We know that
• Gonna owns 5/6 of the section of land.
,• She plants peanuts on 2/3 of her land.
We have to find 2/3 of 5/6, let's multiply these fractions.
[tex]\frac{2}{3}\cdot\frac{5}{6}=\frac{2\cdot5}{3\cdot6}=\frac{10}{18}=\frac{5}{9}[/tex]Therefore, Gonna plants peanuts on 5/9 of her land.Find the x-intercepts and the vertex of the parabola y = (x − 4)(x + 2). Find the x-intercepts of the parabola and write them as ordered pairs. Write the equation y = (x − 4)(x + 2) in standard form. With the standard form of the equation from Part II, use the quadratic formula to identify the x-value of the vertex. Substitute the x-value of the vertex from Part III into the original equation to find the y-value of the vertex. Then, write the coordinates of the vertex.
Given:
The eyuation of the parabola.
[tex]y=(x-4)(x+2)[/tex]Required:
We need to find the x-intercepts, vertex, and standard form of the equation.
Explanation:
Set y =0 and solve for x to find the x-intercepts of the parabola.
[tex](x-4)(x+2)=0[/tex][tex](x-4)=0,(x+2)=0[/tex][tex]x=4,x=-2[/tex]The x-intercepts are 4 and -2.
Multipy (x-4) and (x+2) to find the stansdad form of the equation.
[tex]y=x\left(x+2\right)-4\left(x+2\right)[/tex][tex]y=(x)x+2(x)+(-4)x+(-4)2[/tex][tex]y=x^2+2x-4x-8[/tex][tex]y=x^2-2x-8[/tex]The standard form of the equation is
[tex]y=x^2-2x-8.[/tex]which is of the fom
[tex]y=ax^2+bx+c[/tex]where a =1, b =-2 and c =-8.
[tex]\text{ The x- coordinate of the vertex is }h=-\frac{b}{2a}.[/tex]Substitute b =-2 and a =1 in the equation.
[tex]\text{ The x- coordinate of the vertex is }h=-\frac{(-2)}{2(1)}=1[/tex][tex]substitute\text{ x =1 in the equation }y=x^2-2x-8\text{ to find the y-coordinate of the vertex.}[/tex][tex]y=1^2-2(1)-8=-9[/tex]The vertex of the given parabola is (1,-9).
Final answer:
1)
The x-intercepts are 4 and -2.
2)
The standard form of the equation is
[tex]y=x^2-2x-8.[/tex]3)
The vertex of the given parabola is (1,-9).
Find the surface area of a parallelogram with adjacent sides u= <4,7, -8> and v= <-2, 5, 11>
Given:
The adjacent sides of parallelogram are u = <4,7,-8> and v = <-2,5,11>
Find:
we have to find the surface area of the parallelogram.
Explanation:
Formula:
Conclusion:
Therefore the surface area of the parallelogram is 125.01.
Find the value of z.7Xy3ZV[?]Z =Give your answer in simplest form.Enter
First, lets remember the property of right triangles as follows. Given a right triangle with the form:
The following formula is true:
[tex]Z^2=m\times(m+n)[/tex]So, in our case m=3 and m+n=7+3=10, if this we can find Z:
[tex]Z^2=3\times(7+3)\rightarrow Z^2=30\rightarrow Z=\sqrt[]{30}[/tex]what is the maximum profit
Total Profit=Total Revenue - Total Cost
P(x) = R(x)-C(x)
where x is the number of unit sold
From the question,
R(x) = 20x - 0.1x² and c(x) =4x + 2
P(x) = R(x) - c(x) = 20x - 0.1x² - 4x - 2
= -0.1x² + 16x - 2
Profit = -0.1x² + 16x - 2
We have a quadratic equation;
a=-0.1 b= 16
Maximum occurs when x = -b/2a
substitute the values of a and b in the above
x = -16/2(-0.1) = -16/-0.2 = 80
To find the maximum profit, we will substitute x=80 in our profit function
Profit = -0.1(80)² + 16(80) - 2
= -640 + 1280 - 2
= 638
Hence, the maximum profit is $638
20. f(x) = 6x2 – 3x2 + 4x - 4 and g(x) = 9x2 + x - 1. What is f(x) = g(x)? Show all of your steps and write your final answer in factored form.
Here, we want to subtract g(x) from f(x)
We have this as follows;
[tex]\begin{gathered} f(x)-g(x)=6x^3-3x^2+4x-4-(9x^2+x-1) \\ =6x^3-3x^2+4x-4-9x^2-x+1 \\ =6x^3-3x^2-9x^2+4x-x-4+1 \\ =6x^3-12x^2+3x-3 \\ =3(2x^3-4x^2+x-1)_{} \end{gathered}[/tex]Complete the equation describe how x and y are related
From the given equation and the given table, let the missing are m and b
[tex]y=mx+b[/tex]To find them use two points from the table
Let us use point (0, -2)
[tex]\begin{gathered} x=0,y=-2 \\ -2=m(0)+b \\ -2=0+b \\ -2=b \end{gathered}[/tex]Substitute b in the equation by -2
[tex]\begin{gathered} y=mx+(-2) \\ y=mx-2 \end{gathered}[/tex]Now, use the point (1, 1) to find m
[tex]\begin{gathered} 1=m(1)-2 \\ 1=m-2 \end{gathered}[/tex]Add 2 to both sides
[tex]\begin{gathered} 1+2=m-2+2 \\ 3=m \end{gathered}[/tex]Substitute m by 3 in the equation, then
The equation is
[tex]\begin{gathered} y=3x-2 \\ y=3x+(-2) \end{gathered}[/tex]The answer is y = 3x + (-2)
The missings are 3
A marketing company takes a random sample of 700 men to get their opinion on a new style of car. The marketing company then reports the following: “Four out of five drivers surveyed prefer the new style over the old style.” Explain why this conclusion would be misleading. a. The company only surveyed men but made the claim about all drivers. b. The survey question was biased toward the new style. c. The people surveyed were not randomly selected. d. The sample size of drivers was too small.
According to the information given, the randome sample that was asked about their opinion was 700 men, however the results of the survey were given as "4 out of 5 drivers"
This information is misleading because the results should have been thrown for men and not for drivers since the sample does not give any information saying that all 700 men are drivers.
The correct answer is: A
Find the value of x so that the ordered pair (x, 7) satisfies the equation y = 4x - 5. *
Answer:
x=3
Explanation:
Given the equation:
[tex]y=4x-5[/tex]In the ordered pair, (x,7): y=7
[tex]\begin{gathered} \implies7=4x-5 \\ 7+5=4x \\ 12=4x \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]The value of x so that the ordered pair (x, 7) satisfies the equation y=4x-5 is 3.
In ∆OPQ, q =1.7cm, o=3.8 cm and < P=96°. Find < Q, to the nearest 10th of a degree.
To solve the exercise you can use the law of cosine, which applies to any triangle:
[tex]b^2=a^2+c^2-2ac\cdot\cos (B)[/tex]Where
So, in this case, you have
[tex]\begin{gathered} p^2=o^2+q^2-2oq\cdot\cos (P) \\ p^2=(3.8cm)^2+(1.7cm)^2-2(3.8cm)(1.7cm)\cdot\cos (96\text{\degree)} \\ p^2=14.44cm^2+2.89cm^2-12.92cm^2\cdot\cos (96\text{\degree)} \\ p^2=17.33\operatorname{cm}^2-(-1.35cm^2) \\ p^2=17.33\operatorname{cm}+1.35cm^2 \\ p^2=18.68\operatorname{cm}^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{p^2}=\sqrt[]{18.68\operatorname{cm}^2} \\ p=4.32\operatorname{cm} \end{gathered}[/tex]Now, you can use the law of sine, which applies to any triangle:
[tex]\frac{a}{\sin (A)}=\frac{b}{\sin (B)}=\frac{c}{\sin (C)}[/tex]In this case, you have
[tex]\begin{gathered} \frac{q}{\sin(Q)}=\frac{p}{\sin(P)} \\ \frac{1.7\operatorname{cm}}{\sin(Q)}=\frac{4.32\operatorname{cm}}{\sin(96\text{\degree})} \\ \text{ Apply cross product} \\ 1.7\operatorname{cm}\cdot\sin (96\text{\degree})=\sin (Q)\cdot4.32\operatorname{cm} \\ \text{ Divide by 4.32 cm from both sides of the equation} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\frac{\sin(Q)\cdot4.32\operatorname{cm}}{4.32\operatorname{cm}} \\ \frac{1.7\operatorname{cm}\cdot\sin(96\text{\degree})}{4.32\operatorname{cm}}=\sin (Q) \\ 0.39=\sin (Q) \\ \text{ Apply the inverse function }\sin ^{-1}(\theta)\text{ both sides of the equation} \\ \sin ^{-1}(0.39)=\sin ^{-1}(\sin (Q)) \\ 23.0\text{\degree}=Q \end{gathered}[/tex]Therefore, the measure of angle Q is 23 degrees.
Find the mZRPQ.25°RQ105
Given the figure in the attached image;
[tex]\begin{gathered} m\measuredangle\text{PRQ}=25^{\circ} \\ m\measuredangle QTU=105^{\circ} \end{gathered}[/tex]The angle PQS and QTU are corresponding angles so they are congruent.
[tex]m\measuredangle PQS=m\measuredangle QTU=105^{\circ}[/tex]Also, the angle PQS is an exterior angle to the angles PRQ and RPQ. So, the sum of angles PRQ and RPQ will give the angle PQS;
[tex]m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ[/tex]substituting the given values;
[tex]\begin{gathered} m\measuredangle PQS=m\measuredangle PRQ+m\measuredangle RPQ \\ 105^{\circ}=25^{\circ}+m\measuredangle RPQ \\ m\measuredangle RPQ=105^{\circ}-25^{\circ} \\ m\measuredangle RPQ=80^{\circ} \end{gathered}[/tex]Therefore, the measure of angle RPQ is;
[tex]m\measuredangle RPQ=80^{\circ}[/tex]What is the appropriate domain and range of the line segment below?
Solution
The domain of a function is the set of all possible inputs for the function.
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
From the graph, we can easily see that;
if a flock of ducks is growing by 6 percent per year and starts with a population of 68 about how many ducks will be there in 10 years
We know that the next year the flock of ducks will have 6% more than the current year. If the current year the number of ducks is x, then
0.06 · x = the increase number
Then, the population of ducks next year will be
x + 0.06x = number of ducks next year
we can simplify the equation:
1.06x = number of ducks next year
Two years after, then number of ducks will be:
1.06 · number of ducks next year = number of ducks two years after
using the equation we found:
1.06 · (1.6x) = number of ducks two years after
1.06²x = number of ducks two years after
Similarly, three years after will be
1.06³x = number of ducks three years after
If we keep writing equations for every year, we will find a relation between the number of years that pass and the exponent...
n years after will be:
1.06ⁿx = number of ducks n years after
Since the current year the population is 68, then
1.06ⁿ · 68 = number of ducks n years after
We want to find the number of ducks after 10 years. This is n = 10:
[tex]1.06^{10}\cdot68=\text{ number of ducks 10 years after}[/tex]Since
[tex]\begin{gathered} 1.06^{10}=1.79 \\ 1.79\cdot68\approx121.78 \end{gathered}[/tex]Then, the equation we found says that:
number of ducks 10 years after = 121.78
But it is not possible because we cannor have 121.78 ducks, we always have an integer. Then we round it to the nearest integer: 122
Then
answer - the number of ducks 10 years after will be 122
The table below shows the population and the number of representatives in Congress for the selected states.StateCANYTXFLNCINALPopulation (in millions)29.818.017.012.96.65.54.0Representatives5231302312107 If you were to make a scatter plot of the data, you would be able to determine the line of best fit. Using the regression equationy = 1.73 x + 0.39,predict the number of representatives for Oregon, which has a population of about 3.3 million.a.5 representativesb.6 representativesc.7 representativesd.28 representatives
The number of representatives for Oregon, which has a population of about 3.3 million is 6. Option B is the correct option.
The regression equation is given as y = 1.73 x + 0.39.
The regression equation determined the specific link between one or more independent variables and a dependent variable.
We need to find the number of representatives for Oregon, which has a population of about 3.3 million.
For this, we need to put the value x = 3.3 in the regression equation is y = 1.73 x + 0.39.
We will get;
y = 1.73 * (3.3) + 0.39
= 5.709 + 0.39
= 6.099
≈ 6
Thus, the number of representatives for Oregon, which has a population of about 3.3 million is 6. Option B is the correct option.
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Answer:
6 representatives
Step-by-step explanation:
a dog runs 12 miles per hour select animals that run faster than the doglion 100 miles 2 hrsbear 60 miles in 2 hrszebra 80 miles in 2 hrselk 90 miles in 2 hrs
We were told that a dog runs 12 miles per hour.
If a lion runs 100 miles in 2 hours, it means that the number of miles that the lion runs per hour is 100/2 = 50 miles per hour
If a bear runs 60 miles in 2 hours, it means that the number of miles that the bear runs per hour is 60/2 = 30 miles per hour
If a zebra runs 80 miles in 2 hours, it means that the number of miles that the zebra runs per hour is 80/2 = 40 miles per hour
If an elk runs 90 miles in 2 hours, it means that the number of miles that the bear runs per hour is 90/2 = 45 miles per hour
We can see that all the other animals cover more miles per hour than the dog. Thus,they all run faster than the dog
What is the rate of change of the graph?a.1/32 gallons/mileb.1/64 gallons/milec.64 miles/gallond.32 miles/gallon
Taking two points on the graph
when miles = 160 , gallon = 5
when miles = 64 , gallon = 2
Ben has a basket of 5 red socks, 3 yellow socks, and 2 green socks. What is the theoretical probability that if he randomly selects a sock from the basket it will be red?
the probability of pen being red is,
[tex]p=\frac{^5C_1}{10C_1}[/tex][tex]p=\frac{5}{10}=\frac{1}{2}=0.5[/tex]so the answer is 0.5
If a car travels for 0 hours, it will travel enter your response here mile(s). This means it will pass through the point enter your response here. Use the slope to move 3 units to the right of the origin and enter your response here unit(s) up to find the point enter your response here that can be used to graph the relationship.
If the car travels for 0 hours, it will travel 0 miles. This means that it will pass through the point (0,0). Use the slope to move 3 units to the right of the origin and 186 units up to find the point (3,186) that can be used to graph the relationship.
What is the proportional relationship?The proportional relationship that models this situation is that the distance is obtained as the multiplied of the time and of the velocity, as follows:
d = vt.
The time is the input of the relationship, hence the constant of proportionality of the relation is given by:
The velocity.
The car travels 186 miles in 3 hours, hence the point is of:
(3,186).
As the format of the point is of:
(Input, output) = (Time, Distance).
Then the velocity is of:
v = 186/3 = 62 miles per hour.
Missing InformationThe car travels 186 miles in 3 hours.
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Question Help Which of the following expressions can be used to find the area of the polygon? 4cm 3 cm 3 cm 4 cm 3 cm Choose the correct answer below. 1 O A. (4x3) + z(9x4) 1 OB. 2 (3 x 4)+(9x4) Click to select your answer and then click Check Answer. All parts showing Clear All Check Ans Review progress Question 9 of 10 Back Next
The polygon is formed by a triangle and a rectangle:
Area of a rectangle = lenght x width
A1 = (4 x 3)
Area of a triangle = 1/2 x base length x heigth
A2 = 1/2 (9x4)
Add both areas
Area of the polygon = A1+ A2 = (4 x 3 ) + 1/2 (9 x 4)
answer : option A
In business, you may encounter situations that require you to set up equations with more than just parentheses. For practice, solve the following equation.X = 6{2 + 3[2(8 − 3) + (7 + 1) − 3]}
Given:
[tex]x=6\lbrace2+3[2(8-3)+(7+1)-3]\rbrace[/tex]Required:
To solve the given equation.
Explanation:
Consider
[tex]x=6\lbrace2+3[2(8-3)+(7+1)-3]\rbrace[/tex][tex]\begin{gathered} =6\lbrace2+3[2(5)+8-3]\rbrace \\ \\ =6\lbrace2+3[10+8-3]\rbrace \\ \\ =6\lbrace2+3[15]\rbrace \\ \\ =6\lbrace2+45\rbrace \\ \\ =6\lbrace47\rbrace \\ \\ =282 \end{gathered}[/tex]Final Answer:
[tex]x=282[/tex]Logan opened a savings account 6 years ago the account earns 5% interest compounded annually. if the current balance is $300.00 how much did he deposit initially
Each year, the initial deposit gets multiplied by a factor of:
[tex](1+\frac{5}{100})[/tex]Let L be the initial deposit. 6 years later, the balance of the account will be equal to:
[tex]L\cdot(1+\frac{5}{100})^6[/tex]On the other hand, the current balance is $300. Therefore:
[tex]L\cdot(1+\frac{5}{100})^6=300[/tex]Solve for L:
[tex]\begin{gathered} L=\frac{300}{(1+\frac{5}{100})^6} \\ =\frac{300}{1.05^6} \\ =223.8646\ldots \\ \cong223.86 \end{gathered}[/tex]Therefore, the initial amount of money in the account 6 years ago, was:
[tex]223.86[/tex]These marbles are placed in a bag and twoof them are randomly drawn.What is the probability of drawing two pinkmarbles if the first one is NOT placed backinto the bag before the second draw?Give your answer as a rational number, reduced tosimplest terms.Hint: Multiply the probability of the 1st Event by theprobability of the 2nd Event to get your answer.
Given data:
The total numbers of marbles are n=10.
The expression for the probability of drawing 2 pink marbles one by one without replacement is,
[tex]\begin{gathered} P(2p)=\frac{3}{10}\times\frac{2}{9} \\ =\frac{1}{15} \end{gathered}[/tex]Thus, the probability of drawing 2 pink marbles one by one without replacement is 1/15.
Joey’s sock drawer is unorganized and contains 3 black dress socks, 3 black ankle socks, 6 brown dress socks, and 4 brown ankle socks. What is the probability that Joey chooses a sock at random that is brown or is a dress sock?A) 1, or 100%B) 19/16C) 3/8D) 13/16
EXPLANATION:
Given;
We are told that Joey's drawer contains the following;
Black dress socks = 3
Black ankle socks = 3
Brown dress socks = 6
Brown ankle socks = 4
Required;
If a sock is chosen at random, find the probability that it is brown or is a dress sock.
Step-by-step solution;
The drawer contains a total of 16 socks.
Also, there is a total of 9 dress socks and 10 brown socks.
The probability of choosing a brown or dress sock will be determined by the following formula;
[tex]P[brown\text{ }sock\text{ }OR\text{ }dress\text{ }sock]=P[brown]+P[dress]-P[brown\text{ }and\text{ }dress][/tex]We can now substitute the values given for this experiment as follows;
[tex]P[brown\text{ }OR\text{ }dress]=\frac{10}{16}+\frac{9}{16}-\frac{6}{16}[/tex][tex]P[brownORdress]=\frac{19}{16}-\frac{6}{16}=\frac{13}{16}[/tex]ANSWER:
The probability that Joey would select a sock at random that is brown or is a dress sock is
[tex]\frac{13}{16}[/tex]Option D is the correct answer.
Which equation is true when k= -15A) 3k - 11 = -34B) - 53 + 4k = 7C) k/3 + 17 = 12D) k/5 + 2.5 = 0.5
We are given some equations and asked to find out which equation is true when k = -15
Note that an equation is true when left-hand side of the equation is equal to the right-hand side of the equation.
Let us substitute k = -15 into each of the given equation
A)
[tex]\begin{gathered} 3k-11=-34 \\ 3(-15)-11=-34_{} \\ -45-11=-34 \\ -56\ne-34 \end{gathered}[/tex]As you can see, the equation is not true since the left-hand side is not equal to the right-hand side.
What is the equation of the line through (-2, -3) with an undefined slope?a.y=-3b. -3x + 2y = 0c. -2x – 3y = 0d.x=-2
We have an undefined slope. It means that the line is parallel to the y-axis, that is, the slope could be "defined" as an infinite slope (in rough words).
Therefore, the equation of the line through the point (-2, -3) with an undefined slope is:
x = -2 (option d).
This line is represented as a parallel line to the y-axis (x = -2), and it passes through the point (-2, -3).
what is 3.33333333333 as a whole number?
1/3 = 0.333333333333
Then
3.33333333 is a whole number
= 3 + 1/3
What is the slope of the line connecting the points (1,2) and (-2,1)?
For this type of problem we recall the formula for the slope (m) of a line passing through 2 points and substitute the given points:
[tex]m=\frac{y_1-y_2}{x_1-x_2}=\frac{2-1}{1-(-2)}=\frac{1}{3}[/tex]Answer: m= 1/3.
The cost of a television set is $6980. After three years it depreciates by 6% per annum. if you want to sell this television what is it's value?
Depreciation refers to the diminishing value of an item after a period of time due to a reduction in its original quality
Mathematically depreciation can be defined as
[tex]\begin{gathered} D=P(1-R)^N \\ \text{Where} \\ D\text{ = Depreciation} \\ R\text{ = Rate of depreciation} \\ N\text{ = Period of depreciation} \\ P\text{ = Principal } \end{gathered}[/tex]D = ?
R= 6/100 = 0.06
N = 3 years
P = $6,980
Substituting all these into the formula
[tex]\begin{gathered} D\text{ = }6980(1-0.06)^3_{} \\ D=6980(0.94)^3 \\ D=\text{ 6980 }\times\text{ 0.830584} \\ D=\text{ \$5797.47632} \\ D\approx\text{ \$5797.48} \end{gathered}[/tex]Therefore, in 3 years the value of the television is approximately $5797.48
Nov 15,
What is the image point of (5, 1) after a translation right 5 units and down 2 units?
The required point is (10, - 1 )
What is translation rule ?An operation is a transformation if it moves, flips, or otherwise alters a figure to produce a new figure. Rigid transformations, sometimes referred to as isometry or congruence transformations, do not alter the size or shape of a figure.
Rotations, reflections, and translations are the stiff transformations. The term "image" refers to the transformed new figure. Preimage refers to the original image.
The translation is 5 units to the right indicates +5 to the x-coordinate.
Translation of two units downward denotes a two-unit subtraction from the y-coordinate.
(x, y ) → Translation rule
is (x + 5, y - 2),
therefore (5, 1) = (5 + 5, 1 - 2) (10, - 1 )
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6. In deciding whether to set up a new manufacturing plant, company analysts have established that a reasonable function for the total cost to produce x items is C(x) = 500,000 + 4.75x. (a) Find the total cost to produce 100,000 items. (b) Find the marginal cost of the items to be produced in this plant.
1)
a) Let's find out the total Cost to Produce 100,00 items considering x to stand for "items", so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C(100,000)=500,000+4.75(100,000) \\ C(100,000)=\$975,000 \end{gathered}[/tex]Note that we just had to plug into x, the number of items.
b) The Marginal Cost
On the other hand, the Marginal Cost can be found by taking the first derivative of the Total Cost function, so we can write out:
[tex]\begin{gathered} C(x)=500,000+4.75x \\ C^{\prime}(x)=4.75 \end{gathered}[/tex]The basic idea of the marginal cost is the cost per unit $4.75
3) Hence, the answer is:
a) $975,000
b) $4.75 per unit
all you need is in the photo please answer fast
We can conclude that the height of the ball is increasing