step 1
$1,000 < $7,000
so
the tax rate is 15%
15%=15/100=0.15
0.15*1,000=$150
therefore
The answer is $150Find the volume of the rectangular prism.10 ft4 ft2 ft4 ft10 ft
Given data:
The given figure is shown.
The expression for the volume is,
[tex]\begin{gathered} V=(10\text{ ft)(4 ft)(2 ft)} \\ =80ft^3 \end{gathered}[/tex]Thus, the volume of the rectangular prism is 80 cubic-ft.
Colleen has 1/2 of a bag of popcorn left. She would like to give the rest of her popcorn to five of her friends. If each friend is given the same amount of popcorn what fraction of the original bag of popcorn will each friend get
Colleen has 1/2 of a bag of popcorn left.
She would like to give the rest of her popcorn to five of her friends.
Number of friends = 5
Each friend is given the same amount of popcorn
Divide the amount of poprcorn left by the number of Friends
Each friend will get = 1/2 divided by 5
[tex]\begin{gathered} \frac{1}{2}\text{ }\div5=\frac{1}{2}\times\frac{1}{5} \\ \frac{1}{2}\text{ }\div5=\frac{1}{10} \end{gathered}[/tex]Each friend will get = 1/10 of the bag
If possible, use deductive reasoning and the Law of Detachment to reach a conclusion from the statements. If you are on the basketball team, then you have practice on Thursday. You have practice on Thursday.
This problem is about deductive reasoning.
The given statements are
• If you are on the basketball team, then you have practice on Thursday.
,• You have practice on Thursday.
You can see these problems as consequences from a specific event. For example, the first statement is saying that "if" you are on the team, then you have practice on Thursday, this means that if you are not on the team, then you don't have practice on Thursday.
So, in the second statement is actually saying that you will have practice on Thursday, the question would be What does this mean?
Well, according to the first statement, if you have practice on Thursday that means you are on the basketball team.
First rewrite 10/21 and 4/9 so that they have a common denominator
Answer:
10/21=30/63
4/9=28/63
Step-by-step explanation:
Find the lcm (least common multiple) of 21 an 9, which is 63. Then divide 21 and 9 separately by 63. The multiply that number by the numerator.
Given: D is the midpoint of CE prove : DR = 1/2CE Reason bank simply Transitive property Division property Addition property Given Definition of midpoint Segment Addition postulate
SOLUTION
Statement1: Given a line segment
[tex]CE[/tex]Statement 2: Definition of Midpoint
D as the midpoint
Then we have
Statement 3: Segment addition postulate
[tex]\begin{gathered} CD+DE=CE \\ \text{ } \end{gathered}[/tex]Statement 4: simplify
[tex]CE=DE[/tex]Statement 5: Addition property
Then Adding DE to both sides
[tex]\begin{gathered} CD+DE=DE+DE \\ CD+DE=2DE \end{gathered}[/tex]Then from the diagram,
[tex]CD+DE=CE[/tex]We have
Statement 6: Transitive property
[tex]\begin{gathered} CE=CD+DE=2DE \\ \text{then } \\ CE=2DE \end{gathered}[/tex]statement 7: Division property
Divide both sides by 2
[tex]\begin{gathered} \frac{CE}{2}=\frac{2DE}{2} \\ \\ DE=\frac{1}{2}CE \end{gathered}[/tex]Therefore
DE=1/2 CE implies D is the midpoint of CE
Statement 1= Given
Statement2=Difine a midpoint
Statement 3=Segment addition postulate
statement 4=simplify
Statement5= Addition property
Statement 6=transitive property
Statement 7=Division property
use the Table and example((worth 20 points very easy))Holly is filing as a single taxpayer with a taxable income of $40,300.Find her federal taxes due.
We have to find the federal taxes that should pay Holly, a single taxpayer.
In the single table, we see that the taxes due will be given by
[tex]4,453.5+\frac{22}{100}\text{ of the amount above \$}38,700[/tex]The amount is $40,300, and applying the formula we obtain:
[tex]\begin{gathered} 4,453.5+\frac{22}{100}(40,300) \\ =4,453.5+8,866 \\ =13319.5 \end{gathered}[/tex]This means that the federal taxes due of Holly is $13,319.5.
Pythagorean Theorem:a? + b2 = c2 Re-write the formula solving for b?.
The Pythagorean Theorem states the following:
[tex]a^2+b^2=c^2[/tex]Where "c" represents the hypotenuse of the Right triangle (which is a triangle that has an angle that measures 90 degrees), and "b" and "c" are the legs of the triangle.
To rewrite the formula solving for "b", you can follow the steps shown below:
1. Apply the Subtraction property of Equality by subtracting a^2 from both sides of the equation:
[tex]\begin{gathered} a^2+b^2-(a^2)=c^2-(a^2) \\ b^2=c^2-a^2 \end{gathered}[/tex]2. Now you must apply square root to both sides of the equation:
[tex]\begin{gathered} \sqrt[]{b^2}=\sqrt[]{c^2-a^2} \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]Because remember that:
[tex]\sqrt[n]{m}^n=m[/tex]Therefore, the formula solved for "b", is:
[tex]b=\sqrt[]{c^2-a^2}[/tex]Explain in 5-7 sentences what type of triangles can be used with the sine/cosine/tangent ratios.
The Solution.
The triangle that can be used with sine, cosine, and tangent ratios must have the following characteristics:
1. The triangle must be a right-angled triangle.
2. The triangle must have one of its angles as 90 degrees.
3. Another angle must be indicated as the angle of interest.
4. At least two sides and an angle must be identified/represented with values.
5. The ratios under consideration can be used to find all the angles and all the sides.
y= -x^3+5x-2for this equation state the degreeleading coefficient # of real zeros# of imaginary zerosand the end behavior
1) The leading coefficient = -1
2) Real Zero
A real zero makes the function to be equal to zero
Hence
[tex]\begin{gathered} Afactorofy=-x^3+5x-2\text{ is} \\ x-2 \end{gathered}[/tex][tex]\frac{-x^3+5x-2}{(x-2)}[/tex][tex]=-x^2-2x+1[/tex]The zeroes are three in number
3) there
2. Write the mixed number -5(4/9) as a fraction in three different ways. Thenwrite the mixed number as a decimal.
Fraction #1
[tex]-5\frac{4}{9}[/tex]Fraction #2
[tex]-\frac{49}{9}[/tex]Fraction #3
[tex]-4\frac{13}{9}[/tex]Fraction #4
[tex]-3\frac{22}{9}[/tex]Decimal:
[tex]-5\frac{4}{9}\approx5.4444[/tex]Answer:
[tex]-5\frac{4}{9}[/tex]
[tex]-\frac{49}{9}[/tex]
[tex]-4\frac{13}{9}[/tex]
Decimal: 5.4444
I need help with this question please. Ignore the wording below. Fyi this is a part of a homework practice
So,
Given that the zeros of our polynomial function are:
[tex]3i,2,-4[/tex]We know that there are 2 real zeros, and 2 complex zeros. (3i and -3i).
So, what we're going to do to find the equation of this polynomial, is to multiply all zeros together, such that we obtain an expression that we can simplify. Like this:
[tex](x-2)(x+4)(x-3i)(x+3i)[/tex]Now, we're going to multiply and distribute:
[tex]\begin{gathered} (x^2+2x-8)(x^2+3xi-3xi-9i^2) \\ \to(x^2+2x-8)(x^2-9i^2) \end{gathered}[/tex]Remember that:
[tex]i=\sqrt[]{-1}\to i^2=-1[/tex]So, we can rewrite:
[tex](x^2+2x-8)(x^2+9)[/tex]Multiplying these terms, we got that:
[tex]\begin{gathered} (x^2+2x-8)(x^2+9) \\ \to x^4+9x^2+2x^3+18x-8x^2-72 \\ \to x^4+2x^3+x^2+18x-72 \end{gathered}[/tex]Therefore,
[tex]P(x)=x^4+2x^3+x^2+18x-72[/tex]How many per ounces and which circle do I need to choose
We are asked to determine the unit price of two different packages. The unit price is determined by dividing the price of an item over the quantity used to measure that item at the given price. In this case, the unit of measure is "ounce", therefore, we need to determine the price per ounce. The first unit price is determined by dividing the price of $3.19 for 11.5 ounces, like this:
[tex]P_1=\frac{3.19\text{ dollars}}{11.5\text{ ounces}}=0.28\text{ dollar/ounce}[/tex]Since we are told to round to the nearest cent we take the first two digits after the decimal point and we add 1 to the second digit if the third digit is equal to or greater than 5.
Now we use the same procedure to determine the second unit price:
[tex]P_2=\frac{7.98\text{ dollars}}{30.6\text{ ounces}}=0.26\text{ dollar/ounce}[/tex]Since the unit price for the 30.6 ounces package is less than the price for the 11.5 ounces package this means that the second package is a better buy.
a cuboid has a total surface area of 200cm^
it has a hight of 6
width of 10
length of (a)
what is the length of a
Answer:
2.5 unitsStep-by-step explanation:
The total surface area isS = 2*(ab + bc ac)GivenSides are 6, 10 and a Find the missing value200 = 2(6*10 + 6a + 10a)100 = 60 + 16a16a = 40a = 40/16a = 2.5what is 64 to the power of half
For the function, find the y-intercept of the graph of the function. f(x)=25x2−49
The y-intercept of a graph is the point at which it crosses the y-axis. This point can be found by replacing the variable "x" by 0 in the expression of the function. This is done below:
[tex]\begin{gathered} f(0)=25\cdot0^2-49 \\ f(0)=-49 \end{gathered}[/tex]The y-intercept of this function is the point (0, -49).
What is the absolute value of -4?A. -4B. 0.4C. 1/4D. 4
absolute value of -4 is 4.
The answer is option D.
p varies directly as q and inversely as r. kr kg A) p = B) p = g C) par = k D)p+q-r=k r
p varies directly as q and inversely as r. Thus we have
[tex]\begin{gathered} p\propto q\text{ and also} \\ p\propto\frac{1}{r} \end{gathered}[/tex]This also implies that;:
[tex]p\propto\frac{q}{r}[/tex]and
[tex]p=\frac{kq}{r}[/tex]The answer is option B
rewrite an equivalent expression for 84+96
Answer:
90 + 90
Step-by-step explanation:
How to write and expression in terms of x that represents the number of feet Lucas has traveled since they started walking .
SOLUTION.
We have been told that Lucas and Natalie walked the same distance, and that x is the number of feet Lucas traveled.
a. The expression for the number of feet Lucas has walked = x
b. Since Natalie walked the same distance as Lucas,
The expression for the number of feet Natalie has walked = x
c. The expression for the total number of feet Lucas and Natalie has walked
x + x = 2x
d. The expression for the distance between Natalie and Lucas is
210 - 2x
11 years ago, Sallie invested $21,000.00 into a savings account. She now has$27,064.00. What simple interest rate was her savings account earning? Assume theinterest rate has not changed since the account was opened.
Given:
Principal amount= $21000
Total amount = $27064
Time t=11 years
The simple interest rate is calculated as,
[tex]\begin{gathered} A=P(1+rt) \\ \frac{A}{P}=1+rt \\ rt=\frac{A}{P}-1 \\ r=\frac{1}{t}(\frac{A}{P}-1) \end{gathered}[/tex]Here,
[tex]\begin{gathered} A=27064,P=21000,t=11 \\ r=\frac{1}{t}(\frac{A}{P}-1) \\ r=\frac{1}{11}(\frac{27064}{21000}-1) \\ r=\frac{1}{11}\times\frac{6064}{21000} \\ r=0.02625108 \end{gathered}[/tex]Simple interest rate is,
[tex]\begin{gathered} R=0.02625108\times100 \\ R=2.6251\text{ \%} \end{gathered}[/tex]Answer: 2.6251 %
For which equation would x = 4 be a solution?28 – 5.25 x = 2.754.25 x + 7 = 244.25 x ÷ 8 = 97 + 3.25 x = 29
Given
The equations,
a) 28 – 5.25 x = 2.75
b) 4.25 x + 7 = 24
c) 4.25 x ÷ 8 = 9
d) 7 + 3.25 x = 29.
To find:
For which equation would x = 4 be a solution?
Explanation:
It is given that,
a)
[tex]28-5.25x=2.75[/tex]Put x=4,
[tex]\begin{gathered} \Rightarrow28-5.25(4)=2.75 \\ \Rightarrow28-21=2.75 \\ \Rightarrow7=2.75,\text{ which is a contradiction.} \end{gathered}[/tex]Hence 4 is not a solution of a) 28 – 5.25 x = 2.75.
b)
[tex]4.25x+7=24[/tex]Put x=4,
[tex]\begin{gathered} \Rightarrow4.25(4)+7=24 \\ \Rightarrow17+7=24 \\ \Rightarrow24=24 \end{gathered}[/tex]Hence, 4 is the solution of b) 4.25 x + 7 = 24.
Thus, the answer is option b).
Describe the end behavior f(x)=x^3-4x^2+7
The behavior of the function falls to the left and rises to the right.
Given function f(x)=x^3-4x^2+7,
Firstly identify the degree of the function which is :
3
Now identify the leading coefficient which is :
1
Now, we know that if the degree is odd then the function ends in opposite direction.
And also the leading coefficient is positive which leads to rise of the graph to the right.
By using the degree and leading coefficient we can determine the behavior of the function by using below statements ;
1. Even and Positive: Rises to the left and rises to the right.
2. Even and Negative: Falls to the left and falls to the right.
3. Odd and Positive: Falls to the left and rises to the right.
4. Odd and Negative: Rises to the left and falls to the right
So the behavior of the function falls to the left and rises to the right.
To know about more behavior https://brainly.com/question/15388254
#SPJ1
o MIDSEGMENT THEOREM 12)Triangle ABC has vertices A(-5,2), B(1,5) and C(1,-1). Determine the point of intersection of the medians, and state its coordinate
To determine the point of intersection of the medians and its cordinate:
Let O(x, y) be the centroid of the triangle.
The median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side. There are three medians in a triangle; and the medians of a triangle intersect at a point called the centroid.
The centroid of a triangle is gotten from the average of the x coordinates and the y coordinates of all the three vertices.
For Triangle ABC has vertices A (-5,2) B (1,5) C (1,-1) and centroid O(x, y).
Hence:
[tex]x=\frac{-5+1+1}{3}=-\frac{3}{3}=-1[/tex][tex]y=\frac{2+5+(-1)}{3}=\frac{7-1}{3}=\frac{6}{3}=2^{}[/tex]The centroid is at (-1, 2)
Hence the point of intersection and coordinate = (-1 , 2)
Mrs. Gomes found that 40% of students at her high school take chemistry. She randomly surveys 12 students. What is the probability that at most 4 students have taken chemistry? Round the answer to the nearest thousandth.READ ANSWERS!0.0080.4380.5620.665
If we don't allow to repeat a pick on the sample, than each student we pick will change the probability of picking the next one and, since we don't know the total number of students at her high school, we wouldn't be able to calculate this probability.
Thus, to calculate this with the provided information, we need to assume that we can repeat a student in the sample, that way the probability of picking a chemistry student will always be 40%.
So, with that assumption, we can use binomial probability to calculate the probability of picking at most from from that have taken chemistry on the 12 picked students.
Since we want at most 4, we have the consider the term of the binomial for which 0 students from chemistry were picked, the term for 1 from chesmitry, the term for 2, the term for 3 and the term for 4.
Let p be the probability of picking 1 student from chemistry, n be the total number of students picked and k be the number of students on those that are from chemistry. Then, each term will have the following:
[tex]B(k)=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}_{}[/tex]In this case, n is always 12 and p is always 0.4, so 1 - p is always 0.6.
k will vary from 0 to 4 and the total probability will be the sum of each term.
The term for 0 students from chemistry has k = 0, so:
[tex]B(0)=\frac{12!}{0!(12-0)!}(0.4)^0(0.6)^{12-0}=1\cdot1\cdot(0.6)^{12}=0.0021767\ldots[/tex]The term for 1 student from chemistry has k = 1, so:
[tex]B(1)=\frac{12!}{1!(12-1)!}(0.4)^1(0.6)^{12-1}=12\cdot0.4\cdot(0.6)^{11}=0.0174142\ldots[/tex]The term for 2 student from chemistry has k = 2, so:
[tex]B(2)=\frac{12!}{2!(12-2)!}(0.4)^2(0.6)^{12-2}=\frac{12\cdot11}{2}\cdot(0.4)^2\cdot(0.6)^{10}=0.0638522\ldots[/tex]The term for 3 student from chemistry has k = 3, so:
[tex]B(3)=\frac{12!}{3!(12-3)!}(0.4)^3(0.6)^{12-3}=\frac{12\cdot11\cdot10}{3\cdot2}\cdot(0.4)^3\cdot(0.6)^9=0.1418939\ldots[/tex]The term for 4 student from chemistry has k = 4, so:
[tex]B(4)=\frac{12!}{4!(12-4)!}(0.4)^4(0.6)^{12-4}=\frac{12\cdot11\cdot10\cdot9}{4\cdot3\cdot2}\cdot(0.4)^4\cdot(0.6)^8=0.2128409\ldots[/tex]So, the total probability will be the sum of all these term:
[tex]\begin{gathered} P=B(0)+B(1)+B(2)+B(3)+B(4) \\ P=0.0021767\ldots+0.0174142\ldots+0.0638522\ldots+0.1418939\ldots+0.2128409\ldots \\ P=0.4381782\ldots\approx0.438 \end{gathered}[/tex]So, the probability is approximately 0.438.
Can you help me turn these into an equations?1. Quadratic Function: Reflect across the y axis translate left 6 2. Cubic Function: vertical stretch factor of 2, translates right 6 and down 13. Cosine function: reflects across the x axis, translates left pie/4, vertical stretch factor of 6
Find (and classify) the critical points of the following function and determine if they are local max, local min, or neither: f(x) =x^4 - 2x^2
Solution:
Given:
[tex]f(x)=x^4-2x^2[/tex]To get the local maximum and minimum point, we differentiate the function twice.
[tex]\begin{gathered} f^{\prime}(x)=4x^3-4x \\ \\ To\text{ get the critical points, f'(x)=0} \\ 4x^3-4x=0 \\ \text{Factorizing,} \\ 4x(x^2-1)=0 \\ \text{Thus,} \\ (4x)(x-1)(x+1)=0 \\ \text{Hence, the critical points are;} \\ x=0,x=1,x=-1 \end{gathered}[/tex]To get the maximum and minimum points, we differentiate further,
[tex]\begin{gathered} f^{\prime}(x)=4x^3-4x \\ f^{\doubleprime}(x)=12x^2-4 \\ \\ \text{Inputting the critical points into f''(x),} \\ \text{when x = -1,} \\ f^{\doubleprime}(-1)=12(-1)^2-4=12-4=8 \\ S\text{ ince f''(x)>0, then this is a minimum point.} \\ x=-1\text{ is a minimum} \\ \\ \\ \text{when x = 1,} \\ f^{\doubleprime}(1)=12(1^2)-4=12-4=8 \\ S\text{ ince f''(x)>0, then this is a minimum point.} \\ x=1\text{ is a minimum} \\ \\ \text{when x = 0,} \\ f^{\doubleprime}(0)=12(0^2)-4=0-4=-4 \\ S\text{ ince f''(x)<0, then this is a maximum point.} \\ x=0\text{ is a maximum} \end{gathered}[/tex]Thus,
[tex]\begin{gathered} At\text{ x = 0,} \\ f(x)=x^4-2x^2 \\ f(0)=0^4-2(0^2)=0-0=0 \\ \\ \text{Hence, (0,0) is a local maximum} \\ \\ \\ At\text{ x = -1,} \\ f(x)=x^4-2x^2 \\ f(-1)=(-1)^4-2(-1)^2=1-2=-1 \\ \\ \text{Hence, (-1,-1) is a local minimum} \\ \\ \\ At\text{ x = 1,} \\ f(x)=x^4-2x^2 \\ f(1)=1^4-2(1^2) \\ f(1)=1-2=-1 \\ \\ \text{Hence, (1,-1) is a local minimum} \end{gathered}[/tex]The graph is as shown below;
Therefore,
The local minimum occurs at (-1,-1) and (1,-1)
The local maximum occurs at (0,0)
For which pair of functions is the vertex of g(x) 3 units to the right of the vertex of f(x)?
Answer: A.
[tex]f(x)=x^2\text{ and }g(x)=(x-3)^2[/tex]Explanation
Given:
[tex]f(x)=x^2[/tex]As we want to move the vertex 3 units to the right, this means we have to make a transformation on x (not y). Then, we have to make x = 3 when y = 0, meaning:
[tex]\begin{gathered} x=3 \\ x-3=0 \end{gathered}[/tex]Thus:
[tex]g(x)=(x-3)^2[/tex]We have to subtract 3 inside the parenthesis because if we add/subtract 3 outside, it would have an impact on y.
2. A line segment Shas endpoints (a, a) and (a, -a), for a + 0. Which of thefollowing transformations preserves the position of the line segment?F. Ry=a(S)H. Rx = o(S)G. Ry=x(S)J. Ry=0(S)
First the endpoints of this line segment are : (a, a) and (a, -a)
For a+0 the new endpoints will be :(a, a) and (a, -a) because only zero was added to each coordinate
The transformation that will retain these points will be;
Rx =0 (S) where you only add zero to the x,coordinate
which best describes the solutions for this system? y=3x-4 2y=2x+1infinitely many solution not a solution there one solution??
The equations are y = 3x - 4 and 2y = 2x +1.
If the graph of equation intersect each other at one point then there is one solution, if line lies on one another then there are infinitely many solution and if lines are parallel to each other then there is no solution.
Plot the equation on the graph.
From the graph, it can be observed the lines intersect each other at one point only lies in first quadrant, so there is one solution located in the first quadrant.
Identify the expressions and the value equivalent to 4 times 3 cubed. 3x 3* 4x3 108 243 4x3 x 3 x3 3 x 4 x 4x4 4 + 3 + 3 + 3
The expressions will be:
[tex]4\times3^3[/tex]and
[tex]4\times3\times3\times3[/tex]and
[tex]108[/tex]