Answer:
The data that we have is:
Price per item = $25
spending limit = $200
Now, if you sell x items, then your earnings will be:
E = $25*x
So if you sell two items, we have x = 2
E(2) = $25*2 = $50
But the maximum spending possible will be such that:
$25*x = $200
x = $200/$25 = 8
Then the equation is:
E(x) = $25*x
such that 0 ≤ x ≤ 8
Which means that you can sell any number of units between 0 and 8.
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 hours. What was the average rate of speed for the trip?
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
--------------------------------------------------------
Edit: Thanks to Chegsnut36 for calculation correction
Answer:
≅45.29
Step-by-step explanation:
Hey there!
To find the average rate speed we need to add all the same number.
188 + 197 = 385
4 + 4.5 = 8.5
Now to find the average rate we do,
385 ÷ 8.5 ≅ 45.29
Hope this helps :)
What is the solution to this system of linear equations? 3x – 2y = 14 5x + y = 32 (3, 5) (6, 2) (8, –1) (14, –18)
Answer:
work is shown and pictured
The solution to the system of linear equation is (x, y) = (6, 2)
3x - 2y = 14 (1)
3x - 2y = 14 (1)5x + y = 32 (2)
From (2)
y = 32 - 5x
Substitute y = 32 - 5x into (1)
3x - 2y = 14 (1)
3x - 2(32 - 5x) = 14
3x - 64 + 10x = 14
13x = 14 + 64
13x = 78
x = 78/13
x = 6
Substitute x = 6 into (2)
5x + y = 32 (2)
5(6) + y = 32
30 + y = 32
y = 32 - 30
y = 2
(x, y) = (6, 2)
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A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y. Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season. Which system represents this scenario? x + y = 500. 215 x + 615 y = 187,500 x minus y = 500. 215 x minus 615 y = 187,500 500 x + 500 y = 187,500. 215 x = 615 y 500 x = 500 y. 215 x + 615 y = 187,500
Answer:
x + y = 500
215x + 615y = 187,500
Step-by-step explanation:
The first equation can show the amount of land. The farmer has 500 acres to plant corn, x, and cotton, y.
x + y = 500
The second equation can show the cost. The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.
215x + 615y = 187,500
The system of equations is
x + y = 500
215x + 615y = 187,500
The correct system of represents this scenario will be,
⇒ x + y = 500
⇒ 215x + 615y = 187,500
Where,' x' is plant acres of corn and 'y' is acres of cotton.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.
And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.
Now,
Let us take 'x' is plant acres of corn and 'y' is acres of cotton.
Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.
So, we can formulate;
⇒ x + y = 500
And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.
So, We can formulate;
⇒ 215x + 615y = 187,500
Thus, The correct system of represents this scenario will be,
⇒ x + y = 500
⇒ 215x + 615y = 187,500
Where,' x' is plant acres of corn and 'y' is acres of cotton.
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9. Read the following word problem, then create a linear equation to model the problem. Provide work to show how your linear equation models the problem, such as a brief description, a picture, or a table. Finally, use the linear equation you created to solve the problem.
$2400 is divided between two accounts. One account pays 2% interest, while the other account pays 3.5% interest. At the end of one interest period, the interest earned is $81. How much was invested in each account?
Answer:
$200 at 2%.
$2200 at 3.5%.
Step-by-step explanation:
Let the two amounts be x and y.
x earns 2% interest, and y earns 3.5% interest.
Since the total is $2400, then
x + y = 2400
Now we can solve for y and express the second amount in terms of x.
y = 2400 - y
The two amounts are x and 2400 - x.
In one interest period, the amount of interest earned is the amount of money in the account multiplied by the interest.
2% = 0.02; 3.5% = 0.035
The x amount earns 0.02x interest.
The y amount earns 0.035y interest.
The total interest earned is the sum of the interest amounts of the two accounts.
0.02x + 0.035y
We now replace y with 2400 - x, and we set the sum of the interest amounts equal to the total interest earned, $81.
0.02x + 0.035(2400 - x) = 81
The equation above is the linear equation.
Now we solve it. Distribute on the left side.
0.02x + 84 - 0.035x = 81
Combine like terms on the left side.
-0.015x + 84 = 81
Subtract 84 from both sides.
-0.015x = -3
Divide both side by -0.015.
x = 200
$200 was deposited in the account earning 2%.
y = 2400 - x
y = 2400 - 200
y = 2200
$2200 was deposited in the account earning 3.5%.
Help with alll❤️ Please
Plz
Answer:
A, B, A
Step-by-step explanation:
(3)
Given
- 2x² + 10x + 12 ← factor out - 2 from each term
= - 2(x² - 5x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 5)
The factors are - 6 and + 1, since
- 6 × 1 = - 6 and - 6 + 1 = - 5, thus
x² - 5x - 6 = (x - 6)(x + 1) and
- 2x² + 10x + 12 = - 2(x - 6)(x + 1) → A
(4)
[tex]x^{4}[/tex] - 81 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b), thus
[tex]x^{4}[/tex] - 81
= (x² )² - 9²
=(x² - 9)(x² + 9) ← note that x² - 9 is also a difference of squares
= (x - 3)(x + 3)(x² + 9) ← in factored form
x² - 3 is not a factor → B
(5)
Given
5[tex]x^{4}[/tex] - 320 ← factor out 5 from each term
= 5([tex]x^{4}[/tex] - 64) ← difference of squares
= 5(x² - 8)(x² + 8) → A
Find the length, x,of the third side of the triangle.
====================================================
Explanation:
This is a visual example of the pythagorean theorem. We add the areas of the two squares to get
13+29.25 = 42.25
Then we apply the square root to this to get the value of x, which is the hypotenuse of the right triangle
x = sqrt(42.25) = 6.5
---------
Side note: if you're curious about finding the other lengths of the triangle, apply the square root to those areas. The blue area 29.25 will lead to a side length of approximately sqrt(29.25) = 5.4083269; the red square will follow the same idea.
Answer:
Step-by-step explanation:
area of a square=a²
A=29.25
a=side=√29.25 first square
second square =a=√13
find x(c)
right triangle: a²+b²=c²
(√29.25 )²+(√13)²=c²
29.25+13=c²
c=√(29.25+13)=6.5 unit
Please answer this correct answer now fast
Answer:
WX = 8 mm
Step-by-step explanation:
To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].
We use the law of sines in the blue triangle to do such:
[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]
Now we can use this value in the larger right angle triangle where WX is the opposite side to angle [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:
[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]
which rounded to the nearest integer gives
WX = 8 mm
Please answer it now in two minutes
Answer:
∠ T ≈ 23.6°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin T = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{SU}{ST}[/tex] = [tex]\frac{4}{10}[/tex] , thus
∠ T = [tex]sin^{-1}[/tex] ([tex]\frac{4}{10}[/tex] ) ≈ 23.6° ( to the nearest tenth )
James bought 12 cookies and ate 3 of them. He ate ____% of the cookies. (Make sure to enter the answer using numbers only. Do not enter special characters such as the percent symbol.)
Answer:
25Step-by-step explanation:
Total cookies = 12
Ate = 3 cookies
Now,
Percentage of the cookies that James are:
[tex] \frac{3}{12} \times 100 \: percent[/tex]
Calculate:
[tex] = 25 \: percent[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
answer is 25
Step-by-step explanation:
need help a s a p HURRYYYYY
Step-by-step explanation:
v= 4/3πr³
4/3×314/100×8×8×8
•
= 2,143.573
BRAINLIEST!!! MATH HELP ME ASAP PLS!!!
Answer:
-0.0062 and 27.5
Step-by-step explanation:
You can write the equation of the line using the 2-point form:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The given values of the variables are ...
(h, T) = (10000, -34.5) and (15000, -65.5)
Putting these into the formula, we have ...
T = (-65.5 -(-34.5))/(15000 -10000)(h -10000) +(-34.5)
T = -31/5000(h -10000) -34.5
T = -0.0062h +62 -34.5
T = -0.0062h +27.5
The appropriate choice is ...
-0.0062 and 27.5
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
The new points after dilation are
(3/2, -3) and (9/2,-3)
Step-by-step explanation:
Here in this question, we want to give the new points of the line segment after it is dilated by a particular scale factor.
What is needed to be done here is to multiply the coordinates of the given line segment by the given scale factor.
Let’s call the positions on the line segment A and B.
Thus we have;
A = (1,-2) and B = (3,-2)
So by dilation, we multiply each of the specific data points by the scale factor and so we have;
A’ = (3/2, -3) and B’= (9/2,-3)
halla la medida del lado de un cuadrado cuya diagonal es de 14 cm
Answer:
7√2 cm
Step-by-step explanation:
Aquí, estamos interesados en encontrar la longitud del lado de un cuadrado que tiene una longitud diagonal de 14 cm.
Una diagonal es una línea que se extiende desde un borde del cuadrado hasta el otro borde del cuadrado internamente.
Ahora, una diagonal de un cuadrado junto con dos lados de un cuadrado forman un triángulo rectángulo isósceles, siendo la diagonal la hipotenusa de este triángulo rectángulo.
Sabemos que los lados de un cuadrado tienen la misma longitud y, por lo tanto, llamemos a este lado desconocido x cm.
Matemáticamente, según el teorema de Pitágoras, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los otros dos lados.
Por lo tanto, tenemos;
14 ^ 2 = x ^ 2 + x ^ 2
196 = 2x ^ 2
dividir ambos lados por 2
98 = x ^ 2 x = √98
x = √ (49 * 2)
x = 7√2 cm
Por lo tanto, la longitud del lado del cuadrado es de 7√2 cm
Part 2: describe the shape of your cross section of a slice of banana at 45° angle to a space draw picture of the sheep. Part 3: describe the shape of a cross sections if you slice banana and half with a cut perpendicular to its base draw a picture of the shape (hint remember to think of a banana a cylinder)
Answer:
Part 2:
The shape of a banana cut in 45° angle is that of a curve that is closed with the appearance of a flattened circle or an oval similar to an ellipse therefore having two focal points
The drawing of the angle cross section of a cylinder representing the banana is attached
Part 3:
When the banana is cut in half, perpendicular to the base of the banana, the shape formed is circular withe the center of the banana being about the same location as the center of the circle
The drawing of the perpendicular cross section of a cylinder representing the banana is
Step-by-step explanation:
HELP ASAP!!! BRAINLIEST!
Answer:
( 1/25 x^-12 y^-14 )
Step-by-step explanation:
( 5 x^6 y^7 ) ^-2
We know that ( ab) ^c = a^ c * b^c
( 5^-2 x^6^-2 y^7^-2 )
We know that a^b^c = a^(b*c)
( 5^-2 x^-12 y^-14 )
We know that a^ -b = 1/ a^b
( 1/25 x^-12 y^-14 )
Given trapezoid PQRS, find the length of midsegment TU.
Answer:
Option (4)
Step-by-step explanation:
In the given picture,
Trapezoid PQRS has two points T and U as the midpoints of sides PS and RQ.
Segment TU joins the midpoints of the sides PS and RQ.
Mid-segment theorem states that "If a line joining midpoints of a trapezoid is parallel to the bases, length of this segment is half the sum of lengths of the bases."
Therefore, m(TU) = [tex]\frac{1}{2}(m\text{PQ}+m\text{SR})[/tex]
7x - 26 = [tex]\frac{1}{2}[(3x+23)+(9x-3)][/tex]
7x - 26 = 6x + 10
7x - 6x = 26 + 10
x = 36
m(TU) = 7x - 26
= 7(36) - 26
= 252 - 26
= 226
Therefore, Option (4) will be the answer.
Which movie had the audience with the younger median ?
A. Movie A
B. Movie B
C. Both
D. Cannot be determined
How can we tell? Look at the vertical lines inside the box. This is where the median is located. For movie A, the inner vertical line is somewhere between 30 and 40 (perhaps 35 or so). So this is the median for movie A. Meanwhile, the median for movie B is somewhere between 40 and 50. I'd say maybe 46 or 47 as its a bit higher than the halfway point.
-----------
Extra info:
The left edge of the box is the first quartile (Q1).The right edge of the box is the third quartile (Q3).The tip of the left whisker is the min value, assuming there are no outliers to the left.The tip of the right whisker is the max value, assuming there are no outliers to the right.HELP PLEASEEEE!!!!!
find y-intercept on the graph
Answer:
-4
Step-by-step explanation:
When looking at the graph look at the y axis and look to see where the line passes through
Answer:
-4 is the y intercept.
Step-by-step explanation:
Brainliest? Have a great day!
Please help me... tysm if you do
Answer:
The answer is B.
Step-by-step explanation:
Since x < 1 the circle at the point is open and the arrow points infinitely in the negative direction (which happens to be answer A here)
x is also greater than or equal to -1 so a closed circle at the point -1 will complete this graph.
In a bag containing cards numbered 1 to 10,one of which is drawn at random.Find the probability that it is a 5
Answer:
1/10
Step-by-step explanation:
there are 10 cards, numbered 1 through 10, there is one "5" card. so that's 1 card out of 10 cards, therefore a 1/10the chance or a 10% chance you'll get a 5 (or any specific number)
hey loves!!! PLz help me
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)
Isiah determined that 5a2 is the GCF of the polynomial
a3 – 25a2b5 – 35b4. Is he correct? Explain.
Answer:
No
Step-by-step explanation:
He's not correct because 5a² isn't a factor of a³ or 35b⁴; in order for something to be the GCF of a polynomial, all of the terms must be evenly divisible by it.
Answer:
a^3 – 25a^2b^5 – 35b^4
He is incorrect since the coefficient of the a^3 term is 1, the GCF cannot contain a coefficient of 5. Also, there is no a in all terms, so a^2 is also not a common factor.
Two factory plants are making TV panels. Yesterday, Plant A produced 5000 fewer panels than Plant B did. Five percent of the panels from Plant A and 2% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 450 defective panels
Answer:
10,000 panels
Step-by-step explanation:
A TV panel is being produced by two factory plants
Plant A produced 5000 fewer panels than plant B
Let a represent the number of panels produced by plant A and b represent the number of panels produced by plant B
a= b-5000............equation 1
5% of the panels from plant A were defective
= 5/100
= 0.05
2% of the panels from plant B were defective
= 2/100
= 0.02
The total defective panels of both plants is 450
0.05a + 0.02b= 450..............equation 2
Substitute b-5000 for a in equation 2
0.05(b-5000) + 0.02b= 450
0.05b - 250 + 0.02b= 450
Collect the like terms
0.05b+0.02b= 450+250
0.07b= 700
Divide both side by the coefficient of b which is 0.07
0.07 b/0.07= 700/0.07
b= 10,000
Hence plant B produced 10,000 panels
Type the correct answer in each box. Use the graph to complete the given statements. Enter the letters A, B, C, or D in the boxes. (graph below) The function with the lowest output values as x approaches infinity is ____ . The function with the greatest output values as x approaches infinity is ____ .
As x approaches infinity,
The function with the lowest output is graph A
The function with the greatest output is graph B
===========================================================
Explanation:
As the graphs head to the right, they go up forever. However, the growth rate (how fast they go upward) varies. The red straight line (line A) goes up the slowest. The growth rate is the same throughout the entire function. The rate is the slope of the line. In contrast, the purple curve B goes up the fastest as it has the steepest increase among the four graphs. The graph steadily gets steeper as you move to the right.
The exponential graph will grow the fastest compared to a linear one or parabolic one. Graphs B and C are exponential, where graph B has a steeper curve compared to graph C.
Answer: The function with the lowest output values as x approaches infinity is Graph A.
The function with the greatest output values as x approaches infinity is Graph B.
Step-by-step explanation: I can’t give you a step-by-step explanation, but this is right!
A blueprint for a house has a scale factor n = 10. A wall in the blueprint is 7 in. What is the length of the actual wall?
840 ft.
5.83 in.
70 ft.
5.83 ft.
Answer:
5.83 ft
Step-by-step explanation:
Given that
Scale factor, n = 10
Wall in blueprint = 7 in
To find:
Length of actual wall = ?
Solution:
Whenever a blueprint is created for any house or building, it is made smaller by a scale factor.
Here this factor is 10 times.
That means, the blueprint size is 10 times smaller than that of its actual size.
Or we can say that actual wall of building is 10 times the wall of blueprint.
So, wall of building = 10 [tex]\times[/tex] 7 = 70 inches
Now, we know that 12 inches = 1 ft
1 inch = [tex]\frac{1}{12}\ ft[/tex]
70 inches = [tex]\frac{1}{12}\times 70\ ft = 5.83\ ft[/tex]
so, the answer is Wall of building is 5.83 ft.
What is P(A|B)?
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
What is P(A|B)? 
A.Not enough information
B.0.50 
C.0.10 
D.0.20
Answer:
50
Step-by-step explanation:
The value of P(A|B) = 0.50 which is correct option(B)
What is independent events?
Independent events is defined as an event that is not affected by other events.
A and B are independent events.
P(A) = 0.50
P(B) = 0.20
P(A|B) = P(A∩B)/P(B)
P(A|B) = P(A).P(B)/P(B)
P(A|B) = P(A)
Substitute the value of P(A) = 0.50,
P(A|B) = 0.50
Hence, the value of P(A|B) = 0.50
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Yo tenía $2.00
Mi mamá medio$100
Mi papá medio$100
Mi tío y mi tía me dieron $100
Y yo tenía otros $5.00
Cuanto tenía??
Answer:
$307
Step-by-step explanation:
$2.00 + $100 + $100 + $100 + $5.00 = $307
Find the area of equilateral triangle with side a.
Answer:
[tex]\frac{\sqrt{3} }{4} a^2[/tex]
Step-by-step explanation:
To find the area of an equilateral triangle, we can apply a formula.
[tex]A=\frac{\sqrt{3} }{4} s^2[/tex]
[tex]A= area\\s=side \: length[/tex]
The side length is given a.
Plug a in the formula as the side length.
[tex]A=\frac{\sqrt{3} }{4} a^2[/tex]
Answer:
3 square root over 4 a square
Step-by-step explanation:
simultaneous equations 2x + y = 21 x - y = 6
Step-by-step explanation:
this is substitution method
Answer:
2x + y = 21
+
x - y = 6
_________
3x = 27
x = 27 ÷ 3
x= 9
x - y = 6
9 - y = 6
9 - 6 = y
3 = y
Therefore, x= 9 and y = 3
Julie gathered data about the numbers of pages and chapters in several books by her favorite author.The equation of the line of best fit is y = 15.261x + 8.83. Based on the line of best fit, approximately how many pages are predicted to be in a book with 8 chapters? A. 113 B. 122 C. 131 D. 193
Answer:
C
Step-by-step explanation:
To get the approximate number of pages in the chapters, what we need to do is to substitute for the value of x in the line of best fit equation.
Thus, we have;
y = 15.261(8) + 8.83 = 122.088 + 8.83 = 130.918
This is approximately equal to 131