SOLUTION:
Step 1:
In this question, we are given the following:
If two planes leave an airport at the same time with one flying west at 520 miles per hour and the other flying east at 540 miles per hour,
how long will it take them to be 3180 miles apart?
Step 2:
Let the distance of one of the planes flying west at 520 miles per hour be:
[tex]520\text{ x}[/tex]And let the distance of the other plane flying east at 540 miles per hour be:
[tex]540\text{ x}[/tex]where x , represents the time of flight in hours, such that:
[tex]\begin{gathered} 520\text{ x + 540 x = 3180} \\ 1060\text{ x = 3180} \\ \text{Divide both sides by 1060, we have that:} \\ x\text{ = }\frac{3180}{1060} \\ x\text{ = 3} \end{gathered}[/tex]CONCLUSION:
The time it will take them to be 3180 miles apart will be in 3 hours' time.
Estimate 71.91-56.423 by first rounding each number to the nearest whole number.
Answer:
16
Step-by-step explanation:
71.91 ~ 72
56.423 ~ 56
72-56=16
Find the amount and the percent increase. Fill in the chart
Answer:
Amount of increase = 60
Percent of increase = 40%
Explanation:
The amount of increase is equal to the difference between the new amount and the original amount. So, it is equal to:
New amount - Original amount = 210 - 150 = 60
Then, the percent of the increase is equal to the amount of increase divided by the original amount, so:
Amount of increase/Original amount = 60/150 = 0.4
Therefore, the answers are:
Amount of increase = 60
Percent of increase = 0.4 = 40%
5) Solve for x:X - 7.5 = 186) Solve for x:45x = 14.5
We have the following:
5)
[tex]x-7.5=18[/tex]solving for x:
[tex]\begin{gathered} \text{let's add 7.5 on each side} \\ x-7.5+7.5=18+7.5 \\ x=25.5 \end{gathered}[/tex]6)
[tex]\begin{gathered} 45x=14.5 \\ \\ \end{gathered}[/tex]solving for x:
[tex]\begin{gathered} \text{ divide on each side by 45} \\ x=\frac{14.5}{45} \\ x=0.32 \end{gathered}[/tex]Will give brainlist PLEASE HELP ASAP!!!! If it says college math, that's false.
The graph below represents the money collected at the skating rink on Friday. Find the domain when the maximum number of people allowed in the skating rink is 75 people.
A=0 ≤ x ≤ 75
B= 20 ≤ y ≤ 320
C= 0 ≤ y ≤ 75
D= 20 ≤ x ≤ 320
Answer:
A is correct.
0 < x < 75 represents the correct domain.
(-2,-7);y=-2 the equation is
Answer: -2= 5/2x -2
Step-by-step explanation:
QuestionGetting selected as class secretary is A and having pizza for lunch is B. If these events are independent events, usingP(A) = 0.70, and P(B) = 0.67, what is P(AB)?
From the question, we have two events that do not affect each other. They seem independent events. The probability of occurring the two events at the same time is given by the formula:
[tex]P(A\cap B)=P(A)\cdot P(B)[/tex]Then, since we have that P(A) = 0.70 and P(B) = 0.67, then, we have:
[tex]P(A\cap B)=0.70\cdot0.67=0.469[/tex]Then, P(AB) = 0.469.
Question 15.I need help with this question to make sure that I have the right answer.my answer was number 2
Given the graph that shows the results of the survey, you know that it shows the results of 3 price surveys conducted at 4 area supermarkets in 3 months.
Notice that the white bar represents the results of September, the dashed bar represents the results in November and the black bar represents the results in March.
You can identify that on the x-axis are written the 4 area supermarkets and, on the y-axis are represented the prices in dollars.
Therefore, in order to identify the supermarket that lowered the price of the frozen beef dinners by the greatest dollar amount between September and November, you need to identify the supermarket that has the shortest dashed bars and white bars.
In this case, you can identify that the lowest price in September and November is:
[tex]\text{ \$}1.50[/tex]And it corresponds to Warehouse.
Hence, the answer is: Option (2).
Ten yards of a particular kind of wire cost $15.30 . What is the cost of the wire per foot?
Given:
Length of wire = 10 yards
Total cost of wire = $15.30
To be able to determine the cost of wire per foot, let's first convert the unit of measure of the wire's length from yards to feet.
Recall: 1 yard = 3 feet
Step 1: Convert the measure of the wire length from yards to feet.
[tex]\text{ 10 (yards) x }\frac{\text{ 3 feet}}{\text{ 1 (yard)}}\text{ = }\frac{\text{10 x 3}}{\text{ 1}}\text{ feet}[/tex][tex]\text{ = 30 feet}[/tex]Therefore, 10 yards is equivalent to 30 feet.
Step 2: Divide the total cost by the total length of wire in feet.
[tex]\text{ Cost of wire per foot = }\frac{\text{ Total cost of wire}}{\text{ Total length of wire}}[/tex][tex]\text{ = }\frac{\text{ \$15.30}}{\text{ 30 feet}}[/tex][tex]=\text{ \$0.51 per foot}[/tex]Therefore, the cost of the wire per foot is $0.51
Two students, 100 meters apart on the same path, arewalking towards one other. Student A has a speed of 2meters each second; Student B has a speed of 3 meterseach second. Let's suppose they start to walk to eachother when t=0. How many seconds will it take for thestudents to bump into one another? Give your answer tothe nearest whole number
D = RT
Where
D is distance
R is speed
T is time
Distance of student 1:
[tex]D_1=2t[/tex]Distance of student 2:
[tex]D_2=3t[/tex]Now,
When they meet, their distance would total 100, so we can write:
[tex]D_1+D_2=100[/tex]We can also write:
[tex]D_1=100-D_2[/tex]For each function, determine whether it is a polynomial function.Function(a) g(x) = 5x (x-3)²(b) f(x)=-3√√x(c) v(x)=9x³+4x(d) u(x)=1---XIs the function a polynomial?YesNoOO
Explanation:
A polynomial function is a function where the exponents are whole numbers, i.e. >0 and natural. The coefficients are real.
Answer:
a) Yes
b) No.
c) No
d) No
Suppose y varies directly with x when x is -2 y is 10 write the equation that relates x and y
The form of the equation of the direct proportional is
[tex]y=kx[/tex]k is the constant of variation
We can find it from the initial values of x and y
Since at x = -2 y = 10, then
Substitute x by -2 and y by 10 to find k
[tex]\begin{gathered} x=-2,y=10 \\ 10=k(-2) \\ 10=-2k \end{gathered}[/tex]Divide both sides by -2 to find k
[tex]\begin{gathered} \frac{10}{(-2)}=\frac{-2k}{(-2)} \\ -5=k \end{gathered}[/tex]The value of k is -5
Then the equation is
[tex]y=-5x[/tex]What is the scale factor of XYZ to UVW?y836075V83"1556°4156X9018W410A. 5B.14OOC.011aD. 4
In order to solve this exercise, it is important to remember that when two figures are similar the corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are equal.
In this case, you know that the triangle XYZ and the triangle UVW are similar triangles. Let be "k" the scale factor of XYZ to UVW.
Based on the explained above, you can set up the following:
[tex]k=\frac{UV}{XY}[/tex]You can identify that:
[tex]\begin{gathered} UV=12 \\ XY=60 \end{gathered}[/tex]Then, substituting values into the equation, you get that:
[tex]k=\frac{12}{60}=\frac{1}{5}[/tex]The answer
Order the numbers form least to greatest 99.98, 100.1, 98.89, 100.01
Answer: 98.89, 99.98, 100.01, 100.1
The hypotenuse of a right triangle is 6 meters long, and one leg is 2 meters long. How long is the other leg?
To find the leg, we have to use the Pythagorean's Theorem
[tex]c^2=a^2+b^2[/tex]Where c = 6, a = 2.
[tex]\begin{gathered} 6^2=2^2+b^2 \\ b^2=6^2-2^2 \\ b=\sqrt[]{36-4} \\ b=\sqrt[]{32} \\ b\approx5.7 \end{gathered}[/tex]Hence, the other leg is 5.7 meters long.need help with this problem
First option describes line e: Each point is less than 4 units from the y-axis.
The second option describes line f:
What is the meaning of the slope of the equation in this context?
ANSWER
It is the cost for printing each DVD
EXPLANATION
We want to find out what the slope of the equation represents.
The equation given is a linear equation. The slope of a linear equation represents the rate at which the dependent variable changes with respect to the independent variable.
The independent variable is the number of DVDs while the dependent variable is the cost to make the DVDs.
Hence, the slope represents the cost of the DVDs per DVD. In other words, it represents the cost for printing each DVD.
6. The budget for a new house can only afford 1/4 of the floor area to be done inceramic tile. The rest of the floor area will be carpeted. The size of the kitchen areahas not yet been determined. Not including the kitchen, the architect has alreadydesigned 2200 square feet of floor area, 15% of which has tile floors specified.What area, in square feet, can be planned for the kitchen if its entire floor area is tohave ceramic tile? Assume all values are ex
The budget of a new house can only afford 1/4 of the floor area
the total area of the floor is designed to be 2200 square feet
15% of the floor is tiled
let the budget be x
area to be done in ceramic tile is 1/4 x the total budget
1/4 * 2200 = 550
550 square feet area of the floor will be use for ceramic tiles alone
Given the following figure is a parallelogram, solve for x.
The given figure is a parallelogram. The opposite angles of a parallelogram are congruent.
From the information given,
angle E and angle G are opposite
Thus,
94 = 11x + 6
11x = 94 - 6 = 88
x = 88/11
x = 8
Telephone numbers are in the form NYZ-ABC-XXXX. the following restrictions were placed; N can only be numbers: 2-9; Y can only be numbers 0-7 and A&C cannot be 2. how many phone numbers are there?
Answer
The answer = 5,184,000,000
There are 5,184,000,000 possible phone numbers.
Explanation
The question told us that telephone numbers are in the form NYZ-ABC-XXXX, then proceeds to give us the restrictions on some of the positions available.
- N can only be numbers: 2-9;
- Y can only be numbers 0-7
- and A&C cannot be 2
We are then told to calculate the number of phone numbers possible.
This question is a special type of permutation and combination.
To solve it, it will be a multiplication of the possible numbers that can take up each position.
N, can only be numbers 2 to 9. Number of possible digits = 8
Y, can only be numbers 0 to 7. Number of possible digits = 8
Z, no restriction, can have numbers 0 to 9. Number of possible digits = 10
A, number cannot be 2. Number of possible digits = 9
B, no restriction, can have numbers 0 to 9. Number of possible digits = 10
C, number cannot be 2. Number of possible digits = 9
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
X, no restriction, can have numbers 0 to 9. Number of possible digits = 10
Total number of possible phone numbers
= 8 × 8 × 10 × 9 × 10 × 9 × 10 × 10 × 10 × 10
= 5,184,000,000
Hope this Helps!!!
How to convert 9.4 degrees has feet and inches
Solution
[tex]9.4\text{degree --> inches}[/tex]To convert degrees to inches you must multiply the width of the control surface in inches by the sine of the angle.
How to convert degrees to inches?
First, determine the control surface width.
Measure the control surface width in inches.
Next, determine the angle.
Measure the angle in degrees.
Finally, calculate the deflection.
Calculate the linear deflection in inches using the formula above.
[tex]9.4degree=3.72inches[/tex]Diego bought a new car for 26,525 he was surprised at the dealer than attitude thousand $387.25 what was the sales tax rate for this purchase do not include the percentage sign in your answer
2387.25 is the amount of tax
Take the original price and multiply by x to get the tax added
26525 * x = 2387.25
Divide each side by 26525
x = 2387.25/26525
x =.09
Change this to a percent form
.09 * 100%
x = 9 %
The sales tax percent 9 %
The finishing time for a runner completing the 200-meter dash is affected by the tail-wind speed, s. The change, t, in a runner's performance is modeled by the function shown below:t = 0.0119s^2 - 0.308s - 0.0003Predict the change in a runner's finishing time with a wind speed of 5 meters/second. Note: A negative answer means the runner finishes with a lower time. Round to the nearest hundredth.
The change, t, in a runner's performance is modeled by:
[tex]t=0.0119s^2-0.308s-0.0003[/tex]Here s is the tall-wind speed.
It's required to find the change in a runner's finishing time with a wind speed of s = 5 m/s.
Substitute in the equation:
[tex]t=0.0119(5)^2-0.308(5)-0.0003[/tex]Operating:
[tex]\begin{gathered} t=0.0119(25)-1.44-0.0003 \\ \\ t=0.2975-1.44-0.0003 \end{gathered}[/tex]Calculating:
t = -1.24
Graph the line with the slope -3/4 passing through the point (5,2)
We need to first determine the expression of the line, for that we will use the point slope form, which is given below:
[tex]y-y_1=m\cdot(x-x_1)[/tex]Where m is the slope and (x1, y1) are the coordinates of a known point on the line.
[tex]\begin{gathered} y-2=-\frac{3}{4}(x-5) \\ y=-\frac{3}{4}(x-5)+2 \\ y=-\frac{3}{4}x+\frac{15}{4}+2 \\ y=-\frac{3}{4}x+\frac{15+8}{4} \\ y=-\frac{3}{4}x+\frac{23}{4} \end{gathered}[/tex]Now we need to graph it, for that we need two points. We already know the coordinates of one of them (5,2), now we need another, we can use the point for which x is equal to 0.
[tex]\begin{gathered} y=-\frac{3}{4}\cdot0+\frac{23}{4} \\ y=\frac{23}{4} \end{gathered}[/tex]Now we have (0, 23/4). We need to draw a line that passes
Stephanie and two friends want to Vancouver for a winter weekend Stephanie May 7 cups of apple cider everyone includes Stephanie wants an equal amount of all the the apple cider how much apple cider should each person get
Number of persons = 3
Number of cups of apple made is =7
Then the number of equal cider, everyone must have is:
[tex]\frac{7}{3}\text{ = 2}\frac{1}{3}\text{ cups of apple cider.}[/tex]Find the area of the isosceles triangle.
Check the picture below.
well, we know the triangle is an isosceles, so it has twin sides coming from the "vertex" down to the "base", running an angle bisector from the "vertex" will give us a perpendicular to the "base", let's find its height.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{13}\\ a=\stackrel{adjacent}{5}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{13^2 - 5^2}=h\implies 12=h[/tex]
so we simply need to get the area of a triangle whose base is 10 and height is 12.
[tex]A=\cfrac{1}{2}(\underset{b}{10})(\underset{h}{12})\implies \boxed{A=60}[/tex]
8Σ-(-2): -1-i=1Evaluate each geometric series described. (Find the total sum)
The given expression is
[tex]\sum ^8_{i\mathop=1}-(-2)^{i-1}[/tex]To solve this, we just have to replace each value of the sum in the expression, then we sum. Let's do it
[tex]\begin{gathered} -(-2)^{1-1}=-1 \\ -(-2)^{2-1}=-(-2)^1=2 \\ -(-2)^{3-1}=-(-2)^2=-4 \\ -(-2)^{4-1}=-(-2)^3=8 \\ -(-2)^{5-1}=-(-2)^4=-16 \\ -(-2)^{6-1}=-(-2)^5=-(-32)=32 \\ -(-2)^{7-1}=-(-2)^6=-64 \\ -(-2)^{8-1}=-(-2)^7=-(-128)=128 \end{gathered}[/tex]Now, we sum all these items
[tex]-1+2-4+8-16+32-64+128=85[/tex]Therefore, the total sum is 85.Describe and correct the error a student made in finding the average rate ofchange for f(x) = 0.5x2 over the interval - 4sxs - 2.
ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]Kimberly and Clay leaves a concert hall at the same time, traveling in buses going opposite directions, Kimberly's bus tra els at 40mph and Clay's bus travels at 60mph. In how many hours will Kimberly and Clay be 350 miles apart?
let s1 and s2 be the distance covered by the two buses
s1 + s2 = 350 ................................eqn I
velocity (v) = distance (s)/time (t) .........................eqn II
from eqn II the velocity of the first bus, v1 = s1/t1
s1 = v1t1 .................................eqn III
velocity of the second bus, v2 = s2/t2
s2 = v2t2 ...........................eqn IV
substitute eqn III and eqn IV into eqn I
v1t1 + v2t2 = 350
the time taken for any two moving objects to simultaneously cover any distance is equal. Thus,
t1 = t2 = t
eqn V becomes
v1t + v2t = 350
t(v1 + v2) = 350
v1 = 40
v2 = 60
t(40 + 60) = 350
100t = 350
divide both sides by 100
100t/100 = 350/100
t = 3.5 hours
The parent function of the function g(x) = (x-h)² + k is f(x) = x2. The vertex of the function g(x) is located at (9,-8).
What are the values of h and k?
g(x) = (x-
².
Answer:
The values of h and k are 9 and -8, respectively
Step-by-step explanation:
This is how to determine the values of h and k
The vertex of the function g(x) is located at (9, –8)
The vertex of a function is represented as:
Vertex = (h,k)
This means that:
(h,k) = (9,-8)
By comparison, we have:
h = 9 and k = -8
So, the values of h and k are 9 and -8, respectively
Find the missing side cround to is inches 3 you x inches 1 10 inches
Given,
The measure of the hypotenuse is 15 inches.
The measure of the base is 10 inches.
The measure of the perpendicular is x inches.
By Pythagoras theorem,
[tex]\text{hypotenuse}^2=\text{perpendicular}^2+\text{base}^2[/tex]Substituting the values then,
[tex]\begin{gathered} \text{hypotenuse}^2=\text{perpendicular}^2+\text{base}^2 \\ 15^2=x^2+10^2 \\ 225=x^2+100 \\ 225-100=x^2 \\ x=\sqrt[]{125} \\ x\approx11.18 \end{gathered}[/tex]