we do now in respective cases is add 10 to the x-axis values of each point and add 2 to the y-axis values of each point
Thus, we have;
[tex]\begin{gathered} A(-1,6)\text{ to A'(-1+10, 6+2)= A'(9,8)} \\ B(0,4)\text{ to B'(0+10, 4+2) = B'(10,6)} \\ C(-6,1)\text{ to C'(-6+10,1+2) = C'(4,3)} \end{gathered}[/tex]You're going to the mall with your friendsand you have $200 to spend from yourrecent birthday money. You discover astore that has all jeans for $25 and alldresses for $50. You really, really want totake home 6 items of clothing because you"need" that many new things. How manypairs of jeans and how many dresses youcan buy so you use the whole $200 (taxnot included)?
Given that:
- You have $200 to spend.
- The store sells all jeans for $25 and all dresses for $50.
- You want to take home 6 items of clothing.
Let be "j" the number of jeans and "d" the number of dresses you can buy so you use the whole $200 (not including the tax).
Set up this System of Equations using the data provided in the exercise:
[tex]\begin{cases}j+d=6{} \\ 25j+50d={200}\end{cases}[/tex]You can follow these steps in order to solve the System of Equations using the Elimination Method:
1. You can multiply the first equation by -25:
[tex]\begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases}[/tex]2. Add the equations:
[tex]\begin{gathered} \begin{cases}-25j-25d={-150} \\ 25j+50d={200}\end{cases} \\ ------------ \\ 0j+25d=50 \\ 25d=50 \end{gathered}[/tex]3. Solve for "d":
[tex]\begin{gathered} d=\frac{50}{25} \\ \\ d=2 \end{gathered}[/tex]4. Substitute the value of "d" into the first original equation and solve for "j":
[tex]\begin{gathered} j+(2)=6 \\ j=6-2 \\ j=4 \end{gathered}[/tex]Hence, the answer is: You can buy 2 dresses and 4 jeans.
Thomas wants to invite Madeline to a party. He has 80% chance of bumping into her at school. Otherwise, he'll call her on the phone. If he talks to her at school, he's 90% likely to ask her to the party. What is the probability of Thomas inviting Madeline to the party over the phone?
Recall that the probability must add 1, therefore:
[tex]0.6+x=1[/tex]Solving for x, we get:
[tex]\begin{gathered} x=1-0.6 \\ x=0.4 \end{gathered}[/tex]Therefore, the probability of Thomas inviting Madeline to the party over the phone is:
[tex]0.2\cdot0.4=0.08[/tex]or 8%.
4) Which of the following numbers is an integer?- 9.1,-10,20/3
Given:
[tex]-9.1,-10,\frac{20}{3}[/tex]-10 is an integer.
The data set below provides the monthly rent (in dollars) paid by 7 tenants.990, 879, 940, 1010,950, 920, 1430Suppose the rent for one of the tenants changes from $1430 to $1115.What is the mean before the rent change?What is the mean after the change?
To solve this question, we need to find the mean for both cases. The mean is given by summing the given values and then dividing them by the number of values (or given cases).
We have that, before the rent chance, we have the following monthly rent (in dollars):
990, 879, 940, 1010,950, 920, 1430
There are seven (7) values. Then, the mean, in this case, is:
[tex]m_{\text{before}}=\frac{990+879+940+1010+950+920+1430}{7}=\frac{7119}{7}\Rightarrow m=1017[/tex]Therefore, the mean, in this case, is equal to $1017.
Now, we have that the rent change for the one with $1430 to $1115, now the values are:
990, 879, 940, 1010,950, 920, 1115.
We can proceed as before to obtain the mean:
[tex]m_{\text{after}}=\frac{990+879+940+1010+950+920+1115}{7}=\frac{6804}{7}\Rightarrow m_{after}=972[/tex]Thus, the mean after the change is equal to $972.
In summary, we have that:
• The mean before the rent change is equal to $1017
,• The mean after the rent change is equal to $972.
Give the angle measures in order from least to greatest.
For the given triangle, the greatest angle is ∠D while the smallest one is ∠C
∠D > ∠B > ∠C
In a triangle,
The shortest side is always opposite the smallest interior angle.
The longest side is always opposite the largest interior angle.
In simple word,
for smaller side of a triangle will have smaller angle, and for longest side it will have larger angle.
In case of triangle ΔBCD
BD = 8m
CD = 9m
BC = 13m
as BC = 13m is largest side, so opposite angle ∠D will be largest one.
again BD = 8m is smallest side, so opposite angle ∠C will be smallest one.
BC > CD > BD
so,
∠D > ∠B > ∠C
The greatest angle is ∠D while the smallest one is ∠C
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here is a raffle with 500 tickets. One ticket will win a $960 prize, and the rest will win nothing. If you ave a ticket, what is the expected payoff?
The expected value is a measure of what you should expect to win per game in the long run. Divide the total prize over the number of tickets to find the expected payoff:
[tex]\frac{960}{500}=1.92[/tex]Therefore, the expected payoff is:
[tex]1.92[/tex]Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters highand have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer thanits width.The volume of a rectangular prism is found using the formula V= / w- h, where / is the length, w is the width, and h is the height.
Explanation
The volume of a rectangular prism is given by
[tex]v=length\times breadth\times height[/tex]We have the information:
h =3cm
v=252 cm³
If the width is x
And the length is 5cm longer than the width
L =5+x
Then, we will have
[tex]volume=252=l\times w\times h=(5+x)(x)(3)[/tex]Thus, we will have
[tex]\begin{gathered} 252=3x(5+x) \\ 252=15x+3x^2 \\ 3x^2+15x-252=0 \end{gathered}[/tex]Simplifying further
[tex]x^2+5x-84=0[/tex]Thus, the equation that models the tray will be
[tex]x^2+5x=84[/tex]Part B
To check if a with of 7.5 is possible, we will put x = 7.5c and check if the equation holds true
[tex](7.5)^2+5(3.5)=93.75[/tex]since
[tex]\begin{gathered} 93.75\ne84 \\ The\text{ is false} \\ \end{gathered}[/tex]Therefore, the answer is NO.
It is not possible for the width to be 7.5cm
AN ELECTRIC COMPANY MAKES TWO KINDS OF ELECTRIC RANGES- A STANDARD MODEL WHICH YEILDS A $50.00 PROFIT AND A DELUX THAT YEILDS A $60 PROFIT THE COMPANY CAN PRODUCE UP TO 400 DELUXE RANGES AND 500 STANDARD RANGES PER MONTH BUT BECAUSE OF THE MAN HOUR LIMITATIONS THE COMPANY CAN PRODUCE A COMBINED TOTAL OF NOMORE THEAN 600 RANGES PER MONTH. HOW MANY OF EACH TYPE RANGE SHOULD THE COMPANY PRODUCE PER MONTH TO MAX PROFIT? X= THE # OF THE STANDARD RANGES Y= THE # OF DELUXE RANGESA. THE OBJECTIVE FUNCTION IS:B.THE CONSTRAINTS ARE:
Explanation:
The number of standard ranges is represented as
[tex]x[/tex]The number of delux ranges is represented as
[tex]y[/tex]Hence,
The objective constraint will be
[tex]P=50X+60Y[/tex]The constraints will be given below as
[tex]\begin{gathered} 0\leq X\leq500 \\ 0\leq Y\leq400 \\ X+Y\leq600 \end{gathered}[/tex]