The range is the set of all the values of y.
In coordinate form (x,y) the second number is the value of y
So, for the function:
Which function represents the value of the car after t years?
Given:
The value of car = $ 21000.
Rate of depreciation = 15 %.
Depreciation is an exponential decay function.
Consider the exponential decay function.
[tex]f(x)=a(1-r)^t[/tex]where a is the initial value and r is the rate of percentage.
Substitute a=21000 and r=15 %, we get
[tex]f(x)=21000(1-\frac{15}{100})^t^{}[/tex][tex]f(x)=21000(\frac{100}{100}-\frac{15}{100})^t[/tex][tex]f(x)=21000(\frac{100-15}{100})^t[/tex][tex]f(x)=21000(\frac{85}{100})^t[/tex][tex]f(x)=21000(0.85)^t[/tex]The function that represents the value of the car after t years is
[tex]f(x)=21000(0.85)^t[/tex]Convert the polar equation to a rectangular equation. Then use a rectangular coordinate system to graph the rectangular equation.
Answer:
Step-by-step explanation:
7. Which of the following algebraicrepresentations would result in an enlargement?A. (x, y)=(x, y)B. (3x, 3y)+(x,y)C. (x, y)=(x, y)D. (x, y)=(5x,y)
we know that
Enlargement means increase
If you enlarge a figure is the same that you multiply by a scale factor the dimensions of the figure
Verify each options
In the option A the scale factor is 2/3
so the scale factor is less than 1
so
Is not an elnlargement
Is a reduction
In the option B we have a reduction
In the option C
The scale factor is 3/2
3/2=1.5
1.5 is greater than 1
so
we have an enlargement
In the option D
the scale factor is different for x and y
so
is not an enlargement
The answer is the option C
A book sold 42,500 copies in its first month of release. Suppose this represents 7.9% of the number of copies sold to date. How many copies have been sold to date?Round your answer to the nearest whole number.
Given:
A book sold 42,500 copies in its first month of release. Suppose this represents 7.9% of the number of copies sold to date.
Required:
Total number of copies sold to date.
Explanation:
42500 is just 7.9% of total copies
we need to find total copies
for this
take x number of total copies
[tex]\begin{gathered} x*\frac{7.9}{100}=42500 \\ \\ x=537974.68\approx537975 \end{gathered}[/tex]Final answer:
Total number of copies is 537975
An experiment is performed where a 5-color spinner is spun and then a 3-color spinner is spun. the possible outcomes for each event are red (R) blue (B) yellow (Y) green (G) and violet (V) for the 5-color spinner and red (R) blue (B) yellow (Y) for the 3-color spinner. identify the sample space for this experiment
For the 5-color spinner, we have :
red (R), blue (B), yellow (Y), green (G) and violet (V)
For the 3-color spinner, we have :
red (R), blue (B), and yellow (Y)
The sample space for this experiment is the combination of these two spinners.
Example, red for the 5-color spinner then blue for the 3-color spinner (RB)
another one is yellow for the 5-color spinner and red for the 3-color spinner (YR)
Listing down all the events/sample spaces
{RR, RB, RY, BR, BB, BY, YR, YB, YY, GR, GB, GY, VR, VB, VY}
To what width should mason set his compass when constructing segment FG?
The width that Mason should set his compass when constructing segment FG is A. The distance from B to E.
What is a segment?A segment is a portion of a line, curve, or solid figure that is cut off by an intersecting line, plane, or plane, particularly one that lies between a chord and an arc of a circle.
Width
FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.
Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option A.
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Audrey is also tying ribbons into bows. Audrey sees the same 7 1/2 feet of ribbon measured out and says "Since my bows are bigger than Lura's, that's only enough for me to make 2 1/4 bows." How much ribbon does Audrey use in each bow?
[tex]\begin{gathered} 7\frac{1}{2}=\frac{15}{2} \\ \\ 2\frac{1}{4}=\frac{9}{4} \\ \\ \text{ Now, since she needs 15/2 to 9/4, then she needs} \\ \\ \frac{\frac{15}{2}}{\frac{9}{4}}=\frac{60}{18}=\frac{30}{9}=\frac{10}{3} \\ \\ \text{she needs 3}\frac{1}{3}\text{ to make 1 bow!} \end{gathered}[/tex]
For each inequality, determine if each r value make the inequality true or false.Select the correct choice from each row.
Okay, here we have this:
Considering the provided inequality, we are going to determine the values that make it true and those that make it false, so we obtain the following:
We will first solve for x:
[tex]\begin{gathered} 5x<2 \\ x<\frac{2}{5} \\ x<0.4 \end{gathered}[/tex]First option X=0: Since 0 is less than 0.4 then the option is true.
Second option X=-1: Since -1 is less than 0.4 then the option is true.
Third option X=1: Since 1 is greater than 0.4, then the option is false.
Fourth option X=100: Since 100 is greater than 0.4, then the option is false.
If n=21, ¯x (x-bar)=39, and s=8, find the margin of error at a 90% confidence levelGive your answer to two decimal places.
Given
[tex]\begin{gathered} n=21 \\ \bar{x}=39 \\ s=8 \\ C.I=90\text{\%=1.645} \end{gathered}[/tex]Explanation
The margin of error formula is given as;
[tex]M.E=z_{\frac{a}{2}}\times\frac{s}{\sqrt{n}}[/tex]Therefore, we will have;
[tex]\begin{gathered} M.E=1.645\times\frac{8}{\sqrt{21}} \\ M.E=2.87 \\ \end{gathered}[/tex]Answer: 2.87
6 2/3 x 2 1/4Just confused
start my multipliying the outside number to the numerator
[tex](\frac{12}{3})\cdot(\frac{2}{4})[/tex]simplify the fractions
[tex](4)\cdot(\frac{1}{2})[/tex]apply the multiplication like this
[tex]\frac{a}{b}\cdot\frac{c}{d}=\frac{cd}{bd}[/tex][tex](4)\cdot(\frac{1}{2})=\frac{4}{2}[/tex]SImplify
[tex](4)\cdot(\frac{1}{2})=\frac{4}{2}=2[/tex]I was bad at math in school and I want to get better
Given, the dimensions of 3 rooms
For each room, we will find the area which is the product of the dimensions
Room 1: 4.5 meters by 3 meters ⇒ Area of room 1 = 4.5x3 = 13.5 m²
Room2: 2 meters by 1.5 meters ⇒Area of room 2 = 2x1.5 = 3 m²
Romm3: 4 meters by 2 meters ⇒Area of room 3 = 4x2 = 8 m²
Total area = 13.5 + 3 + 8 = 24.5 m²
So, the answer is Total area = 24.5 m²
May I please get help with this problem for I am confused and tried multiple times
Given:
Radius, r = 7.5 in
Cost of lead = $0.36 per in³
Let's determine how much it will cost to make one ball.
The perimeter of a rectangle is 85 feet.The length of the rectangle is 2(x+16) andthe width is 3x - 1. What is the length of therectangle?A- 45.75 feetB- 36.6 feetC- 55 feetD- 23.3 feet
The perimeter of a rectangle is 85 feet. Therefore the perimeter is expressed as;
[tex]\begin{gathered} P=2(L+W) \\ P=2(2\lbrack x+16\rbrack+\lbrack3x-1\rbrack) \\ P=2(2x+32+3x-1) \\ P=4x+64+6x-2 \\ \text{Where the perimeter is 85, you now have} \\ 85=4x+6x+64-2 \\ \text{Collect like terms, and you have} \\ 85-64+2=4x+6x \\ 23=10x \\ \text{Divide both sides by 10} \\ 2.3=x \\ \text{The length of the triangle is therefore;} \\ L=2(x+16) \\ L=2(2.3+16) \\ L=2(18.3) \\ L=36.6ft \end{gathered}[/tex]The correct option is B; 36.6 feet
A store bought a rabbit for $40.19 and sold it for $111.01. What was the markup percentage? Round your answer to the nearest tenth.
we know that
Markup is the difference between a product's selling price and cost as a percentage of the cost
so
In this problem
$40.19 -------> represent tyhe 100%
the difference is -------> 111.01-40.19=$70.82
Applying proportion
Find the percentage
100%/$40.19=x/70.82
x=70.82(100%/$40.19)
x=176.21%
the answer is 176.21%
Find the perimeter of a square that has a side that is 4.5 meters long.A. 4.5 metersB. 9 metersC. 13.5 metersD. 18 meters
The square has all four sides equal therefore the perimeter is four times the length of any side of the square.
[tex]P=4L[/tex]In this case, we have that all four sides are equal to 4.5. Then, L=4.5.
Using the perimeter formula:
[tex]P=4(4.5meters)[/tex][tex]P=18\text{meters}[/tex]Hence, the perimeter is equal to 18 meters. The correct answer is
option D.
3. Box A is 2 centimeters high, 3 centimeters wide, and 5 centimeters long. It can hold 40 grams of clay. a. Box B has twice the height, three times the width, and the same length as the first box. How many grams of clay can it hold?b. Box C has double the length, width, and height of the original box. How many grams of clay can it hold? Explain your thinking.c. By changing just one dimension of box A, design a box that can hold 80 grams of clay.
Explanation
In this question, the boxes can hold a particular amount of clay. This implies that the volume of the box is what would contain the grams of clay.
To find the volume of any of the boxes, we will use the formula below;
[tex]\text{Volume=length x width x height}[/tex]Therefore, the volume of box A is;
[tex]\text{Volume of box A =2 x 3 x 5}=30\operatorname{cm}[/tex]Part A
Since Box B has twice the height, three times the width, and the same length as the first box;
This would give the dimensions of box B as;
[tex]\begin{gathered} \text{length}=5\operatorname{cm} \\ \text{width}=3\times3=9\operatorname{cm} \\ \text{height}=2\times2=4\operatorname{cm} \end{gathered}[/tex]Therefore the volume of the second box is
[tex]\text{Volume of the second box = 5 x 9 x 4 = 180}[/tex]Hence,
[tex]\begin{gathered} \text{Volume of box A = 30cm}^3;\text{ Amount of clay = 40g} \\ \text{Therefore, amount of clay in box B is }\frac{180\times40}{30}=240\text{grams} \end{gathered}[/tex]Answer A
[tex]240\text{ grams}[/tex]Part B
Box C has double the length, width, and height of the original box. This gives the dimension as;
[tex]\begin{gathered} \text{length }=\text{ 5 x 2=10cm} \\ wid\text{th }=3\times2=6\operatorname{cm} \\ Height=2\times2=4\operatorname{cm} \\ \end{gathered}[/tex]Therefore the volume of box C is
[tex]\text{Volume of Box c=10 x 6 x 4=240 cm}^3[/tex]Hence, the amount of clay in box c is
[tex]\begin{gathered} \text{Volume of box A = 30cm}^3;\text{ Amount of clay = 40g} \\ \text{Therefore amount of clay in box C is }\frac{240\times40}{30}=320\text{grams} \end{gathered}[/tex]Answer B
[tex]320\text{ grams}[/tex]The idea behind the solutions is to use direct proportion to find the missing values. This implies that an increase in the volume of the box would lead to a corresponding increase in the amount of clay the box can hold.
Part C
We can design a box that can hold 80 grams of clay If we double the height of box A.
Therefore the length becomes
[tex]New\text{ length = 2 x 3 =6cm}[/tex]Which equation represents a line which is parallel to the line given
start by writing the equation in standard form
[tex]y=-2x-8[/tex]two lines are parallel when both of them have the same slope.
then the correct equation parallel to the line is
[tex]y=-2x-4[/tex]Ms. Reed goes to the gym 5 times a week. Each time she goes, she runs 2.5 miles on thetreadmill and then she uses the elliptical machine. She exercises for a total of 50 miles eachweek. How many miles does she complete on the elliptical each day?
In a week(5 days) she completes = 50 miles
In a week ,at treadmill she runs 5x 2.5 miles= 12.5 miles
Then she spends in elliptical machine 50 - 12.5= 37.5 miles in a week
So then
in a day she spends 37.5/5 = 7.5 miles
ANSWER is 7.5 miles in elliptical machine,by day
Simplify the following expression. cos2x +cos2x cot2x. Show all work for full credit.
The on simplification we got {sin2xcos2x + cos2x² }sin2x.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
Here, the trigonometric function is given as :
f(x) = cos2x +cos2x cot2x
now, we have to simply it,
also, we known that :
cotθ = cosθ/sinθ
Now,
f(x) = cos2x +cos2x cot2x
f(x) = cos2x +cos2x (cos2x/sin2x )
f(x) = cos2x + (cos2x)²/sin2x
f(x) = {sin2xcos2x + cos2x² }sin2x
Therefore, the on simplification we got {sin2xcos2x + cos2x² }sin2x.
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an expression is shown below √18+√2which statement is true about the expression A) it is rational and equal to 3B) it is rational and equal to 4C) it is rational and equal to 3√2D) it is rational and equal to 4√2
EXPLANATION
Given the expression √18+√2, the statement that is true about the expression is the following:
It is an irrational number an equal to 4√2
2 2/3 * 3/4 answer that
We are given the following expression
[tex]2\frac{2}{3}\cdot\frac{3}{4}[/tex]Firstly, we have to convert the mixed fraction into a simple fraction.
[tex]\frac{2\cdot3+2}{3}=\frac{6+2}{3}=\frac{8}{3}[/tex]Now we can simply multiply the two fractions together as
[tex]undefined[/tex]the employees of a company were surveyed on questions regarding their educational background ( college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is?
Number employees N = 600
Then
Probability of Single + College degree = ?
Probability of single S = 100/600 = 1/6
Probability of College graduate G = 400/600 = 2/3
So then probability of both S and G is
Prob Single or Graduate = 1/6 + 2/3 = 1/6 + 4/6 = 5/6
. = 0.833
Then answer is
Probability of Single or Graduate = 5/6= 0.8333
Is also 83.33%
which graph shows the dilation image of rectangle ABCD with the center of dilation at the origin and a scale factor of 1/3
To dilate an image with the dilation center at the origin, you have to multiply the coordinates of each vertex by the dilation factor k, you can write the rule as:
[tex](x,y)\to(kx,ky)[/tex]• If the dilation factor is greater than 1, ,k > 1,, then the dilation will be an ,enlargement,, and the resulting shape will be greater than the original.
,• If the dilation factor is less than 1, ,k < 1,, then the dilation will be a reduction, and the resulting shape will be ,smaller ,than the original.
The rectangle ABCD was dilated using a scale factor k=1/3.
The scale factor is less than one, so the dilation will be a reduction and the image will be smaller than the preimage.
To determine the dilation you can calculate it, first determine the coordinates of each vertex of rectangle ABCD
A(-3,0)
B(0,-3)
C(3,0)
D(0,3)
Next, multiply each coordinate by the scale factor to determine the coordinates of the dilated rectangle A'B'C'D'
A(-3,0) → A'(1*3*(-3),1/3*0)=A'(-1,0)
B(0,-3) → B'(1/3*0,1/3*(-3))=B'(0,-1)
C(3,0) → C'(1/3*3,1/3*0)=C'(1,0)
D(0,3) → D'(1/3*0,1/3*3)=D'(0,1)
So the coordinates of the rectangle A'B'C'D' are
A'(-1,0)
B'(0,-1)
C'(1,0)
D'(0,1)
And the graph that corresponds to a dilation using scale factor 1/3 of the given quadrilateral is the second one (the smaller image).
The cone of the volcano has a height of 402 meters and a diameter of 434 meters. Find the volume of thecone. Round your answer to the nearest hundred thousand. Use 3.14 for .The volume of the cone is aboutm3
The volume of a cone with height h and radius r is given by the formula:
[tex]V=\pi r^2\frac{h}{3}[/tex]Since the volcano has a heihgt of 402 meters, then h=402m. Since the radius is half the diameter and the diameter of the volcano is 434 meters, then r=217m. Substitute those values, using 3.14 for the constant π:
[tex]\begin{gathered} V=3.14\times(217m)^2\times\frac{402m}{3} \\ =3.14\times47089m^2\times134m \\ =19,813,167.64m^3 \end{gathered}[/tex]To the nearest hundred thousand, then:
[tex]V=19,800,000m^3[/tex]i need help super bad
For this problem we use the propeties of log functions and get:
[tex]\log _{b\text{ }}2+log_b3=log_b(2\cdot3)=\log _b6[/tex]is 3.2% or 32% bigger
If we write 3.2% and 32% in their decimal form, we have the following:
[tex]\begin{gathered} 3.2\text{ \%=}\frac{3.2}{100}=0.032 \\ 32\text{ \%=}\frac{32}{100}=0.32 \end{gathered}[/tex]as we can see,32% is bigger than 3.2%
2. The polynomial, p(x) (seen below), is 9th degree. A. Create a table of values that have the x-intercepts of p(x) in the first column and their multiplicities in the second column.B. Write an equation for p(x).
Roots Multiplicity
The multiplicity of a root affects the shape of the graph of a polynomial as follows:
* If the root has odd multiplicity (1, 3, 5, etc), the graph will cross the x-axis at the root.
* If the root has even multiplicity (2,4,6, etc), the graph will touch the x-axis but won't cross it.
As a rule for both cases, when the multiplicity increases, the graph flattens more and more near the root.
With all of the above into consideration, we can see the graph has 3 distinct roots at x=-1, x=1, and x=3 respectively.
The root at x=-1 has an even multiplicity and its shape is steep.
The root at x=1 has an even multiplicity and its shape is more flattened than the other root.
The root at x=2 crosses the x-axis, thus it has odd multiplicity.
A.
Considering the polynomial is of degree 9, the roots and their multiplicities are:
x-intercept multiplicity
-1 2
1 4
2 3
B.
The equation for p(x) is:
[tex]p(x)=a(x+1)^2(x-1)^4(x-2)^3[/tex]The value of a will be determined by the approximate values shown in the graph. For example, for x=0, p(0)=5, thus:
[tex]p(0)=a(0+1)^2(0-1)^4(0-2)^3=a(1)(1)(-8)=5[/tex]Solving for a, we have a = -5/8
Now the final equation of the polynomial is:
[tex]p(x)=-\frac{5}{8}(x+1)^2(x-1)^4(x-2)^3[/tex]write an expression for double five then add 26 I want to see if I'm right or not
The expression would be;
[tex](2\text{ x 5)+26}[/tex]The parenthesis is very important in order not to distort the correct order of operation of the signs.
A cube has an edge of 3 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.
The volume of a cube is defined as
[tex]\begin{gathered} V_{\text{cube}}=s^3 \\ \text{where} \\ s\text{ is the edge of the cube} \end{gathered}[/tex]Then we can write it as a function of m as
[tex]\begin{gathered} V(m)=s^3_{} \\ \\ \text{Since }s\text{ increases at a rate of }2\text{ feet per minute then} \\ s=3+2m \end{gathered}[/tex]We can now rewrite it as
[tex]\begin{gathered} V(m)=s^3 \\ \text{substitute }s=3+2m \\ \\ V(m)=(3+2m)^3 \end{gathered}[/tex]need help with this problem drop down 2: 1, 2, 3
Given,
The equation is
[tex]2xy+3x+2[/tex]To find: Identify the polynomial.
Solution:
The given polynomial is trinomial which has three terms 2xy, 3x, and 2.
The degree of the polynomial is 2. Because in the first term there are two variables.
Thus, the polynomial is a trinomial with degree 2.
