The table shows information recorded about the location and speed of an airplane during an overseas flight.
a) Determine the altitude in miles.
b) Determine the ground speed in miles per hour.
c) Determine the headwind in miles per hour.
d) Determine the temperature in degrees Fahrenheit using the formula
F=9/5 C+32
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
Part a
The altitude = 9770 meters
To convert meter to miles, divide the length by 1609
Therefore,
9770 meters = 9770/1609
=6.07 miles
Part b
The ground speed = 707 km/hours
To convert km per hour to miles per hour, divide the speed value by 1.609
707 km/hour = 707/1.609
= 439.30 miles per hour
Part c
The head wind = 184 km/hour
To convert km per hour to miles per hour, divide the speed value by 1.609
184 km/hour = 184/1.609
= 114.35 miles per hour
Part d
The outside air temperature = -41 degree C
F = (9/5)C + 32
= (9/5)×-41+32
= -41.8 degrees Fahrenheit
Hence,
Part a
The altitude in miles = 6.07 miles
Part b
Head wind in miles per hour = 439.30 miles per hour
Part c
The headwind in miles per hour = 114.35 miles per hour
Part d
The temperature in degree Fahrenheit = -41.8 degrees Fahrenheit
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Mark made the following shape using two rectangles and one triangle. What is the area of the figure he made?
Answer:
44 square centimetres.
Explanation:
The shape consists of two rectangles and one triangle with the following dimensions:
• A rectangle (Rectangle 1) with dimensions of 4cm by 2cm.
,• A rectangle (Rectangle 2) with dimensions 6cm by 4cm.
,• A triangle with base 6cm and height of 4cm.
Thus, the area of the figure made will be:
[tex]\begin{gathered} \text{Area of figure=Area of rectangle 1+Area of rectangle }2+\text{Area of }\triangle \\ =(4\times2)+(6\times4)+(\frac{1}{2}\times6\times4) \\ =8+24+12 \\ =44\operatorname{cm}^2 \end{gathered}[/tex]The area of the figure is 44 square centimetres.
suppose that 18 inches of wire cost 72 cents. using the same rate how much in cents will 36 inches cost?
Please help me on my assignment The ? Options are x and y
x, x
1.7
[tex]\lbrack1,7\rbrack[/tex]Explanation
Step 1
we can see in the graph, that :
the solutions of the equation f(x)=0, are the values where y =0 , it is when the line crosses the x-axis, so the solution of the first blank is
x
Step 2
and, the solution of the inequality
[tex]f(x)>0[/tex]is the set of values wich the graph is above the x-axis
Step 3
now, for the next question, let's check the points where the line crosses the x-axis, and the intervals where the lines is above the x-axis
we can see the solution of f(X)=0 are
[tex]\begin{gathered} x=1\text{ and x=7} \\ so \\ Input\text{ in the blank} \\ 1,7 \end{gathered}[/tex]Finally, check the interval where the graph is above the x-axis, it is from a to 7, in interval notation
[tex]\lbrack1,7\rbrack[/tex]
I hope this helps you
In January 1, Juan weighed 247 pounds and decided to diet and exercise. Kn June 30, Juan weighed 221 pounds. Determine the percent decrease in Juans weight from January 1 to June 30.
Given the initial value, w1, and the final value, w2, the percent decrease can be calculated as:
[tex]P=\frac{w_1-w_2}{w_1}\times100\%[/tex]The initial value is 247 and the final one is 221, so:
[tex]\begin{gathered} P=\frac{247-221}{247}\times100\% \\ P=\frac{26}{247}\times100\% \\ P=0.10526\ldots\times100\% \\ P\approx10.53\% \end{gathered}[/tex]So, the percent decrease is approximately 10.53%.
I just need to quickly know if my answers are correct thank you!
1) All of these questions are about evaluating those functions for each input.
9) So, let's check them out evaluating each one.
[tex]\begin{gathered} f(4)\Rightarrow f(x)=(\frac{1}{2}x)+13 \\ f(4)=(\frac{1}{2}\cdot4)+13 \\ f(4)=2+13\Rightarrow f(4)=15 \\ D \end{gathered}[/tex]10)
[tex]\begin{gathered} f(x)=\frac{3}{5}x-10 \\ f(5)=\frac{3}{5}(5)-10 \\ f(5)=3-10 \\ f(5)=-7 \end{gathered}[/tex]11)
[tex]\begin{gathered} f(x)=x^2+7 \\ f(-1)=(-1)^2+7\Rightarrow f(-1)=1+7\Rightarrow f(-1)=8 \end{gathered}[/tex]12)
[tex]\begin{gathered} f(x)=3x^3-12x^2 \\ f(2)=3(2)^3-12(2)^2 \\ f(2)=24-48 \\ f(2)=-24 \end{gathered}[/tex]100 POINTS ANSWER CORRECTLY PLS
Answer:
1.) y = -3/4x +2
2.) y = x - 4
3.) y = 2/3x - 4
4.) y = -1/2x + 5
5.) y = 8/3x +5
Step-by-step explanation:
1.)
Parallel means that the slopes will be the same.
So, m = -3/4
To find the equation, we must first use point-slope form.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
y-(-1) = -3/4(x-4)
Now we clean this up and solve for y to get the answer in slope intercept form.
y+1= -3/4x + 3 => y = -3/4x +2
2.)
Perpendicular means that the slope is the negative reciprocal of the slope of the first line.
So, m = 1 as the negative reciprocal of -1 is +1.
Once again, we use point-slope form and the clean it up and solve for y to get the answer in slope-intercept form.
y - (-3) = 1(x-1) => y + 3 = x-1 => y = x - 4
3.)
Similar to the previous one, but with slope m = 2/3 (negative reciprocal)
y - (-4) = 2/3 (x - 0) => y + 4 = 2/3x => y = 2/3x - 4
4.)
Similar to the previous one, but with slope m = -1/2 (negative reciprocal)
y - 4 = -1/2(x-2) => y - 4 = -1/2x +1 => y = -1/2x + 5
5.)
Similar to the previous one, but with slope m = 8/3 (negative reciprocal)
y - (-3) = 8/3(x - (-3)) => y + 3 = 8/3x +8 => y = 8/3x +5
What is the sign of 37+(-37)? Choose 1 answer: Positive Negative Neither positive nor negative the sum is zero
Are the triangles congruent using AAS?
True
False
Answer: True
Step-by-step explanation:
If you look both triangles have the same angles, so that means that they are congruent.
Consider the function f(x) = (x+4)(x+2), Dilate f(x) by x to create a new function of a higher degree,
a. Write the dilation of f(x) as g(x).
b. Sketch the graph of g(x).
c. identify the zeros of the graph of the function g(x)
The dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
What is scale factor? How it is used in Dilating coordinates?Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-
K = a/b.
If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).
Given is the function -
f(x) = (x+4)(x+2)
[A] -
For dilating the given f(x) by [x] times -
g(x) = [tex]x[/tex] f(x)
g(x) = x(x + 4)(x + 2)
Therefore, the dilated function g(x) will be -
g(x) = x(x + 4)(x + 2)
[B] -
The graph of the function g(x) is attached with the answer.
[C] -
The points where the graph of g(x) touches or cuts the x - axis, will represent the zeroes of the function g(x) = x(x + 4)(x + 2). It can be seen that the points are -
x = 0
x = - 4
x = - 2
The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2.
Therefore, the dilated function g(x) will be g(x) = x(x + 4)(x + 2). The zeroes of function g(x) = x(x + 4)(x + 2) will be x = 0, x = - 4, x = -2. The graph of the function g(x) is attached.
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what variable expression should you subtract from both sides of the equation so that you are left with no variables on the right hand side
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
What variable expression should you subtract from both sides of the equation so that you are left with no variables on the right-hand side?
The variable expression is: subtract 5x from both sides so that you are left with no variables on the right-hand side
[tex]\begin{gathered} 6x\text{ - 10 = 5x + 15} \\ \text{Subtract 5 x from both sides, we have that:} \\ 6x\text{ - 5x - 10 = 5x - 5x + 15} \\ x\text{ - 10 = 15} \\ \text{Now, add 10 to both sides, we have that:} \\ x\text{ - 10 + 10 = 15 + 10} \\ x\text{ = 25} \\ \text{check:} \\ 6x\text{ - 10 = 5x + 15} \\ \sin ce,\text{ x = 25 , we have that:} \\ 6(25)\text{ - 10 = 5(25) + 15 } \\ 150\text{ - 10 = 125+ 15= 140 ( COR}\R ECT) \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = 25}[/tex]
The measure of three angels of a triangle are 43, 70, and x what is the value of x
According to the given data we have the following:
measure of three angels of a triangle are 43, 70, x
x?
The sum of the measures of the three angles of the triangle is 180
Therefore, to calculate the value of x we would have to make the following calculation:
43 + 70 + x = 180
113+ x=180
x=180-113
x=67
Therefore, the value of the angle of x would be 67
In one classroom homework is worth 25% of the final grade, each of the three projects is worth 10%, and the final exam is worth 45%. If student has an 87 on a homework average and a 94 on the first project, what is the students grade at this point if that same student from part a gets a 71 on the second project and a 78 on the third project what is the lowest grade the student can get on the final exam to get an 80 over on the course
Answer
• a) 30.9
,• b) 76
Explanation
Given
• Homework: 25%
,• Project: 10% (each)
,• Final exam: 45%
A student has:
Part A
• Homework: 86
,• First project: 94
Part B
• Second project: 71
,• Third project: 78
,• Total grade: 80
Procedure
• a)
To know the student's grade at the point where he has an 86 homework average and 94 on the first project. We have to multiply the ponderation of each category times the grade to find the final grade (TG), meaning:
[tex]TG=86(0.25)+94(0.10)[/tex]Simplifying:
[tex]TG=21.5+9.4[/tex][tex]TG=30.9[/tex]• b)
Following the same procedure, now we have to multiply the ponderations of the new grades, as follows:
[tex]TG=FE+30.9+71\cdot(0.1)+78\cdot(0.1)[/tex][tex]TG=FE+30.9+7.1+7.8[/tex][tex]TG=FE+45.8[/tex]Next, as we are asked to find the calculations of the grade of the exam to get a final grade of 80, we have to consider the latter and the ponderation for the exam:
[tex]80=x\cdot0.45+45.8[/tex]where x is the grade of the exam.
Solving for x:
[tex]x=\frac{80-45.8}{0.45}[/tex][tex]x=76[/tex]The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q. What is the value of Q
Given:-
The mean of 40,50 and 90 is P. If the mean of 40,50,90 and P is Q.
To find:-
The value of Q.
So now the mean of 40,50 and 90 is P. so we get,
[tex]\frac{40+50+90}{3}=\frac{180}{3}=60[/tex]So the value of p is 60.
Also we have the mean of 40,50,90 and P is Q. so we get,
[tex]\frac{40+50+90+60}{4}=\frac{240}{4}=60[/tex]So the value of q is 60.
The mode of data 33, 22, 10, 0, 33, 40, 33 is _____
Please explain this to me
If a perpendicular b and b parallel to c, then the value of x = 8
Here b and c are parallel lines
The parallel lines are two lines in the same plane that are at equal distance from each other and that do not intersect at any point
Then a is perpendicular to b
The perpendicular lines are the line that forms the angle of 90 degrees for both angles
Therefore the given angles are 90 degrees
9x+18 = 90
9x = 90-18
9x = 72
x = 72/9
x = 8
Hence, If a perpendicular b and b parallel to c, then the value of x = 8
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True or false? In deductive thinking, you start with a given set of rules and cinditions and determine what must be true as a consequence
In deductive thinking, you start with a given set of rules and conditions and determine what must be true as a consequence - True
In deductive thinking, conclusions are reached based on premises that are typically taken to be true. A conclusion is based on the concordance of several premises typically presumed to be true in this logical procedure. Top-down logic is another name for deductive thinking. It only makes use of data that is believed to be reliable. It excludes sentiments, feelings, and unsupported assumptions because it is challenging to assess the integrity of this data.
Making logical assumptions and basing a conclusion on them are the foundations of deductive thinking. It enables the individual to combine the information from two or more assertions to arrive at a sound conclusion. If something is presumptively true and a different object is connected to the first presumption, then the original truth must also apply to the second. Therefore, In deductive thinking, if you start with a given set of rules and conditions and determine what must be true as a consequence holds true.
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Mr. Anderson grows fruit which hesells at a farmers' market.- His truck has a total payloadcapacity (total weight ofpassengers and cargo) of1,200 pounds.- Mr. Anderson weighs 190 pounds.- The table he sells his fruit onweighs 10 pounds.- He transports his fruit in crates.Each crate weighs 3 pounds.- A crate can hold up to 22 poundsof fruit.Write and solve an equation to findC, the greatest number of fullcrates of fruit that Mr. Anderson cancarry in his truck along with himself and the table
We will have that the expression that represents the problem is:
[tex]1200>(3+22)C+190\Rightarrow1200>25C+190[/tex][tex]\Rightarrow1010>25C\Rightarrow C<40.4[/tex]So, at most he will be able to carry 40 crates with him.
Simplify the expression. Write your answer as a power.(-8.3)8 (-8.3)4(-8.3)? (-8.3)3The simplified expression is
This will be simplified with this law of indices
[tex]\frac{a^e}{a^y}=a^{e-y}[/tex][tex]\begin{gathered} \text{Therefore the initial question becomes:} \\ ((-8.3)^{8-7})\text{ }\cdot\text{ (}(-8.3)^{4-3}) \end{gathered}[/tex][tex]\begin{gathered} (-8.3)^1\cdot(-8.3)^1 \\ (-8.3)^{1+1} \\ (-8.3)^2 \\ \end{gathered}[/tex]Going further, we can simplify to:
[tex]\begin{gathered} (-8.3)\times(-8.3) \\ =68.89 \end{gathered}[/tex]Discuss the relationship between the discriminant of a quadratic polynomial and the quantity of real roots it possesses. Explain the positioning of the roots of the polynomial on its graph with respect to the discriminant and the sign of the discriminant.
The relationship between the discriminant of a quadratic polynomial and the number of real roots is that the discriminant let us know the number and type of the solutions.
Basically for a quadratic polynomial ax²+ bx + c = 0, the b² - 4ac is the discriminant.if the discriminant is greater than zero (b²- 4ac > 0), the graph intersects the abscissa twice which means it has two real solutions, whereas if the discriminant is equal to zero ( b² - 4ac = 0), then the graph intersects once the abscissa which means it has a single real solution and at last if less than zero (b² - 4ac < 0), then the graph doesn't at all intersect the abscissa which, it has imaginary solutions.
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What does n mean?????
a. Data values are 13.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
b. ∑x = 91
c. n = 6
What is mean and data values?Adding all numbers in the data and then dividing by the number of values is called mean. Median is defined as the middle value when a data set is in such a way that it goes from least to the greatest value. Whereas the number that occurs most often in a data set is mode. Sample size is represented by "n". Whereas, symbol Σ denotes the summation.
For the given mean,
The data values are 3.4, 16.3, 14.2 , 15.4 , 14.2 ,17.5
Summation, ∑x = 3.4+ 16.3+ 14.2 + 15.4 + 14.2 +17.5
= 91
n is the number of data that is 6.
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At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?
0.029
0.050
0.120
0.091
The standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
How to find the standard error for the sample mean?Let the value of mean be [tex]$P(\bar{X} < 0.95)$$[/tex]
Normal Distribution, [tex]$\mu=1, \sigma=0.1, n=12$[/tex]
[tex]$P(\bar{X} < 0.95)=$[/tex] Area to the left of 0.95
we convert this to standard normal using
[tex]$z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$[/tex]
[tex]$z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$[/tex]
[tex]$P(\bar{X}[/tex] < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)
P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex]
Therefore, the standard error for the sample mean exists
[tex]$P(\bar{X} < 0.95)=0.0418=4.18 \%$$[/tex].
The complete question is;
What is the probability that the sample mean will be below 0.95 centimeters?
At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.
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Mathematics. Sets Question. Answer Fast
Answer:
B
Step-by-step explanation:
the full domain is
(-∞,-7[ ∪ ]-7,+∞)
In triangle JKL, tan(b°) = 3/4 and sin(b°) = 3/5 If triangle JKL is dilated by a scale factor of 3, what is cos(bº)?
ANSWER
cos(bº) = 4/5
EXPLANATION
When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.
Using the relationship between these three trigonometric ratios:
[tex]\tan (bº)=\frac{\sin (bº)}{\cos (bº)}[/tex]We can find the cosine:
[tex]\cos (bº)=\frac{\sin (bº)}{\tan (bº)}[/tex][tex]\cos (bº)=\frac{\frac{3}{5}}{\frac{3}{4}}=\frac{3}{5}\colon\frac{3}{4}=\frac{3}{5}\times\frac{4}{3}=\frac{4}{5}[/tex]Lin is paid $90 for 5 hours of work. She used the following table tocalculate how much she would be paid at this rate for 8 hours of work.1. What is the meaning of the 18that appears in the table?IAmount earned($)Time worked(hours)9052. Explain how Lin used this table tosolve the problem3. At this rate, how much would Linbe paid for 3 hours of work? For21 hours of work?1811448
From the table :
Lin worked for 5 hours and earned 90$
LIn worked for 1 hour and earned 18$
Lin worked for 8 hour
so the earning is
[tex]8\times18=144[/tex]Lin worked for 8 hours so the earning is 144$
If lin works for 3 hours then the earning is
So the answer for 3 hours is 54$.
[tex]3\times18=54\text{ dollar}[/tex]If lin works for 21 hours then the earning is
[tex]21\times18=378\text{ dollar}[/tex]so the answer for 21 hours is 378$.
Which value of X Satisfy 2(x +5.3) =4.2
SOLUTION
This question simply means we should find the value of x,
[tex]2\mleft(x+5.3\mright)=4.2[/tex]First we expand by using 2 to multiply the items in the bracket, we have
[tex]\begin{gathered} 2\times x+2\times5.3=4.2 \\ 2x+10.6=4.2 \\ 2x=4.2-10.6 \\ 2x=-6.4 \\ \text{dividing both sides by 2, we have } \\ \frac{2x}{2}=\frac{-6.4}{2} \\ x=-3.2 \end{gathered}[/tex]Hence the answer is -3.2
Timothy Tools is a company that produces hand-crafted hammers and wrenches. The following equations can be used to determine how many hammers the company can produce each day if x people are making hammers
The domain of the function of the equation cannot include zero because h(0) is not real.
A scale used to weigh objects is analogous to an equation. When the two pans are filled to the same level with anything, the scale will balance and the weights will be considered to be equal (such as grain).
To keep the balance in check, whenever any grain is taken out of one of the balance's pans, an equal amount must be taken out of the other pan. In general, if the same operation is carried out on both sides of an equation, the equation remains in balance.Equations that involve one or more functions and their derivatives are known as differential equations. By locating a derivative-free formulation for the function, they can be resolved.The equation is given as [tex]h(x) = \sqrt{2x^2+5x+3}[/tex]
The equation at x=0 given
h(0) = √(0+0-3)
or, h(0) = √(-3) which is an imaginary number
Therefore for the equation the value of x at 0 is undefined.
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What values complete each statement?Enter your answers in the boxes.(16−−√)2 = in simplest form.By the Power of Power rule, (16 1/2)2=16 2/2. So, 16 1/2 must equal in radical form.
Box 1 )
[tex](\sqrt[]{16})^2=16[/tex]Box 2 )
[tex]16^{\frac{1}{2}}=\sqrt[]{16}[/tex]F(x) = 3 + 5x to the second power - x + 5, 2f(3-) - f(4) =
the given equation is
[tex]f(x)=3x^2-x+5[/tex]calculate f(-3) by putting x = -3
[tex]\begin{gathered} f(-3)=3(-3)^2-(-3)+5 \\ f(-3)=27+3+5=35 \\ \end{gathered}[/tex]now, f(4)
[tex]\begin{gathered} f(4)=3(4)^2-4+5 \\ f(4)=48+1=49 \end{gathered}[/tex]now the final calculation
[tex]\begin{gathered} 2f(-3)-f(4) \\ 2\times35-49 \\ 70-49 \end{gathered}[/tex]that is 70 -49 = 21
so the correct answer is 21
2f(-3) - f(4) = 21 .
Help please. Catching up on missed work from being out due to medical issues. Thank you in advance!
Let B be the number of cups of boiling water that we should mix with I cups of ice to get 3 cups of 110°F water.
Therefore, we can set the following equation:
[tex]\begin{gathered} B+I=3, \\ 220B+32I=110\cdot3. \end{gathered}[/tex]Subtracting B from the first equation we get:
[tex]\begin{gathered} B+I-B=3-B, \\ I=3-B\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]220B+32(3-B)=330.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} 220B+96-32B=330, \\ 188B+96=330. \end{gathered}[/tex]Subtracting 96 to the above equation we get:
[tex]\begin{gathered} 188B+96-96=330-96, \\ 188B=234. \end{gathered}[/tex]Dividing the above equation by 188 we get:
[tex]\begin{gathered} \frac{188B}{188}=\frac{234}{188}, \\ B\approx1.24. \end{gathered}[/tex]Substituting B=1.24 at I=3-B we get:
[tex]I=3-1.24=1.76.[/tex]Answer:
[tex]\begin{gathered} 1.26\text{ cups of boiling water.} \\ 1.74\text{ cups of ice.} \end{gathered}[/tex]