The width of a rectangle is 3/4 its length.
[tex]w=\frac{3}{4}l[/tex]The perimeter of the rectangle is 420 ft.
Recall that the perimeter of a rectangle is given by
[tex]P=2(w+l)[/tex]Let us substitute the value of the given perimeter and the width
[tex]\begin{gathered} P=2(w+l) \\ 420=2(\frac{3}{4}l+l) \end{gathered}[/tex]Now simplify and solve for length
[tex]\begin{gathered} 420=2(\frac{3}{4}l+l) \\ 420=\frac{3}{2}l+2l \\ 420=3.5l \\ l=\frac{420}{3.5} \\ l=120\: ft \end{gathered}[/tex]Therefore, the length of the rectangle is 120 feet.
3 4. Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio. (Lesson 2-1) (A.) The ratio of kids to pizzas is 7 : 3. B.) The ratio of pizzas to kids is 3 to 7. The ratio of kids to pizzas is 3: 7. (D. The ratio of pizzas to kids is 7 to 3. E. For every 7 kids, there need to be 3 pizzas.
The statements in (A), (B), (E) are correct and satisfy the conditions in question.
What is ratio and proportion?
Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. Because b is not equal to 0, the ratio establishes the link between two quantities such as a:b.
Given, for every 7 kids, pizzas needed = 3 --(iii)
Therefore, for every 1 kid, pizza needed = (3/7)
Thus, for every x kids, pizza needed = (3/7)x
Again, ratio of pizzas to kids is = 3:7 --(i)
Also, the ratio of kids to pizza is = 7:3 --(ii)
From (A), using (ii), the statement in (A) is correct.
From (B), using (ii), the statement in (B) is correct.
From (C), using (i), the statement in (C) is incorrect.
From (D), using (i), the statement in (D) is incorrect.
From (E), using (iii), the statement in (E) is correct.
Thus, the statements in (A), (B), (E) are correct and satisfy the conditions in question.
To learn more about this, tap on the link below:
https://brainly.com/question/12024093
#SPJ9
polynomials - diving polynomialssimplify the following expression with divisionbare minimum of steps
A third friend wants to offer Rebecca andSteve some of the animal models she hasalready made. The model she has of thegiant squid is 5 inches tall. Using thesame scale (2 in:5ft), how tall would thegiant squid be in real life?
From the present question, it is said that the scale of a model is equal to:
[tex]e=\frac{2in}{5ft}[/tex]It means that the ratio of the size of the model and the real size of the giant squid must be always this same value. It was given that the size of the model is 5 in. Because we don't know the size of the real-life giant squid, we will use it as x. From this, we can write the following relation:
[tex]\frac{5in}{x}=\frac{2in}{5ft}[/tex]Now, we just need to isolate x in the present relation to find how tall would be a giant squid in real life.
[tex]\begin{gathered} \to2in\times x=5in\times5ft \\ x=\frac{5in\times5ft}{2in}=\frac{25}{2}ft=12.5ft \end{gathered}[/tex]From the solution developed above, we conclude that the real-life giant squid would be 12.5 ft tall.
what is the factored form of his expression ? 2x^3+5x^2+6x+15
The given expression is:
[tex]2x^3+5x^2+6x+15[/tex]It is required to write the expression in factored form.
[tex]\begin{gathered} \text{ Factor out }x^2\text{ in the first two terms of the expression:} \\ x^2(2x+5)+6x+15 \end{gathered}[/tex]
Next, factor out 3 in the last two terms of the expression:
[tex]x^2(2x+5)+3(2x+5)[/tex]Factor out the binomial 2x+5 in the expression:
[tex](2x+5)(x^2+3)[/tex]The expression in factored form is (2x+5)(x²+3).From the given information. Write the recursive and explicit functions for each geometric sequence. Please use these terms. recursive f(1) = first term, f(n) = pattern*f(n-1). what is the 1st term and pattern? explicit is y = pattern^x * 0 term. work backwards to find 0 term
We know that a geometric sequence is given by:
[tex]f(n)=f(1)r^{n-1}[/tex]where r is the common ratio of the sequence.
For this sequence we have that the common ratio is r=2, this comes from the fact that in the first day we have 6 dots, for the second day we have twelve and for the third day we have 24. We also notice that the first term is:
[tex]f(1)=8[/tex]Therefore the sequence is given by:
[tex]f(n)=8(2)^{n-1}[/tex]Now, to find the zeoth term we plug n=0 in the sequence above, therefore the zeroth term is:
[tex]\begin{gathered} f(0)=8(2)^{0-1} \\ f(0)=8(2)^{-1} \\ f(0)=4 \end{gathered}[/tex]Use the graph shown to the right to find each of the following
The x intercept is the value of x at the point where the curve touches the x axis of the graph. Looking at the graph,
x intercept = - 1
It is written as (- 1, 0)
The zeros of the quadratic function is the same as the x intercept. Since the curve touches the x axis at only x = - 1, the zeros would be
x = - 1 twice
(f o g)(x) = x(g o f)(x) = xwrite both domains in interval notation
the fact that both functions are polynomial of degree 1 we get that the domain and range of both functions are the real numbers. In intervalo notation this is:
[tex]\begin{gathered} \text{domain:}(-\infty,\infty) \\ \text{range:}(-\infty,\infty) \end{gathered}[/tex]15=g/7 what does g equal to
Answer:
g = 105
Explanation:
We want to find the value of g if
[tex]15=\frac{g}{7}[/tex]We multiply both sides of the equation by 7
[tex]\begin{gathered} 15\times7=\frac{g}{7}\times7 \\ \\ 105=g \end{gathered}[/tex]Therefore, the value of g is 105
Answer:
[tex]15=g/7[/tex]
We can get the value of g by multiplying the denominator, which in this case is 7.
So,
[tex]g = 15 x 7\\ g=105[/tex]
The probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, what is the probability that two or more of them will fail the test
If the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
The probability of failing a test = 0.115
Total number of people = 12
We have to find the probability that two or more of them will fail the test
We know the binomial distribution
P(X≥2) = 1 - P(X<2)
= 1 - P(X=0) - P(X=1)
P(X≥2)= 1 - [tex](12C_{0}) (0.115^0)(1-0.115)^{12}[/tex] - [tex](12C_{1}) (0.115^1)(1-0.115)^{11}[/tex]
= 0.41
Hence, if the probability of failing a test is 0.115 if you consider a group of 12 people taking a test on a given day, then the probability that two or more of them will fail the test is 0.41
Learn more about probability here
brainly.com/question/11234923
#SPJ1
In the circle below, if the measure of arc ACB = 260 °, find the measure of < B.
Given:
There is a figure given in the question as below
Required:
If
[tex]arcACB=260\degree[/tex]than find the value of angle B
Explanation:
Value of arcADB is
[tex]arcADB=360\degree-arcACB=360\degree-260\degree=100\degree[/tex]Now to find the angle B
[tex]\angle B=\frac{1}{2}arcADB=\frac{1}{2}*100=50\degree[/tex]Final answer:
a
f(x)=x^6+10x^4 - 11x^2
You can notice that the given function is symmetric respect to the y-axis.
It means that the value of the function for both x and -x is the same:
[tex]f(-x)=f(x)[/tex]This is the characteristic of a even function.
Hence, the answer is B
The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5
Use the trapezoidal approximation to estimate he distance the turtle traveled from 0 to 10 seconds.
we have that
The trapezoidal approximation is equal to
[tex]A=\frac{1}{2}\cdot\lbrack f(a)+f(b)\lbrack\cdot(b-a)[/tex]where
a=0
b=10
f(a)=f(0)=0.05
f(b)=f(10)=0.043
substitute given values
[tex]\begin{gathered} A=\frac{1}{2}\cdot\lbrack0.05+0.043\lbrack\cdot(10-0) \\ A=0.465\text{ m} \end{gathered}[/tex]therefore
the answer is 0.465 meterswhat is the answer to 850x+40(x)
ANSWER
854x
EXPLANATION
We have that:
850x + 40(x)
First, expand the bracket:
850x + 40x
Because the two terms are of the same kind (terms of x) we can add them up:
850x + 4x = 854x
That is the answer.
Take a look at the graph below. In the text box provided, describe to the best of yourability the following characteristics of the graph:Domain & RangeIs it a function?InterceptsMaximum/Minimum• Increasing/Decreasing intervals
we know that
The domain is the set of all possible values of x and the range is the set of all possible values of y
so
In this problem
The domain is the interval {-6,5}
[tex]-6\leq x\leq5[/tex]The range is the interval {-2,1}
[tex]-2\leq y\leq1[/tex]Intercepts
we have
x-intercepts (values of x when the value of y is equal to zero)
x=-5,x=0 and x=3
y-intercepts (values of y when the value of x is equal to zero)
y=0
Maximum value y=1
Minimum value y=-2
Increasing intervals
{-6,4}, {2,3}
Decreasing intervals
{-1,2} and {3,5}
how many seconds does it take until the ball hits the ground ?
Given:
The quadratic model of the ball is given as:
[tex]h(t)=-16t^2+104t+56[/tex]Required:
Find the time when it takes to hit the ground.
Explanation:
When the ball hits the ground then h(t)=0.
[tex]\begin{gathered} -16t^2+104t+56=0 \\ -8(2t^2-13t-7)=0 \\ 2t^2-13t-7=0 \end{gathered}[/tex]Solve the quadratic equation by using the middle term splitting method.
[tex]\begin{gathered} 2t^2-14t+t-7=0 \\ 2t(t-7)+1(t-7)=0 \\ (t-7)(2t+1)=0 \\ t=7,-\frac{1}{2} \end{gathered}[/tex]Since time can not be negative.
So t = 7 sec
Final Answer:
The ball will take 7 sec to hits the ground.
The long-distance calls made by South Africans are normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes for 1500 south Africans what is the expected number of callers whose calls last less than 15 minutes?
The question provides the following parameters:
[tex]\begin{gathered} \mu=16.3 \\ \sigma=4.2 \end{gathered}[/tex]For 15 minutes, the z-score is calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]At x = 15:
[tex]z=\frac{15-16.3}{4.2}=-0.3[/tex]The probability is calculated using the formula:
[tex]P(X<15)=Pr(z<-0.3)=Pr(z<0)-Pr(0From tables, we have:[tex]\begin{gathered} Pr(z<0)=0.5 \\ Pr(0Therefore, the probability is given to be:[tex]\begin{gathered} P(X<15)=0.5-0.1179 \\ P(X<15)=0.38 \end{gathered}[/tex]The expected number of callers will be calculated using the formula:
[tex]\begin{gathered} E=xP(x) \\ At\text{ }x=1500 \\ E=1500\times0.38 \\ E=570 \end{gathered}[/tex]Therefore, the expected number of callers whose calls last less than 15 minutes is 570 callers.
the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours
Length of screwdriver = 0.75
Length of road = 18cm
Number of screws that can be placed on a road
[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]If triangle JKL = triangle TUV , which of the following can you NOT conclude as being true? __ ___JK = TU
If two triangles are said to be congruent, then they must have equal side lengths and equal angle measures.
See a sketch of triangles JKL and TUV below:
As shown in the sketch above:
- The side JK is equal in length as with the side TU
- The angle L is equal in measure as with the angle V
- The side LJ is equal in length as with the side VT
- The angle K is equal in measure as with the angle U
Therefore, we can NOT conclude that the angle J is equal in measure as with the angle V: Option B
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the Equation.
Answer: y=80+2x
Step-by-step explanation:
In y=mx+b format the answer is y=80+2x
In a survey of 200 college students it is found that:61 like cooking32 like reading73 like video games19 like both cooking and reading23 like cooking and video games92 like reading or video games6 like all 3 hobbiesa. How many do not like any of these hobbiesb how many like reading onlyc how many like reading and video gamesd how many do not like cooking or video games
Given:
The number of total students = 200
The number of students like cooking = 61
The number of students who like reading = 32
The number of students who like both cooking and reading= 19
The number of students who like video games = 73
The number of students who like cooking and video games= 23
The number of students who like reading and video games = 92
The number of students who like all 3 hobbies = 6
Required:
(a)
I need help with the work question Find area of regular polygon.Round to nearest tenth
Given:
The number of sides in a given polygon is n = 5.
The length of each side is s = 8
The length of the apothem is a = 5.5
To find:
The area of the regular polygon
Explanation:
The formula of the area of the regular polygon is,
[tex]\begin{gathered} A=\frac{1}{2}\times n\times s\times a \\ A=\frac{1}{2}\times5\times8\times5.5 \\ A=110\text{ units}^2 \end{gathered}[/tex]Thus, the area of the given regular polygon is 110 square units.
Final answer:
The area of the regular polygon is 110 square units.
7. Julie has $250 to plan a party. There is a one-time fee of $175 to reserve a room. It also cost $1.25 perperson for food and drinks. What is the maximum number of people that can come to the dance?
Julie has $250 to plan the party.
The room costs $175 to reserve plus $1.25 per person for food and drinks.
Let "x" represent the number of people she can invite, you can express the total cost for the party as follows:
[tex]175+1.25x\leq250[/tex]From this expression, we can determine the number of people she can invite, without exceeding the $250 budget.
The first step is to pass 175 to the right side of the expression by applying the opposite operation "-175" to both sides of it:
[tex]\begin{gathered} 175-175+1.25x\leq250-175 \\ 1.25x\leq75 \end{gathered}[/tex]Next, divide both sides of the equation by 1.25 to reach the value of x:
[tex]\begin{gathered} \frac{1.25x}{1.25}\leq\frac{75}{1.25} \\ x\leq60 \end{gathered}[/tex]She can invite up to 60 people to the party
16. Solve for "x".
a. 6
b. 100
c. 36
Answer:
A. 6
Step-by-step explanation:
Using the Pythagorean theorem which states that: Hypotenus² = Opposite² + Adjacent²
Where: hypotenus = 10, opposite = x, adjacent = 8
So:
[tex] {10}^{2} = {x}^{2} + {8}^{2} [/tex]
Solving for x
[tex]100 = {x}^{2} + 64[/tex]
Collect like terms to make x the subject of formula
[tex]100 - 64 = {x}^{2} →36 = {x}^{2} [/tex]
[tex]36 = {x}^{2} ⟹ {x}^{2} = 36[/tex]
square root both sides of the equation to find the value of x
[tex] \sqrt{ {x}^{2} } = \sqrt{36} →x = 6[/tex]
Therefore: Option A is correct
Use inductive reasoning to find a pattern then make a reasonable conjecture for the next three items in the pattern p g q h r I
Consider the first, third, and fifth terms of the sequence: p,q,r; these are consecutive letters starting with p.
Similarly, as for the second, fourth, and sixth terms: g,h, i; these are consecutive letters starting with g.
Thus, the seventh term has to be the letter that follows r; this is, s.
Analogously, the eighth and ninth terms are
[tex]\begin{gathered} \text{ eighth}\to\text{letter that follows i}\to j \\ \text{ ninth}\to\text{ letter that follows s}\to t \end{gathered}[/tex]Thus, the missing terms are: s, j, and t.
Write the number 0.2 in the form a over b using integers to show that it is a rational number
Hello! Let's solve this exercise:
We have some ways to show it, look:
[tex]\begin{gathered} \frac{a}{b}=0.2 \\ \\ \frac{1}{5}=0.2 \\ \\ \frac{2}{10}=0.2 \end{gathered}[/tex]So, as it can be written as a fraction, is a rational number.
Help with number one a and b is both parts of number one
Solving the operation_
We are given two figures that represent a garden. We are asked to determine its areas.
The shape of figure A is a rectangle of 9 ft by 12 ft. The area of a rectangle is the product of its dimensions therefore, we have:
[tex]A_A=\left(9ft\right)\left(12ft\right)[/tex]Solving the operations:
[tex]A_A=108ft^2[/tex]The shape of figure B is a circle of radius 5ft. The area of a circle is:
[tex]A_B=\pi r^2[/tex]Where "r" is the radius. Substituting we get:
[tex]A_B=\pi\left(5ft\right)^2[/tex][tex]A_B=25\pi ft^2[/tex]In decimal notation, the area is:
[tex]A_B=78.54ft^2[/tex]drag and drop the matching inequality from the left into the box on the right
The first problem is modeled by the following inequality:
[tex]40+5x\ge95-4x[/tex]The second problem is represented by
[tex]95+4x<40+5x[/tex]The third problem is represented by
[tex]95-4x<40+5x[/tex]Observe that, "spending" refers to subtraction, "earnings" refers to addition. Also, the variables represent time. Additionally, "less than" is expressed as "<", "as much as or more than" is expressed as >=.
Two ships left a port at the same time. Onetravelled due north and the other due eastat average speeds of 25.5 km/h and 20.8 km/h,respectively. Find their distance apart
Given:
Two ships left a port at the same time.
One travelled due north at an average speed of 25.5 km/h
And the other ship was due east at average speeds of 20.8 km/h
We will find their distance apart using the Pythagorean theorem.
The distance = Speed * Time
Let the time = t
So, the distance of the first ship = 25.5t
And the distance of the second ship = 20.8t
So, the distance between the ships (d) will be as follows:
[tex]\begin{gathered} d^2=(25.5t)^2+(20.8t)^2 \\ d^2=1082.89t^2 \\ \\ d=\sqrt{1082.89t^2} \\ d=32.907t \end{gathered}[/tex]So, the answer will be:
The distance in terms of time = 32.907t
We will find the distance when t = hours
So, distance = 164.54 km
How do you determine a relation is function on a GRAPH?
To Determine: How to determine a relation is function on a GRAPH
In other to achieve this, we will use the vertical test
If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function
Check the image below for a better clarification
With the use of the vertical line test, the graph in OPTION C and OPTION D are functions and the graph in OPTION A and B are not functions
In summary, you determine a relation is a function on a graph by using a vertical line test