Answer:
D; f = 15,000 - 25t
Step-by-step explanation:
From the question;
per gallon, the number of miles traveled is 25, given traveling speed is 500 miles per hour
So after t hours, if traveling at 500 miles per hour, the amount of fuel expended will be 25 * t = 25t gallons
So, to get the amount remaining, we subtract 25t from what we have at the start of the trip
Mathematically, we have this as;
f = 15,000 - 25t
Given 2n-1 x 8^n = 2048, find the value n.
Jamal bought a diamond ring at a 20% discount. He paid $2640 for the ring. Naomi bought a similar ring but was given a discount of $924. What was the percentage discount given to Naomi?
Answer: 72%
Step-by-step explanation:
Set Jamal's original ring price = x
[tex]x - x(0.2) = 2640\\x(1-0.2)=2640\\x(0.8)=2640\\x=\frac{2640}{0.8}=3300[/tex]
Jamal's original ring price = $3300
Set Naomi's discount = y
[tex]3300-3300(y)=924\\=3300(1-y)=924\\1-y=\frac{924}{3300} \\-y=\frac{924}{3300} -1\\y=1-\frac{924}{3300}=1-0.28=0.72[/tex]
Naomi's discount is 0.72 = 72%
David is paid a salary of $1850 per month. He is also paid time and a half for work in excess of 40 hours a week. He worked 62 hours last week. What is his gross pay?
Answer:
$1,471.5625
Step-by-step explanation:
Monthly salary = $1850
Weekly salary = $1850/4 weeks
= $462.5
Hourly rate = $462.5/40 hours
= $11.5625
Overwork time = 62 hours - 40 hours
= 22 hours
Time and a half = 1.5 times the normal salary
Overwork time payment per hour = 1.5 × $11.5625
= $17.34375
Overwork time payment for 22 hours = 22 × $17.34375
= $381.5625
Last week salary = weekly salary + overtime payment
= $462.5 + $381.5625
= $84.0625
Gross salary for the month = 3 weeks regular salary + last week salary
= (3 × $462.5) + $84.0625
= $1387.5 + $84.0625
= $1,471.5625
Help me ASAP please
Step-by-step explanation:
similar triangles are simply like a linear protection, a "zoom" without distortion from one triangle to the other.
so, all linear distances and connections change by the same scaling factor.
therefore also the height EF of the smaller triangle colors the same scaling factor as the other lines. and EF is half the length of CG.
the area of a triangle is defined as baseline × height /2.
so, 2 linear distances are multiplied.
each one now contains the same scaling factor. so, the formula for the similar triangle multiplies the original distances and fire each also the scaling factor leading to the square of the scaling factor.
so, area new = area old × scaling²
in our example the scaling factor is 2, and 2² = 4.
so the area of ABC is 4 times as large as the area of ADE.
Which equation represents the graphed function?
O-3x + 2 = y
0 x+2=y
ox-3=y
O 2x - 3= y
Answer:
y = 3/2x -3
Step-by-step explanation:
The general equation of a straight line is;
y = mx + b
where m is slope and b is the y-intercept
Here, we can see that the graph intercepts the y-axis at the point y = -3
So b = -3
To get m, we can substitute any other point values on the plot
We can select (2,0)
So we have;
y = mx -3
0 = 2m -3
2m = 3
m = 3/2
so;
y = 3/2x -3
if C{1,2} and D={4,5,6}, find C×D by tabulation method. i need for exam
Answer:
Step-by-step explanation:
C * D = {(x,y): x is an element of C and y is an element of D.}
C * D = { (1,4), (1,5), (1,6), (2,4), (2,5), (2,6) }
HELP SOMEONE PLSSSSS
true or false,the diagonal of a rectangle is longer than any of its sides. I want the answer with explanation If u don't I will report
Answer:
True
Step-by-step explanation:
Yes! The diagonal of a rectangle is longer than any of its sides.
Consider PQRS as a rectangle. It is known to us that each interior angle of a rectangle measures 90°. Now, after making the diagonal of the rectangle PQRS, the rectangle has been split into 2 right-angled triangles i.e, ∆PRS and ∆RPQ. In the right angled triangle, hypotenuse is always the longest side. Here, in ∆PRS and ∆RPQ, the bases are RS and QP ; perpendiculars are PS and QR and both triangles' hypotenuse is PR. As, hypotenuse is always the longest side, so PR will be longer than RS,QP,PS and QR. Clearly, the diagonal of a rectangle is longer than any of its sides.
Please help me in the question of commission ! Grade - 9 .
Answer:
Step-by-step explanation:
Commission for amount Rs. 5,00,00 = [tex]\frac{2}{100}*500000[/tex]
= 2* 5000
= Rs. 10,000
total commission = Rs. 32,000
Remaining commission = 32500 - 10000
= Rs. 22500
Let remaining amount of the restaurant = Rs. x
Commission on Rs. x = 22500
3% of x = 22500
[tex]\frac{3}{100}*x=22500\\\\x=22500*\frac{100}{3}\\\\x = 7500*100[/tex]
x = Rs. 750000
Price of the restaurant = 750000 + 500000
=Rs . 1250000
A group of friends wants to go to the amusement park. They have no more than $365 to spend on parking and admission. Parking is $16.25, and tickets cost $38.75 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
Inequality: [tex] 38.75p + 16.25 \le 365 [/tex]
Solution: [tex] p \le 9 [/tex]
Step-by-step explanation:
Let p = number of people.
Ticket for 1 person: $38.75
Tickets for n people: 38.75p
Parking: $16.25
[tex] 38.75p + 16.25 \le 365 [/tex]
[tex] 38.75p \le 348.75 [/tex]
[tex] p \le 9 [/tex]
Answer
380≥20.75p+15.5
Step-by-step explanation:
good luck
please help me i need this asap
Answer:
-2, -1
Step-by-step explanation:
B is the answer for you. Have a good day!
If US=52, ST=30, UT=40, VW=27, and XW=36, find the perimeter of ΔVWX. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answer:
The perimeter is 109.8
Step-by-step explanation:
As we can see here, the angles of the triangles are congruent so we can say that both triangles are congruent
When two triangles are congruent, the ratio of their corresponding sides are equal
So we can get the scale factor here by looking at the sides facing each specific angle in both triangles
In the bigger triangle,
The side facing 34 degrees has a length of 30
In the smaller triangle,
The side facing 34 degree has a length of 27
So the scale factor to get the smaller from the bigger is 27/30 = 9/10 or 0.9
Likewise the side facing 51 degrees in the bigger is 40 while for the smaller, it is 36
So the ratio still stands at 36/40 = 9/10 or 0.9
In essence, the smaller triangle will have a perimeter that is 0.9 times that of the bigger
The perimeter of the bigger is simply the sum of the side lengths
We have this as;
(52 + 30 + 40) = 122
so that of the smaller would be;
122 * 0.9 = 109.8
someone please please help me!
Answer:
[tex]mDE=90[/tex]°
Step-by-step explanation:
In this problem, one is asked to find the measure of the arc in degrees. This problem provides one with a diagram since the center is unnamed, call the center point (O). One is given the information that angle (<DOE) has a measure of (90) degrees. One is asked to find the degree measure of the surrounding arc (DE).
The central angles theorem states that if an angle has its vertex on the center of a circle, the degree measure of the angle is equal to the degree measure of the surrounding arc. One can apply this here by stating the following:
[tex]m<DOE = mDE\\[/tex]
Substitute,
[tex]90=mDE[/tex]
Need help, please answer this
Answer:
In this exercise we need to solve the equation
3(x-2) = 2x + 6 - 2
We operate the parentheses and the right side
3(x-2) = 2x + 4
3x - 6 = 2x + 4
We add 6 to both sides
3x -6 + 6 = 2x + 4 + 6
3x = 2x + 10
We substract 2x
3x - 2x = 2x + 10 - 2x
x = 10
x = 10
Step-by-step explanation:
Identify the parent function.
Answer:
Reciprocal
Step-by-step explanation:
write an expression for 8 less than 2 times a number
show your work
Answer:
Step-by-step explanation:
Let's call the number x. The statement "...2 times a number" if the number is x looks like this:
2x
"8 less than" that looks like this:
... - 8
Putting the whole thing together:
2x - 8
Carlos is 46 years old, 5’10” and weighs 225 pounds. He has diabetes and dislikes taking his diabetes medications. What wellness strategy would his doctor most likely recommend to help him reduce his diabetes medications?
A.
lose weight
B.
use stress management techniques
C.
get immunized
D.
brush his teeth regularly
E.
increase his daily fruit intake
Suppose that the natural rate of unemployment in a particular year is 4 percent and the actual unemployment rate is 13 percent. Instructions: Enter your answers as a whole number. a. Use Okun's law to determine the size of the GDP gap in percentage-point terms. percent b. If potential GDP is $500 billion in that year, how much output is forgone because of cyclical unemployment? $ billion
Answer:
a. 18 percent
b. $90 billion
Step-by-step explanation:
a. Calculation to use Okun's law to determine the size of the GDP gap in percentage-point terms.
First step is to find the difference between ACTUAL RATE of unemployment and NATURAL RATE of unemployment
Difference=13%-4%
Difference= 9%
Based on the information above calculation we can see that the ACTUAL RATE of unemployment EXCEEDS the NATURAL RATE of unemployment by 9%, which indicates a CYCLICAL UNEMPLOYMENT.
Thus, According to Okun's law, this translates into an 18 % GDP gap in percentage-point terms (= 2 × 9%).
Therefore the the size of the GDP gap in percentage-point terms is 18 percent
b. Calculation to determine how much output is forgone because of cyclical unemployment
Forgone Output :
By applying Okun’s law we known that the GDP gap is 18%, which means that we are 18% below the GDP amount which is given as $500 billion,
Hence,
Output forgone = (18/100) ×$500 billion
Output forgone=0.18×$500 billion
Output forgone=$90 billion
Therefore the Forgone Output is $90 billion
In right triangle PQR, m∠Q = 90° and sin R=5/13
What is the value of cos R?
a) 5/13 b)5/12 c) 12/13 d) 12/5
Answer:
C
Step-by-step explanation:
Given
sinR = [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a 5- 12- 13 triangle with legs PQ = 5, QR = 12, hypotenuse PR = 13
cosR = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{QR}{PR}[/tex] = [tex]\frac{12}{13}[/tex]
Find the smallest number by which 2250 should be multiplied ,so that the product is a perfect square.
Answer:
10
Step-by-step explanation:
[tex]2250[/tex] = 2x5x5x5x3x3
therefore,2and 5 don't have a pair so , 2x5=10 .
So, the smallest number by which 2250 is 10
A certain ferry moves up and down a river between Town A and
B. It takes the ferry two hours to travel to Town A and only an
hour and thirty minutes to return to Town B. If the current is 5mph
how far apart are the two cities?
Answer: 60 miles
Step-by-step explanation:
Given
It takes ferry 2 hours to travel to town A and only [tex]1.5\ hr[/tex] to travel back to town B.
Speed of current is [tex]u=5\ mph[/tex]
Suppose the speed of the ferry is [tex]v[/tex] mph
Distance traveled in both the cases is same, but it took more time traveling to city A that is, ferry is moving upstream and downstream for returning time.
[tex]\Rightarrow 2(v-5)=1.5(v+5)\\\Rightarrow 2v-10=1.5v+7.5\\\Rightarrow 0.5v=17.5\\\Rightarrow v=35\ mph[/tex]
Distance between the towns is [tex]2\times (35-5)=60\ \text{miles}[/tex]
Answer:
The distance between the two towns is 60 miles.
Step-by-step explanation:
Let the distance between A and B is d.
A to B , t = 2 hour
B to A , t' = 1.5 hour
Speed of current, u = 5 mph
Let the speed of ferry is v.
distance = speed x time
d = (v - 5) x 2 = (v + 5) x 1.5
2 v - 10 = 1.5 v + 7.5
0.5 v = 17.5
v = 35 mph
So, the distance is
d = (35 - 5) x 2 = 60 miles.
Here is the distribution of blood types from a group
of randomly selected people:
o
А
B
AB
Blood
Type:
Probability:
0.49
0.27
0.20
?
What is the probability of type AB blood?
A rectangle has an area of 18 cm2
The lengths of the sides are whole numbers.
How long could the sides of the rectangle be?
Give all the examples you can think of
Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
PROVE that x² + y² = r². you must explain your answer.
Answer:
Suppose f(x,y)=x2+y2
Let’s look at the partial derivatives of this function:
∂f∂x=2x
∂f∂y=2y
So apparently, at each (x,y) coordinate pair (black dots below), the gradient of f(x,y) is pointing in the same direction as the position vector itself (it is only twice as large). Knowing that an isocline f(x,y)=C (a curve on which f(x,y) is constant) must be perpendicular to the gradient of f(x,y) . This yields the following image:
This image depicts for two position vectors (black dots), the gradient (blue vectors), and the perpendicular direction in which f(x,y) is constant (red line fragments).
Doing this for many positions we see that this creates circles:
Therefore setting f(x,y)=C , yields a circle in the 2D plane, with radius r=C−−√ .
EDIT: again, thanks to Gilles Castel for the nice graphics!
A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are thehyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it was sometimes called a fourth type of conic section.
In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section and all conic sections arise in this way. The most general equation is of the form
The conic sections described by this equation can be class
Consider a triangle with hypotenuse r and angle θ . As θ goes from 0 to 2π it traces out a circle.
The x and y coordinates are give by the basic trig equations:
x=rsin(θ)
y=rcos(θ)
Now if we compute x2+y2 we get
x2+y2
=r2sin2(θ)+r2cos2(θ)
=r2(sin2(θ)+cos2(θ))
=r2(1)
Hence x2+y2=r2 .
A certain polygon has its vertices at the following points: (1, 1), (1, 8), (8, 1), and (8, 8)
Answer:
Can u explain more pls?
Step-by-step explanation:
Answer:
Square
Step-by-step explanation:
Evaluate: 2(6+4) - 3(5)
70
1
5
85
Answer:
[tex]2(6 + 4) - 3(5) \\ 12 + 8 - 15 \\ = 5[/tex]
Answer:
1
Step-by-step explanation:
2*6+4-3*5
12+4-15
16-15
1
Finding
What is |-1|?
Answer:
1.
Step-by-step explanation:
.
3. Find the volume of the figure. Simplify.
Cube
x + 4
Answer:
[see below]
Step-by-step explanation:
V = s^3
V = (x+4)^3
V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3
V = x^3 + 12x^2 + 48x + 64
Hope this helps.
PLS HELP ASAP¡!!!
A P E X MATH
Answer:
Step-by-step explanation:
Is there an image to see?
Which number line shows the solution to −4 − (−1)?
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to 4 is shown. Above this, another arrow pointing from 4 to 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 5 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
A number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.
Answer:
number line is shown from negative 5 to 0 to positive 5. There are increments of 1 on either side of the number line. All the numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 4 is shown. Above this, another arrow pointing from negative 4 to negative 3 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow
