The profit function can be gotten using the formula below:
[tex]P(x)=R(x)-C(x)[/tex]where R(x) is the revenue function and C(x) is the cost function.
As previously calculated, the revenue and cost functions are given to be:
[tex]\begin{gathered} R(x)=425x \\ C(x)=315x+15600 \end{gathered}[/tex]Therefore, the profit function is:
[tex]\begin{gathered} P(x)=425x-(315x+15600) \\ P(x)=425x-315x-15600 \\ P(x)=110x-15600 \end{gathered}[/tex]The profit to be made is $50,000. Equating the profit function to this amount, we can get the number of kayaks required. This is shown below:
[tex]\begin{gathered} 50000=110x-15600 \\ 110x=50000+15600 \\ 110x=65600 \\ x=\frac{65600}{110} \\ x=596.4 \end{gathered}[/tex]Therefore, the number of kayaks that must be sold is approximately 597 kayaks to make $50,000 in profits.
find 264 + 638 using drawings of place value blocks. please show the work
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
264 + 638
Step 02:
place value blocks
264
+ 638
_______
902
That is the full solution.
PLEASE HELP. FUNCTIONS AND RELATIONS. The height of a model rocket, h(t), is a function of the time since it was launched, t. What is the domain of h(t)?
Recall that the domain is all the values of the graph from left to right.
From the given graph we get that its domain consists of all values greater than or equal to 0 and less than or equal to 42.
Then the domain of the given function in algebraic notation is:
[tex]0\leq t\leq42.[/tex]Answer: Option D.
disconnect me pls c bc
tutor loses connection for 30+
If each pair of 2 students share one regular size popcorn, how many cups of popcorn will each student get? (1 cup= 14.4in³)
Answer:
4 cups
Explanation:
First, we calculate the volume of the regular size popcorn:
[tex]\begin{gathered} \text{Volume}=5\times3\times8 \\ =120\; in^3 \end{gathered}[/tex]Given that:
[tex]\begin{gathered} \text{14}.4in^3=1\text{ cup} \\ 120in^3=x\text{ cups} \\ \frac{14.4}{1}=\frac{120}{x} \\ 14.4x=120 \\ x=\frac{120}{14.4} \\ x=8.33\text{ cups} \end{gathered}[/tex]Thus, if each pair of 2 students share one regular-size popcorn, each student will get approximately 4 cups.
Find the surface area of a square pyramid:b= 8 m, sh = 12 mSA= perimeter slant height +B (area of the base)2If that does not make sense there is a picture and no links
Take into account that the surface area of the given pyramid is the sum of the four triangular faces. Use the given equation for the surface area:
can you break it down and help me out please?
Given
[tex]x^2+x-2\ge0[/tex]To find the solution.
Now,
It is given that,
[tex]x^2+x-2\ge0[/tex]Using factorization method,
[tex]\begin{gathered} x^2+x-2=0 \\ x^2-x+2x-2=0 \\ x(x-1)+2(x-1)=0 \\ (x+2)(x-1)=0 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} x+2\ge0,x-1\ge0 \\ x\ge-2,x\ge1 \end{gathered}[/tex]Hence, the solution set is,
[tex]undefined[/tex]The sales tax on a table is $15.96find the purchase price The total price
Answer:
[tex]\begin{gathered} a)\text{ Purchase Price = \$190} \\ b)\text{ Total Price = \$205.96} \end{gathered}[/tex]Explanation:
Here, we want to get the purchase price and the total price
a) The purchase price before tax
In the question, we have it that the tax is 8.4% of the purchase price
Let the purchase price be $P
8.4% of this is $15.96
Mathematically:
[tex]\begin{gathered} \frac{8.4}{100}\times\text{ P = 15.96} \\ \\ 8.4P\text{ = 100}\times15.96 \\ P\text{ = }\frac{100\times15.96}{8.4} \\ P\text{ = \$190} \end{gathered}[/tex]b) The total price is the sum of the tax and the purchase price
Mathematically, we have this as:
[tex]\text{ 190 + 15.96 = \$205.96}[/tex]Please help me on the question I don’t get it c) For architects, by what percent did the median earnings increase for those who held a graduate degree compared to those who were recent college graduates? (round to the nearest integer)d) For nurses, by what percent did the median earnings increase for those who held a graduate degree compared to those who were recent college graduates? (round to the nearest integer)
(a) From the graph, the average recent college graduate engineer makes $65000, and the average recent college graduate accountant makes $40000. Therefore, an engineer makes $65000 - $40000 = $25000 more than the accountant.
(b) In marketing, the average graduate degree holder makes approximately $80000 (rounded down to the nearest thousand), and the average recent college graduate makes approximately $35000 (rounded down to the nearest thousand). Therefore, the average graduate degree holder makes $80000 - $35000 = $45000 more than the average recent college graduate
(c) graduate degree holder architect average earning: $75000 (rounded down to the nearest thousand)
average recent college graduate architect average earning: $35000 (rounded down to the nearest thousand)
The percent increase is computed as follows:
[tex]\begin{gathered} \text{percent increase = }\frac{\text{ degr}ee\text{ holder - college graduate}}{\text{college graduate}}\cdot100 \\ \text{percent increase = }\frac{75000-35000}{35000}\cdot100 \\ \text{percent increase }\approx114\text{ \%} \end{gathered}[/tex](d) graduate degree holder nurse average earning: $ 80000 (rounded down to the nearest thousand)
average recent college graduate nurse average earning: $45000 (rounded down to the nearest thousand)
The percent increase is computed as follows:
[tex]\begin{gathered} \text{percent increase = }\frac{\text{ degr}ee\text{ holder - college graduate}}{\text{college graduate}}\cdot100 \\ \text{percent increase = }\frac{80000-45000}{45000}\cdot100 \\ \text{percent increase = 78 \%} \end{gathered}[/tex](e) Comparison between average earning of a degree holder and of a college graduate for each area:
Engineers
Increase = degree holders - college graduate
Increase = 110000 - 65000
Increase = 45000
Nurses
Increase = degree holders - college graduate
Increase = 80000- 45000
Increase = 35000
Finance
Increase = degree holders - college graduate
Increase = 100000 - 45000
Increase = 55000
Accountant
Increase = degree holders - college graduate
Increase = 85000 - 40000
Increase = 45000
Architects
Increase = degree holders - college graduate
Increase = 75000 - 35000
Increase = 40000
Marketing
Increase = degree holders - college graduate
Increase = 80000 - 35000
Increase = 45000
The greatest increase from college graduates to degree holders is in Finance
which of the venn diagrams represents"not x"
The complement of a set x is everything in the in x by not 4 sets is denoted by: x'
The diagram contains a rectangle labeled with italic capital y. There is an oval inside the rectangle labeled with an pituitary capital X The region outside the oval but Inside the rectangle is shaded.
The outside of that figure is "not = x" or the logical nation of x.
A Venn diagram consists of two or three intersecting circles each representing a class labeled with a capital letter. Lowercase x and shading is used to indicate the presence or absence of some member of a particular class.
To solve the three-circle Venn diagram first enter the number of elements common to all three file sets. Then enter the remaining number of items in the Overlap area for each statement pair. Enter the number of remaining items in each set. Finally, find missing values using all known sums.
Learn more about A Venn diagram here:-https://brainly.com/question/24713052
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Given:• VU is tangent to Circle Q• UV = 20• UT = 8U2000TSFind the length of the radius of the circle.6O 1202142
To solve this question and find the radius of the circle, we will use the s
I need help with math
We have the following problem:
Using the kinematic equation, we know that for movements with constant acceleration the position is
[tex]h(t)=h_0+v_0t-\frac{gt^2}{2}[/tex]I already wrote the variables convenient for our problem, where
t = time (s)
h₀= initial height (m)
v₀ = initial velocity (m/s)
g = gravity acceleration (m/s²)
h = height after t seconds
We also know that
t = independent variable
h₀= 10m
v₀ = 56 m/s
g ≅ 10 m/s²
h = dependent variable
Therefore our quadratic will be
[tex]\begin{gathered} h(t)=10+56t-\frac{10t^2}{2} \\ \\ h(t)=10+56t-5t^2 \end{gathered}[/tex]Now we can answer the question in fact.
a)
The rocket will hit the ground when the height is equal to zero, hence, h(t) = 0. In fact, we are looking for the zeros of the quadratic
[tex]\begin{gathered} 10+56t-5t^2=0 \\ \\ t=\frac{-56\pm\sqrt{56^2-4\cdot(-5)\cdot(10)}}{2\cdot(-5)} \\ \\ t=\frac{-56\pm\sqrt{3136+200}}{-10} \\ \\ t=\frac{56\pm\sqrt{3336}}{10} \\ \\ t=11.38\text{ s or }-0.18\text{ s} \end{gathered}[/tex]See that we have one negative zero, but we will ignore that because it's physically impossible, therefore the rocker will reach the ground after 11.38 seconds
b)
To find the maximum height we must find the max value of the quadratic, we know that the vertex of a quadratic is its max/min, also, we can write it as
[tex]\begin{gathered} y_V=-\frac{\Delta}{4a} \\ \\ x_V=-\frac{b}{2a} \end{gathered}[/tex]Where
[tex](x_V,y_V)[/tex]Is the vertex. Here, we want to find the y coordinate, because y here is the height, therefore
[tex]\begin{gathered} \max h=-\frac{\Delta}{4a} \\ \\ \operatorname{\max}h=-\frac{3336}{4\cdot(-5)} \\ \\ \operatorname{\max}h=\frac{3336}{20} \\ \\ \operatorname{\max}h=166.8\text{ m} \end{gathered}[/tex]The max height of the rocket is 166.8m
c)
Now we have a similar problem, it's also the vertex but now the coordinate x, that here, represents the time, then
[tex]\begin{gathered} t_{\max}=\frac{-b}{2a} \\ \\ t_{\operatorname{\max}}=\frac{-56}{2\cdot(-5)} \\ \\ t_{\operatorname{\max}}=\frac{56}{10} \\ \\ t_{\operatorname{\max}}=5.6\text{ s} \end{gathered}[/tex]The rocket will reach the maximum height after 5.6 seconds.
Answer the following word problem by setting up an equation and then solving. Type the answer as "first number = " and "consecutive number = The sum of two consecutive numbers is 85, find the numbers.
From the question we're told that the sum of two consecutive numbers is 85,
Let the 1st number by y,
And the consecutive number be y+1
So, the sum of these two numbers will be equal to 85;
[tex]y+(y+1)=85[/tex]Let's go ahead and solve for y in the above equation;
[tex]\begin{gathered} 2y+1=85 \\ 2y=84 \\ y=42 \end{gathered}[/tex]So the first number is 42.
Let's find the consecutive number;
[tex]y+1=42+1=43[/tex]Therefore, the "first number = 42" and "consecutive number = 43"
21.Find the indicated angle measure to the nearest degree.1613?А.510B. 39С C36549
using trigonometric ratio,
let
the unknown angle = x degrees
[tex]\tan x=\frac{opposite}{\text{adjacent}}[/tex][tex]\begin{gathered} \tan x=\frac{13}{16}^{} \\ x=\tan ^{-1}0.8125 \\ x=39.0938588862 \\ x\approx39^{\circ} \end{gathered}[/tex]Find the standard deviation of x for the given points: {(-2,-1), (1,1), (3,2)}.Round your solution to three decinal places.
The x coordinates of the points are -2, 1 and 3
To find standard deviation, take the average or mean of thegiven numbers.
[tex]\begin{gathered} \text{Let n be the total count of numbers} \\ Mean,x_i=\frac{\text{Sum of numbers}}{n} \\ =\frac{-2+1+3}{3}=\frac{2}{3} \end{gathered}[/tex]Now subtract the mean from eah number and take their squares.
[tex]undefined[/tex]Find the volume of a cone with a slant height of 15 inches and a radius of 9 inches. Leave your answers in terms of π
Given:
height(h)=15 inches
radius(r)=9 inches
Volume of cone:
[tex]V=\pi\times r^2\times\frac{h}{3}[/tex][tex]V=\pi\times9^2\times\frac{15}{3}=\pi\times81\times5[/tex][tex]V=\pi\times405[/tex][tex]V=405\pi\text{ cubic inches}[/tex]-3|2x+1|<4 how is this solved
Answer:
True for all x
Step-by-step explanation:
Multiply by -1. This reverses the inequality.[tex]-3\left|2x+1\right| < 4\\\left(-3\left|2x+1\right|\right)\left(-1\right) > 4\left(-1\right)[/tex]
Remember: Negative * Positive = NegativeRemember: Negative * Negative = Positive[tex]3\left|2x+1\right| > -4:\:Solve\\4\times -1 = -4\\\left(-3|2x+1|\right)\left(-1\right)\\\left(-3\times -1\right)\\\left(-3|2x+1|)[/tex]
Divide by 3[tex]=\frac{3\left|2x+1\right|}{3} > \frac{-4}{3}[/tex]
___________
[tex]\frac{3\left|2x+1\right|}{3}\\\frac{3}{3}\\= \frac{1}{1}[/tex]
___________
[tex]= \frac{1}{1} > \frac{-4}{3}[/tex]
___________
[tex]-\frac{4}{3}\\= -\frac{4}{3}[/tex]
Because absolute values are greater than or equal to 0, the problem will be classified as "True" for any value of x no matter what.Hope this helps.
Simplify 5(3p - 2) + 2(p +4)
Here, we want to simplify the expression
To do this, we shall use the term outside the bracket to multiply the terms inside the brackets before we proceed to add them together
We have this as follows;
[tex]\begin{gathered} (5\times3p)-(5\times2)\text{ + (2}\times p_{})\text{ + (2}\times4) \\ =\text{ 15p - 10 + 2p + 8} \\ =\text{ 15p}+2p-10+8 \\ =\text{ 17p -2} \end{gathered}[/tex]Cuánto es 71/4 menos un entero 3/4
7 1/4 - 1 3/4
[tex]7\frac{1}{4}-1\frac{3}{4}=\frac{28+1}{4}-\frac{4+3}{4}=\frac{29}{4}-\frac{7}{4}=\frac{22}{4}=5\frac{2}{4}=5\frac{1}{2}[/tex]Respuesta:
5 1/2
[tex]5\frac{1}{2}[/tex]
11) Tell whether (3, 20) is a solution of y = 4x +8 A) Yes B) No
y = 4x + 8
To tell if (3, 20) is a solution, we will substitute the value of x = 3 and y= 20
into the equation to see if the left-hand side equals the right-hand side of the equation
So, upon substituting
20 = 4 x 3 + 8
20 = 12 + 8
20 = 20
Since the left-hand side of the equa
A local grocer cut his marketing budget by 54% last year. He spent only $650 on marketing this year and is happy with his decision. How much did the grocer spend on marketing last year? Round your answer to the nearest cent. Do not include units with your answer.
Given that the grocer spent only $650 on marketing this year, you know that this is 54% of his marketing budget last year.
You can rewrite a percent as a Decimal Number by dividing it by 100:
[tex]\frac{54}{100}=0.54[/tex]Let be "x" the amount of money (in dollars) the grocer spent on marketing last year.
Knowing all the data, you can set up the following equation:
[tex]x-0.54x=650[/tex]When you solve for "x", you get:
[tex]0.46x=650[/tex][tex]\begin{gathered} x=\frac{650}{0.46} \\ \\ x\approx1413.04 \end{gathered}[/tex]Hence, the answer is: He spent $1,413.04 .
I need help please I can’t figure this out and it’s my last question
QUAD magnified 4 times gives Q'U'A'D'
D(7,0)
Q(0,0)
Then center of rectangle is at (D -Q)/2= 3.5
Area of rectangle QUAD= (7-0)•(5-0) = 35
4times area QUAD = 4x35= 140
Then
Q'= (0,0)
Q'U'= 4xQU = 4x5 = 20
what is the surface area for a m rectangular prism. with the measurements as: height = 9 length = 3width = 7
Answer:
Surface area = 222 square cm
Explanation:
Given the following data
Length = 3 cm
Height = 9 cm
Width = 7 cm
Surface area = 2(wl + hl + hw)
Surface area = 2(7 * 3 + 9 * 3 + 9 * 7)
Surface area = 2( 21 + 27 + 63)
Surface area = 2( 111)
Surface area = 222 square cm
Therefore, the surface area is 222 square cm
fill in the blanks.6x20=6x2x_____5x100=______x10x10
ANSWER
1. 10
2. 5
EXPLANATION
We want to expand the expressions given:
1. 6 x 20 = 6 x 2 x ____
To do this, we have to divide 20 by 2, because 20 was expanded to give 2 x __.
20 divided by 2 is 10, so the answer is:
6 x 20 = 6 x 2 x 10
2. 5 x 100 = ___ x 10 x 10
This is straightforward, since 10 x 10 is 100.
The answer is:
5 x 100 = 5 x 10 x 10
Consider the following graph. List the ordered pairs corresponding to the points in the graph?
Answer:
A(-6, 1)
B(-6, -7)
C(7, -9)
D(-8, -8)
Explanation:
From the graph, we can see that at point A, x = -6 and y = 1. Therefore, the ordered pair can be written as A(-6, 1)
At point B, x = -6 and y = -7. The ordered pair can be written as B(-6, -7)
At point C, x = 7 and y = -9. Its ordered pair will be C(7, -9)
At point D, x = -8 and y = -8. Its ordered pair will be D(-8, -8)
Jason pays a $100 installation fee and a $40 monthly service charge for his telephone . Which equation shows the amount that Jason pays for x months of telephone service ? A. y= 40 + 100x B. y = 100 + 40xC . y = 100 - 40x
Given
x: months of telephone service
$100 installation fee (one time)
$40 monthly fee
Equation
[tex]y=100+40x[/tex]
Where 100 is the initial cost and 40 is the monthly cost
How can we tell when every point on the graph is a solution to the problem?
One way to verify that if a point exist on both lines is to substitute the x- and y-values of the ordered pair into the equation of each line. If the substitution results in a true statement, then you have the correct solution!
Which number has a repeating decimal form? A [tex] \sqrt{15} [/tex]B 11/ 25 C. 3/20 D. 2/6
Answer
Explanation
To know which is correct, we simply write the given numbers in decimal form
√15 = 3.8729
(11/25) = 0.44
(3/20) = 0.15
(2/6) = 0.333333333
We can easily see that
The circumference of a big circle is 36 pi. The area of a smaller circle located inside the bigger circle is 16 pi. If you randomly pick a point inside the big circle, what is the probability the point lands in the smaller one?
Given:
a.) The circumference of a big circle is 36 pi.
b.) The area of a smaller circle located inside the bigger circle is 16 pi.
The probability that the point lands in the smaller one is,
[tex]\text{ Probability = }\frac{Area_{Small\text{ Circle}}}{Area_{Big\text{ Circle}}}[/tex]However, only the circumference of the big circle is given. To be able to get the probability, we must first determine the area of the circle.
a.) Area of the big circle.
[tex]\begin{gathered} \text{ Circumference = }2\pi r \\ 36\pi\text{ = 2}\pi r \\ \frac{36\pi}{2\pi}\text{ = r} \\ 18\text{ = r} \end{gathered}[/tex][tex]\begin{gathered} \text{ Area = }\pi r^2 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{ = }\pi(18)^2 \\ \text{ = }\pi(324) \\ \text{ Area = 324}\pi \end{gathered}[/tex]b.) Let's now determine the probability.
[tex]\text{ Probability = }\frac{Area_{Small\text{ Circle}}}{Area_{Big\text{ Circle}}}[/tex][tex]\text{ = }\frac{16\pi}{324\pi}[/tex][tex]\text{ = }\frac{16}{324}\text{ = }\frac{\frac{16}{4}}{\frac{324}{4}}\text{ = }\frac{4}{81}[/tex][tex]\text{ Probability = }\frac{4}{81}[/tex]Therefore, the probability that the point lands in the smaller one is 4/81.
at a baseball game a vender sold combined total of 103 sodas and hotdogs . The numbers of sodas was sold was 57 more than the number of hot dogs sold . Find the number sodas sold and the number of hot dog sold
Number of sodas sold = 80
Number of hot dogs sold = 23
Explanation:Let th number of sodas be xs
Let the number of hot dogs be h
The vendor sold a combined total of 103 sodas and hot dogs
s + h = 103............(1)
The nmber of soda sold was 57 more tha n the number of hot dogs sold
s = h + 57........()
Subtitute equation (2) into equation (1)
h + 57 + h = 103
2h = 103 - 57
2h = 46
h = 46/2
h = 23
Substitute h = 23 into equation (2)
s = 23 + 57
s = 80
Number of sodas sold = 80
Number of hot dogs sold = 23
Cecil wrote the fraction 6/4. Susie wants to write anequivalent fraction. Whichof the following could be herfraction? A. 2/3 B. 6/9 C. 8/12 D. All of the above.
ANSWER
8/12. Option C
EXPLANATION
In a simple term: Equivalent fraction can be determined by simply multiplying the numerator and the denominator by the SAME NUMBER.
That is,
if you have 2/3 the equivalent fraction will be 4/6 (when multiplied by 2) or 6/9 (when multiplied by 3) or 8/12 (when multiplied by 4) etc.
So, from the question above:
The equivalent fraction of 4/6 (when multiplied by 2) is 8/12