In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
polynomials
Step 02:
applications of polynomials:
The polynomials can be represented graphically, and are used in many economics and engineering problems. In economics they appear, for example, to model markets, showing how prices vary over time; how raising or lowering the price of a product affects its sales; or also in the calculation of taxes.
In forestry engineering, for example, we need geometry to calculate areas, but also polynomials in problems such as calculating how many trees we need to replant after having cut down an area of a forest.
Other uses of polynomials are the calculation of the trajectory of projectiles (they are parabolic trajectories), or in the calculation of orbits of satellites or rockets.
That is the full solution.
One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a
large amount of pink paint using 14 cups of red paint.
a. How many batches of pink paint did she make?
Answer:
7
Step-by-step explanation:
14/2=7
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Based on the graph of the function shown, we can logically deduce the following:
Domain = -2 ≤ x < 0.Range = 0 ≤ x < 2.The relation is a continuous function.How to identify the range and domain of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Similarly, the horizontal extent of a graph represents all domain values and they are also read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph of the given function shown above, we can reasonably and logically deduce the following:
The domain is equal to -2 ≤ x < 0.The range is equal to 0 ≤ x < 2.In conclusion, the function which this graph represent is a continuous function because both the domain and range is defined for all set of values in the interval above.
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MATHEMATICAL PHRASES_____5. the quatient of y and seven is eight_____6. thrice a number is eighteen_____7. the sum of twice a number and five is nine_____8. a number decreased by seven is twenty-eight
Explanation
Part A: The quotient of y and seven is eight.
Answer: y/7 =8
Part B: Thrice a number is eighteen
Answer: 3x = 18
Part C: The sum of twice a number and five is nine
Answer: 2x+5 =9
Part D: A number decreased by seven is twenty- eight
Answer: x-7 =28
For each of the variables described below, indicate whether it is a quantitative or a categorical (qualitative) variable. Also, indicate the level of measurement for the variable: nominal, ordinal, interval, or ratio. Make sure your responses are the most specific possible.
Part A.
From the given table, we can see that the variable occupation is a Categorical variable becasue the occupation can divide a set of people into groups. Then, the level of measurement is Nominal because the occupation describes the objects by labels, with no quantitative value.
Part B.
Temperature is a Quantitave variable because we can measure the temperature of an object. Regarding the level of measurement, the temperature is an Interval variable because zero temperature is not the lowest possible temperature.
Part C.
The price is a Quantitative variable because the price is a numerical value with a meaningful order. Regarding the level of measurement, the price is a Ratio variable because it has a true zero, meaning that we can take ratios of values.
Type the correct answer in type the answer in the box.Consider functions fand g.f(x)=(x+1)^3g(x) = 3sqrtx + 1Evaluate the function composition.(fg)(-64) = _
f(x) = (x + 1)^3
g(x) = cubic root x + 1
f(g)(x) =
[tex]\begin{gathered} f(g(x))\text{ = (3}\sqrt[]{x}+2)^3 \\ f(g(x))\text{ = x + 6(3}\sqrt[]{x})^2\text{ + 12(3}\sqrt[]{x})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(3}\sqrt[]{-64})^2\text{ + 12(3}\sqrt[]{-64})\text{ + 8} \\ f(g(-64))\text{ = -64 + 6(16) - 48 + 8} \\ f(g(-64))\text{ = -64 + 96 - 48 + 8} \\ f(g(-64))\text{ = 104 - 112} \\ f(g(-64))\text{ = -8} \end{gathered}[/tex]result
f(g(-64)) = -8
In an office building, 42 offices are currently being rented. This represents 30% of the total units. How many offices are there in the building?
Let the total number of offices in the building be x.
We can represent the information provided in the question mathematically as:
[tex]30\text{ \% of x = 42}[/tex]Solving for x:
[tex]\begin{gathered} \frac{30}{100}\text{ }\times\text{ x = 42} \\ \frac{30x}{100}\text{ = 42} \\ \end{gathered}[/tex]Cross-Multiply:
[tex]\begin{gathered} 30x\text{ = 4200} \\ \text{Divide both sides by 30} \\ \frac{30x}{30}\text{ = }\frac{4200}{30} \\ x\text{ = 140} \end{gathered}[/tex]Hence, there are 140 offices in the building.
Answer: 140 offices
The line of best fit is given as y = 9 - 3x. Find the value of y when x = -3.091827
Solution
We are given the equation
[tex]y=9-3x[/tex]We want to find y when x = -3. We only need to put x = -3
[tex]\begin{gathered} y=9-3x \\ y=9-3(-3) \\ y=9+9 \\ y=18 \end{gathered}[/tex]Therefore, the answer is
[tex]\begin{equation*} 18 \end{equation*}[/tex]dentashboard/home
Town policy requires that a certain number of trees be planted for every tree that is cut down.
For example, if 8 trees are cut down, 48 trees will be planted. A homeowner is going to cut down
5 trees on his property.
Solve Problems with Ratios and Unit Rates-Instruction-Level F
How many trees will be planted when 5 are cut down?
Trees Planted
Trees Cut Down
48
8
5
This can be solved using ratio and proportions.
What is ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of lemons to oranges is 6:8 (or 3:4), while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive. A ratio in mathematics illustrates how many times one number contains another.
First, we find the ratio of trees planted to trees cut
= 48/8 = 6
So, no. of trees to be planted when 5 trees are cut = 5x6 = 30
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Find an equation in point-slope form for the line having the slope m=-3 and containing the point (4,2).
The equation of a line in point-slope form is given by
[tex]y-y_1=m(x-x_1)[/tex]Where
[tex]\begin{gathered} m=-3 \\ y_1=2 \\ x_1=4 \end{gathered}[/tex]Thus, if we substitute the above values into the equation:
[tex]y-2=-3(x-4)[/tex]<1 is in a triangle work <4 and a 53° angle . what is the sum of the measures of these two angles
In the small triangle
There are a right angle and an acute angle of measure 53 degrees
Since the sum of the angles of a triangle is 180 degrees
Then 90 + 53 + < 1 = 180 degrees
Then 143 + < 1 = 180
Subtract 143 from both sides
Then < 1 = 37 degrees
Since <2 is an exterior angle of the small triangle
Then its measure = the sum of <1 and 90 degrees
Then < 2 = 37 + 90 = 127 degrees
In the triangle of angles 2, n3 and 30
< 2 + < 3 + 30 = 180
127 + < 3 + 30 = 180
Add 127 and 30
157 + <3 = 180
<3 = 23
The answer is < 2 = 127 degrees and < 3 = 23 degrees
Write the correct equation for the following statement.
The quotient of x and seven is twelve
Answer:
Step-by-step explanation:
x/7=12
Colleen truman earns 5% commission on all sales in june her sales totaled 54,000$ how much did she earn in commission?
The amount earned as commission in the month of June is $2700
How to determine the amount earned as commission?From the question, we have the following parameters that can be used in our computation:
Commission percentage = 5%
Total sales in the month of June = $54000
The amount earned as commission in the month of June is then calculated as
Amount = Commission percentage x Total sales in the month of June
Substitute the known values in the above equation
So, we have
Amount = 5% x 54000
Evaluate
Amount = 2700
Hence, the commission amount is $2700
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i need help with this pls
Hello!
What is an x-intercept:
⇒ value of x when the value of y equals '0'
[tex]8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}[/tex]
x-intercept is 25/8
What is a y-intercept:
⇒ value of y when the value of x equals '0'
[tex]8x+5y=25\\8(0)+5y=25\\5y=25\\y=5[/tex]
y-intercept is 5
Hope that helps!
The table and graph show the population or Oregon
From the given table, it is found that:
a. The average population decline was of 2,250 deer a year.
b. The population would have reached 225 thousand deer during the years of 2017 and 2018.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input of the function. Hence, over an interval [a,b], the average rate of change is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In 1984 and 2018, the populations are given as follows:
1984: 250 thousand.2018: 173.5 thousand.Hence the rate of change is given as follows:
r = (173.5 - 250)/34 = -2.25.
(2.25 thousand = 2,250).
For item b, the following linear function is built:
y = 230.5 - 1.45x.
The amount would be of 225 when:
230.5 - 1.45x = 225
1.45x = 5.5.
x = 5.5/1.45
x = 3.79.
Hence between the years of 2017 and 2018.
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50 points again!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
f(x)=|5x|
f(2)= |5(2)| Substitute 2 for x
f(2)= 10 Answer
Answer:
f(2) = | 5 • 2 | = | 10 | = 10
Step-by-step explanation:
Replace x with 2 then solve with the absolute value
Find the vertex of the function given below.
y = 3x² + 6x +1
A. (1,7)
B. (-1,-2)
C. (-4,9)
D. (-1,-1)
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+1} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(3)}~~~~ ,~~~~ 1-\cfrac{ (6)^2}{4(3)}\right) \implies \left( - \cfrac{ 6 }{ 6 }~~,~~1 - \cfrac{ 36 }{ 12 } \right) \\\\\\ (-1~~,~~1-3)\implies {\Large \begin{array}{llll} (-1~~,~~-2) \end{array}}[/tex]
Henry purchased compact disks for $112. The compact discs cost $16 each.Which of the following equations could you use to find how many compact disks, x, Henry purchased?$16 = $112xO $112 = $16xXO $112=16$112 = x - $16
Problem
Henry purchased compact disks for $112. The compact discs cost $16 each.
Which of the following equations could you use to find how many compact disks, x, Henry purchased?
Solution
We can set up the following notation:
x= number of disks
total cost = (number of disks)* (unitary price)
Total cost = $112
number of disks =x
unitary price = $16
Replacing we got:
112 = x*16
For this case the correct equation would be given by:
$112 = $16x
The two plots below show the heights of some sixth graders and some seventh graders:Sixth Graders+52 53 54 55 56 57Height (inches)Seventh Graders52 53 54 55 56 57Height (inches)The mean absolute deviation (MAD) for the first set of data is 1.2 and the MAD for the second set of data is 1.0. Approximately how manytimes the variability in the heights of the seventh graders is the variability in the heights of the sixth graders? (Round all values to the tenthsplace.)
From the information given,
MAD for the heights of some sixth graders = 1.2
MAD for the heights of some seventh graders = 1
Number of times = MAD of data1/MAD of data 2 = 1.2/1
The answer is 1.2
Two motorcycle dealers sell the same motorcycle for the same original price. Dealer A advertises that the motorcycle is on sale for 7.5% off the original price. Dealer B advertises that it is reducing the motorcycle’s price by $599. When Bonnie compares the sale prices of the motorcycles in both dealers, she concludes that the sale prices are equal.
Let p represent the motorcycle’s original price.
Which equation models this situation?
0.075p = p − 599
0.925p = p + 599
0.075(p−599) = p
0.925p =
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Considering the definition of an equation, the equation 0.925p= p - 599 models the following situation: the sale prices of the motorcycles in both dealers are equal.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.Equation in this caseBeing "p" the motorcycle’s original price, you know that:
Dealer A advertises that the motorcycle is on sale for 7.5% off the original price → Sale price A= 100%×p - 7.5%×p → Sale price A= (100% - 7.5%)× p → Sale price A= 92.5%p → Sale Price A= 0.925p (expressed as decimals)Dealer B advertises that it is reducing the motorcycle’s price by $599. → Sale price B=p - 599If the sale prices are equal, the equation in this case is:
Sale price A= Sale price B
0.925p= p - 599
Finally, the equation 0.925p= p - 599 represent the situation.
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I need help finding the area I have a huge test tomorrow and I’m nervous.
The given figure can be divided into a rectangle and a triangle
The rectangle has the dimensions 10 m by 12 m
so, the area of the rectangle = 10 x 12 = 120 square meters
Now, we will find the area of the triangle:
Base = 12 - 10 1/4 = 1 3/4 m
Height = 15 - 10 = 5 m
Area = 1/2 x base x height =
[tex]\frac{1}{2}\cdot1\frac{3}{4}\cdot5=\frac{1}{2}\cdot\frac{7}{4}\cdot5=\frac{35}{8}=4\frac{3}{8}m^2[/tex]So, the total area =
[tex]120+4\frac{3}{8}=124\frac{3}{8}m^2[/tex]A city has a population of 250,000 people. Suppose that each year the population grows by 6%. What will the population be after 5 years?Use the calculator provided and round your answer to the nearest whole number.
The population after 5 years is approximately 337,465 people
Explanation:The population of the city is 250,000
Annual growth rate is 6%
The population after t years is:
[tex]P=P_oe^{rt}[/tex]After 5 years, t = 5 and the population becomes:
[tex]\begin{gathered} P=250000e^{\frac{6}{100}\times5} \\ \\ =250000e^{0.3} \\ \\ \approx337465 \end{gathered}[/tex]The population after 5 years is approximately 337,465 people
400 in savings for 20 years compounded 5% monthly
Answer:1,086
Step-by-step explanation: Initial Deposit
$400
Contributions
$0
Investment Time Span
20
Estimated Rate of Return
5.00%
Alicia has 10 paintings and wants to hang them side by side on the wall. How many ways can she hang the paintings?
The total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
What are permutation and combination?The variety of possible arrangements of a set is its permutation however order is important in permutations but not in combinations.
It is given that:
Alicia wants to place her ten paintings side by side on the wall.
We can get the factorial of 6 and use that knowledge to calculate how many ways there are to multiply 6 by multiplying it by all positive integers that are more than or equal to that number, in this case, 6.
Alicia can arrange her six paintings:
6! = 6x5x4x3x2x1
6! = 720
Thus, the total number of ways she can hang the painting is 720 after applying the concept of permutation and combination.
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When do you know you can stop the long division process when converting a fraction to a decimal number?
Division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.
What is Division?a division is a process of splitting a specific amount into equal parts.
We can stop the long division process when converting a fraction to a decimal number.
There can be two situations in converting fractions to decimals:
When division stops after a certain number of steps as the remainder becomes zero.
When division continues as there is a remainder after every step.
Hence When division stops after a certain number of steps as the remainder becomes zero and When division continues as there is a remainder after every step.
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Find the variance and standard deviation of the set of data to the nearest tenth (one decimal place){4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}
Hello there. To solve this question, we'll need to remember how to find the variance and standard deviation of a data set.
First, given a data set with values:
[tex]\mleft\lbrace x_1,x_2,x_{3,\ldots}\mright\rbrace[/tex]The variance can be calculated by the formula:
[tex]\sum ^{}_{}\frac{(x_i-\mu)^2}{n}[/tex]In this case, μ is the arithmetic mean of the data set and x_i is the i-th element of the data set.
The data set given is:
{4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 9}
To calculate the mean, we add every term and divide by the number of terms:
[tex]\frac{4+5+5+5+5+5+6+6+6+6+7+7+7+7+8+9}{16}=\frac{98}{16}=6.125[/tex]Now, we calculate the square of the difference between every term and mean.
Notice we have some repeated terms, we rewrite the sum like this:
[tex]\frac{(4-6.125)^2+5\cdot(5-6.125)^2+4\cdot(6-6.125)^2+4\cdot(7-6.125)^2+(8-6.125)^2+(9-6.125)^2}{16}[/tex]Adding the terms and calculating the squares, we have:
[tex]\begin{gathered} \frac{(-2.125)^2+5\cdot(-1.125)^2+4\cdot(-0.125)^2+4\cdot(0.875)^2+(1.875)^2+(2.875)^2}{16} \\ \\ \frac{4.515625+6.328125+0.0625+3.0625+3.515625+8.265625}{16} \\ \\ \frac{25.75}{16}\text{ = }1.609 \end{gathered}[/tex]This is the variance of the values of this data set. We can round it up to the nearest tenth as 1.6
The standard deviation is the square root of the variance.
Then, we calculate:
[tex]\sigma\text{ = }\sqrt[]{1.6}=1.268[/tex]Again, rounding it to the nearest tenth, we have 1.3;
The final answer is: The variance of this data set is 1.6 and its standard deviation is 1.3.
Solving the second question:
We apply the same formula. First, find the mean of the values:
[tex]\mu\text{ = }\frac{4.3+6.4+2.9+3.1+8.7+2.8+3.6+1.9+7.2}{9}=4.54[/tex]Now, as every term is different from each other, we apply the formula and get the following:
[tex]\frac{(4.3-4.54)^2+(6.4-4.54)^2+(2.9-4.54)^2+(3.1-4.54)^2+(8.7-4.54)^2+(2.8-4.54)^2+(3.6-4.54)^2+(1.9-4.54)^2+(7.2-4.54)^2}{9}[/tex]Calculating the difference, squaring it, adding the values and dividing by 9, we get:
Variance is approximately equal to 4.84
The Standard deviation is the square root of the variance, namely 2.2
What is the measure of a?
In the figure below, C D bisects ∠A C B
AB=B C
∠ B E C=90° and
∠D C E=42°
Find the measure of ∠A
The measure of "a" in the above-given right-angled triangle is 32°
What is a triangle?Note that a triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.
Key properties of a right-angled triangle to note are:
One angle is always 90° or a right angle.The side opposite angle of 90° is the hypotenuse.The hypotenuse is always the longest side.The sum of the other two interior angles is equal to 90°.The other two sides adjacent to the right angle are called base and perpendicular.The Sum of all three interior angles is equal to 180°To solve for "a" recall the following. It is given that:
AB = BC
∠BEC=90°
∠DCE=42°
Because CD bisects ∠ACB, Hence,
∠ACD = ∠DCB = x.............................1
∠DCE= ∠BCE + ∠DCB .....................2
= ∠BCE + x = 42° ................................3
To find ∠A, we use deductive reasoning to state:
∠A +∠E +∠ACD + ∠DCB + ∠BCE = 180° (Sum of Interior Angles)
Recall equation 1 hence, replacing ∠ACD with ∠DCB we have:
∠A +∠E +∠DCB + ∠DCB + ∠BCE = 180°
Recall equation 2, where ∠DCB = x, hence
∠A +∠E +x + x + ∠BCE = 180°
Recall equation three where 3 where ∠BCE + x = 42°, hence
∠A +∠E +x + (x + ∠BCE) = 180°
⇒ ∠A +∠E + x + 42° = 180°
Recall that ∠E = 90° so
⇒ ∠A +90° + x + 42° = 180° (Collect like terms)
⇒ ∠A + x = 180° - 90° - 42° = 48°; Hence
∠A + x = 48°...........................4
Recall that in Δ ABC
AB = BC (given)
Hence, ABC is an Isosceles triangle. Since this is true, then
⇒ ∠A = ∠ACB = 2x ...........................5 (Two angles opposite the equal sides are equal)
Substituting 2x in equation 5 into equation 4, we have
2x + x = 48°
3x = 48
x = 48/3
x = 16°
Recall that
∠A = 2x...........equation 5, hence,
∠A = 2 * 16
∠A = 32°
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A manufacturer knows that their items have a lengths that are skewed right, with a mean of 17.6 inches, andstandard deviation of 3.3 inches.If 37 items are chosen at random, what is the probability that their mean length is greater than 18.9 inches?(Round answer to four decimal places)Question Help: D VideoSubmit Question
The probability is 0.9999
Explanation:Given that the mean is 17.6 inches
standard deviation is 3.3/37 = 0.089
We have:
z(18.9)
[tex]z=\frac{x-\mu}{\sigma}[/tex][tex]\frac{18.9-17.6}{0.089}=14.6067[/tex]Now, we have
P(x > 18.9) = P(z > 14.6067)
= 0.9999
z(0.394) = 0.6532
2.2.30QuesticFind a quadratic function that includes the set of values below.(0,6), (2,8), (3,0)The equation of the parabola is y=0
The form of quadratic is:
[tex]y=ax^2+bx+c[/tex]Since (0,6) is given, we know c = 6, thus we have:
[tex]\begin{gathered} y=ax^2+bx+c \\ ax^2+bx+6 \end{gathered}[/tex]Point 2 is (2,8), replace x and y and find equation:
[tex]\begin{gathered} y=ax^2+bx+6 \\ 8=a(2)^2+b(2)+6 \\ 8-6=4a+2b \\ 4a+2b=2 \end{gathered}[/tex]Putting point 2 (3,0), we have:
[tex]\begin{gathered} y=ax^2+bx+6 \\ 0=a(3)^2+b(3)+6 \\ 9a+3b=-6 \end{gathered}[/tex]Solving the 2 simulatenous equations for a and b, we get:
a = -3
b = 7
Now u have all the values, a, b, and c.
Just put it in the general form of parabola :
[tex]y=-3x^2+7x+6[/tex]y = -3x^2 + 7x + 6
This diagram shows a pre-image A ABC, and its image, A A"B'C", after a series of transformations. Select from the drop-down menus to correctly complete the statements. C A A A ABC is X Choose. B to becomeA ABC'. Then A A'BC' is C C Choose.. to become A A"B"C" . Because the transformations are Choose... the pre- image and image are Choose..
The pre-image ABC in order to become the reflection at A'B'C' is reflected across the x-axis.
The pre-image ABC in order to become A"B"C" both are CONGRUENT, because the image and pre-image are BOTH RIGID.
**Please note that the rules for the transformation from ABC to A"B"C" were not provided**
. If g= 12 and h = 19, what is the value of3h(h-g)?A. 13B. 43C. 252D. 399
Solution
For this case we have the following:
g = 12 and h=19
And we want to find 3h(h-g)
If we replace we got:
3*19 (19-12) =57*7=399
Then the answer would be:
D. 399