Given:
One custodian cleans a suite of offices in 8 hours.
So, the rate of the custodian to clean the office = 1/8
When a second worker is asked to join the regular custodian, the job takes only 4 hours.
So, the rate of both custodians = 1/4
Let the rate of the second custodian = x
So,
[tex]\frac{1}{8}+x=\frac{1}{4}[/tex]Solve for x:
[tex]x=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}[/tex]So, the rate of the second custodian = 1/8
This means he will take 8 hours to clean the office alone
So, the answer will be:
The second worker can do the same job alone in 8 hours.
The n = 3 row of Pascal's Triangle has the following entries: 1, 3, 3, and 1TrueFalse
Ok, in the Pascal Triangle, the element in the row number n and column number p is given by:
So let's take n=3 and find all the entries of that row. We are going to use 0, 1, 2 and 3 as possible values for p.
For p=0:
[tex]\frac{3!}{0!(3-0)!}=\frac{6}{1\cdot3!}=\frac{6}{6}=1[/tex]For p=1:
[tex]\frac{3!}{1!\cdot(3-1)!}=\frac{6}{2!}=\frac{6}{2}=3[/tex]For p=2:
[tex]\frac{3!}{2!\cdot(3-2)!}=\frac{6}{2\cdot1!}=\frac{6}{2}=3[/tex]And for p=3:
[tex]\frac{3!}{3!\cdot(3-3)!}=\frac{3!}{3!\cdot0!}=\frac{3!}{3!}=1[/tex]So the four entries in the third row of Pascal's Triangle are 1, 3, 3 and 1 so the statement is true.
Dertermine weshrer the fraction is 9 over 12 and 9 over 6 are equivalent
9/12 and 6/8 are equivalent fractions
Explanation:
[tex]\begin{gathered} \text{Given fractions:} \\ \frac{9}{12}\text{ and }\frac{6}{8} \end{gathered}[/tex][tex]\begin{gathered} \text{let's break down the fraction:} \\ \text{for }\frac{9}{12}\text{ we'll divide both numerator and denominator by 3} \\ \frac{9\div3}{12\div3}\text{ = }\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} \text{for }\frac{6}{8},\text{ we will divide both numerator and denominator by 2} \\ \frac{6\div2}{8\div2}\text{ = }\frac{3}{4} \end{gathered}[/tex]We can see when break down both fractions, their simplest term is the same.
Hence, 9/12 and 6/8 are equivalent fractions
I'm confused about how to solve this using the special right triangles method
ANSWER:
[tex]x=4\sqrt[]{2}[/tex]STEP-BY-STEP EXPLANATION:
We can calculate the value of x, by means of the trigonometric function sine
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \text{opposite = }4 \\ \theta\text{ =60\degree} \\ \text{hypotenuse = x} \end{gathered}[/tex]Replacing:
[tex]\begin{gathered} \sin 45=\frac{4}{x} \\ x=\frac{4}{\sin45} \\ \sin 45=\frac{\sqrt[]{2}}{2} \\ x=\frac{4}{\frac{\sqrt[]{2}}{2}} \\ x=\frac{8}{\sqrt[]{2}}\cdot\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ x=\frac{8\sqrt[]{2}}{2} \\ x=4\sqrt[]{2} \end{gathered}[/tex]The school band brought cheese and pepperoni pizzas in ratio represented in the tape diagram for their end of year party.
ANSWER
2 pepperoni pizzas
EXPLANATION
From the tape diagram, the ratio of cheese pizzas to pepperoni pizzas is:
3 : 1.
They bought 6 cheese pizzas.
Let the number of pepperoni pizzas be x.
So, by comparison, we have that:
3 : 1 = 6 : x
or
[tex]\begin{gathered} \frac{3}{1}\text{ = }\frac{6}{x} \\ \text{Cross multiply to find x:} \\ 3\cdot\text{ x = 6 }\cdot\text{ 1} \\ \text{Divide through by 3:} \\ x\text{ = }\frac{6}{3} \\ x\text{ = 2} \end{gathered}[/tex]Therefore, they bought 2 pepperoni pizzas.
Which is a solution toy ⩽ -2x + 1 (-3,8)(2,-2)(0,5)(-1, 3)
To find the right solution, we just have to evaluate the expression with each given point
(-3,8)[tex]\begin{gathered} 8\leq-2\cdot(-3)+1 \\ 8\leq6+1 \\ 8\leq7 \end{gathered}[/tex](2,-2)[tex]\begin{gathered} -2\leq-2\cdot2+1 \\ -2\leq-4+1 \\ -2\leq-3 \end{gathered}[/tex](0,5)[tex]\begin{gathered} 5\leq-2\cdot0+1 \\ 5\leq1 \end{gathered}[/tex](-1,3)[tex]\begin{gathered} 3\leq-2\cdot(-1)+1 \\ 3\leq2+1 \\ 3\leq3 \end{gathered}[/tex]As you can observe, the last choice satisfies the inequality.
Hence, the answer is (-1,3).which equation doesn't represent a linear function? [tex]a. \: y = \frac{1}{2}x \: + 2[/tex][tex]b . \: y = {x}^{2} \\ c . \: y = 2x \\ d. \: y = x - 2[/tex]
The general equation for linear equation is,
[tex]y=mx+b[/tex]The equation y = x^2, consist of power term on the variable x. So this equation does not follow the linear equation and is a quadratic equation.
Thus, equation y = x^2 is not a linear function. Option B is correct answer.
The table below shows the cost of mailing packages that weigh different amounts. Cost of Mailing Packages Package Weight (ounces) Cost Up to 1.00 $1.17 1.01 to 2.00 $1.34 2.01 to 3.00 $1.51 3.01 to 4.00 $1.68 4.01 to 5.00 $1.85 If the cost continues to increase as shown in the table, how much will it cost to mail a package that weighs exactly 11 ounces? F $2.87 G $4.87 H $3.04 J $5.87
which of the following are accurate of the distribution below
A: An outlier is a point that is an exception compared to the distribution of the data. In a histogram, it would appear as a bar away from the distribution with a lower height. We can't observe this in this distribution.
A do not apply.
B: A cluster is an accumulation of point in a certain interval. The interval given is 0 to 39. In the distribution, there are no points for this interval, so no cluster.
B do not apply.
Since A and B do not apply, C do apply.
Find the equation of the line containing the point (3,5) and having slope: 4A. y=4x+24B. y=4x+7C. y=4x+17D. y=4x
Data
Point = (3, 5)
slope = 4
Equation of a line
y - y1 = m(x - x1)
m = slope = 4
x1 = 3
y1 = 5
Substitution
y - 5 = 4(x - 3)
Simplifying
y - 5 = 4x - 12
y = 4x - 12 + 5
Result
y = 4x - 7
What is the value of t? 76 T
Those are vertical angles, which are two non-adjacent angles formed by intersecting two lines. The intersection forms two pair of vertical angles. So:
[tex]m\angle t=76[/tex]identify the correct trigonometry formula to use to solve for the given anglea. sin-¹(1.41)b. cos-¹(1.41)c. sin-¹(.71)d. tan-¹(.71)
The definition of arctan is opposit side by adjesent side.
[tex]\begin{gathered} \text{Angle}=tan^{-1}(\frac{Oppos\text{ side}}{\text{Adjesent side}}) \\ =\tan ^{-1}(\frac{34}{48}) \\ =\tan ^{-1}(0.71) \end{gathered}[/tex]Thus, the correct option is option d.
FIRST ANSWER WILL GET BRAILIEST! AND 50 PTS!
Which division problem is represented with this model?
Responses
1/5÷6
1/6÷2
1/2÷5
1/5÷2
Answer: Choice B
1/6÷2
Reason:
We have 6 slips of paper side by side. Shading one of those 6 represents the fraction 1/6.
Then split that shaded piece of paper in half as shown in the diagram. The blue region in that diagram represents 1/6÷2 which simplifies fully to 1/12.
If you were to do this to all 6 pieces of paper, then we'd have 2*6 = 12 smaller pieces. One of which is shaded, so that explains how we get 1/12.
In other words:
[tex]\frac{1}{6} \div 2 = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}[/tex]
The graph shows the distance Kendrick walks in different lengths of time.How many kilometers does Kendrick walk per hour?5kilometersHow long does it take Kendrick to walk 111 kilometer?hours
Solution
For this case we can do this:
[tex]\frac{10-5}{2-1}=\frac{5\operatorname{km}}{hr}[/tex]5 kilometers
We have the following equation
Km = m*hours
hours= 1km/ (5km/hr) =0.2hr
The following figure shows the entire graph of a relationship.Does the graph represent a function?A.yesB.No
For the given graph to be a function, it must obey the vertical line test that is an element of the domain must not be marked to more than one element of the codomain.
Since all the domain of the functions has a unique co-domain, hence the entire graph of a relationship is a function.
Rewrite the product (15y)(4x) using the Commutative Property of Multiplication.(15x)(4y)19xy(4x)(15y)(4y)(15x)
Answer:
(4x)(15y)
Explanation:
The commutative property of multiplication says that
(a)(b) = (b)(a)
Where a and b are the factors. In this case, the factors are 15y and 4x, so
(15y)(4x) = (4x)(15y)
Therefore, the answer is
(4x)(15y)
For each of the following letters, find the equation for a polynomial function whose graph resembles the given letter: U, N, M, and W.
We are asked to determine polynomic functions which graph resembles the given letters.
For the letter U we will use a second-degree polynomial, which means a polynomial of the form:
[tex]y=ax^2+b[/tex]Is we take the values of "a" and "b" to be:
[tex]\begin{gathered} a=1 \\ b=0 \end{gathered}[/tex]We get the function:
[tex]y=x{}^2[/tex]The graph is the following:
Now, to determine a function that resembles the letter N we will use a polynomic function of third-degree, this means a function of the form:
[tex]y=ax^3+bx^2+cx+d[/tex]We will use the following values for the constants:
[tex]\begin{gathered} a=\frac{1}{4} \\ \\ b=1 \\ c=0 \\ d=0 \end{gathered}[/tex]Substituting we get:
[tex]y=\frac{1}{4}x{}^3+x^2[/tex]The graph of the function is:
To determine a polynomial that resembles the letter "m" we will use a polynomial that has 3 x-intercepts and the end-points are pointing down. This means that the function is of the form:
[tex]y=-(x-a)(x-b)^2(x-c)[/tex]The middle term has a square because we want the middle intercept to be tangent to the x-axis. Giving values to the constant we get:
[tex]y=-(x+1)(x-1)^2(x-3)[/tex]The graph of the function is:
Now, we determine a function that resembles the letter "W". We will use a polynomial with two intercepts that are tangent to the x-axis and the end behavior must be upwards. Therefore, the function must be of the form:
[tex]y=(x-a)^2(x-b)^2[/tex]We will use a = -1 and b = 1:
[tex]y=(x+1)^2(x-1)^2[/tex]The graph is:
Dan is a software salesman. His base salary is $2200, and he makes an additional $120 for every copy of History is Fun he sells.Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 23 copies of History is Fun.
We will have the following:
The equation in this case is:
[tex]P=120N+2200[/tex]So, if he sells 23 copies, he will make:
[tex]P(23)=120(23)+2200\Rightarrow P(23)=4960[/tex]So, he would make $4960.
The circle is inscribed in the square. Find the area of the shaded region.
We can solve this by calculating the area of the square and subtracting the area of the inscribed circle. The area of the square is:
[tex]Square=10\cdot10=100cm^2[/tex]The formula for the area of a circle is:
[tex]A=\pi r^2[/tex]The radius of the inscribed circle is half the length of the side of the square, then, the radius is r = 5 cm
[tex]Circle=\pi5^2=25\pi\text{ }cm^2[/tex]Now, we rest:
[tex]Square-Circle=100cm^2-25\pi cm^2\approx21.46cm^2[/tex]The answer is 21.46cm²
Are the pair of lines y = 1/3x - 1 and y = 3x parallel, perpendicular, or neither?
A line with slope m and y-intercept b has the following slope-intercept form equation:
[tex]y=mx+b[/tex]If two lines have the same slope, they are parallel. If they have slopes that are the negative reciprocal of each other, then they are perpendicular.
If none of the above cases happen, then they are neither parallel nor perpendicular.
The line y = (1/3)x - 1 has slope 1/3.
The line y = 3x has slope 3.
As we see, the slopes are different, so the lines are not parallel. Also, the negative reciprocal of 3 is -1/3, not 1/3.
Therefore, the given lines are neither parallel nor perpendicular.
solve y=f(x) for x. then find the inputs when the output is -3
Answer:
Given that,
[tex]f(x)=-7x-2[/tex]To find the inputs when the output is -3
that is, when f(x)=-3, to find the value of x
Put f(x)=-3 in the above equation we get,
[tex]-3=-7x-2[/tex][tex]-7x=-3+2[/tex][tex]\begin{gathered} -7x=-1 \\ x=\frac{1}{7} \end{gathered}[/tex]Answer is: x=1/7.
One sample t for means You want to know if the average customer rating fro your store is about a 7.0 on a 1-10 scale. Your collect a sample of 100 customers. Their average rating was 7.3, with a standard deviation of 2.0.
Given:
A sample of 100 customers.
The first day they go to Dreamy Delights. Jack buys a cone with 3.0 oz of frozen yogurt for $9.20. Ianbuys a cone with 5.75 oz of frozen yogurt for $16.95.It says to summarize the information in a table
To summarize the information in a table:
In the column # of ounces of frozen yogurt put in the first cell the 3.0 oz that Jack bought and in the second cell the 5.75 oz that Ian bought.
In the column total cost in dollars put in the first cell the $9.20 that Jack paid and in the second cell the $16.95 that Ian paid
What is the magnitude of the resultant vector of 8 meters North and 8 meters East displacement. Use the WRISd editor icon Vito answer this question. You canwrite using the pento right. Your drawing will be ttransfered to actural writing
In order to find the total displacement of a 8 meters north vector and a 8 meters east vector, we first need to know that these vectors forms a right angle (because the north and east directions forms a 90° angle).
So, to find the final displacement, we need to sum these vectors, and this sum can be calculated using the Pythagoras' theorem in the resultant triangle:
[tex]\begin{gathered} d^2=8^2+8^2 \\ d^2=64+64 \\ d^2=128 \\ d=\sqrt{128=8\sqrt{2=}}11.31 \end{gathered}[/tex]So the total displacement is 11.31 meters.
Find all values of j for which the quadratic equation has no real solutions.7x^2+9x+j=0Write your answer as an equality or inequality in terms of j.
The discriminant of a quadratic equation tells us whether there are two solutions, one solution or no real solutions and it is described as the part inside the root
[tex]D=b^2-4a\cdot c[/tex]the conditions are:
[tex]\begin{gathered} D>0;\text{ two real solutions } \\ D=0;\text{ one real solution} \\ D<0;\text{ no real solution} \end{gathered}[/tex]give values to a, b, and c, which are 7, 9, and j respectively.
using the third condition find the values for j that make the quadratic equation have no solution
[tex]\begin{gathered} 9^2-4\cdot7\cdot j<0 \\ \end{gathered}[/tex]solve the inequality
[tex]\begin{gathered} 81-28j<0 \\ -28j<-81 \\ 28j>81 \\ j>\frac{81}{28} \end{gathered}[/tex]Edward deposited 9,000 into a savings account 2years ago tthe simple interest is 2% how much money did edward earn in intrest
We just need to use the simple interest formula:
[tex]I=PV\cdot r\cdot t[/tex]Where:
I = Interest
PV = Principal or initial investment = 9000
r = interest rate = 0.02
t = time = 2
[tex]\begin{gathered} I=9000\times0.02\times2 \\ I=360 \end{gathered}[/tex]$360
62 - 12 ÷ 3 + (15-7)
62 - 12 ÷ 3 + (15-7)
First, solve the parenthesis:
62-12÷ 3 + 8
Then, solve the division:
62-4+8
Add And subtract
66
Leo is researching an electric bicycle. He finds this graph, which shows how much range, measured in kilometers, the bicycle gains based on charging time:Leo wants an equation he can use to find how many kilometers of range the bicycle gains (k) based on how many minutes it charges (t). Complete Leo's equation.
Equation of line in slope intercept form is
k = 4t is the equation which shows how many kilometers of range the bicycle gains (k) based on how many minutes it charges (t)
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The graph passes through (5, 20), (10, 40), (15, 60)
Slope =
[tex]\frac{40 -20}{10 - 5}\\\\\frac{20}{5}\\\\4[/tex]
Equation of line
k - 20 =4(t - 5)
k - 20 = 4t - 20
k = 4t
This is the equation which shows how many kilometers of range the bicycle gains (k) based on how many minutes it charges (t)
To learn more about equation of line in slope intercept form, refer to the link-
brainly.com/question/25514153
#SPJ1
Answer:
Step-by-step explanation:
k=4t
i know this because i just answered this question on khan
Suppose the main income of firms in the industry for a year is $80 million with a standard deviation of $13 million. If incomes for the industry are distributed normally what is the probability that a randomly selected firm will earn less than $96 million? Round your answer to four decimal places
Given that
The mean income of firms in the industry for a year is $80 million with a standard deviation of $13 million. and we have to find the probability that a randomly selected firm will earn less than $96 million.
Explanation -
We have to find the probability that a firm will earn less than $96 million.
The mean is $80 and the standard deviation is $13.
Then, it is written as
[tex]\begin{gathered} P(x<96)=P(z<\frac{96-80}{13}) \\ \\ The\text{ formula to find the z is \lparen here z is the z value\rparen} \\ z=\frac{x-\mu}{\sigma} \\ \mu\text{ is mean and }\sigma\text{ is the standard deviation.} \\ \\ P(<96)=P(z<\frac{16}{13})=P(z<1.2) \end{gathered}[/tex]The table to find the z value is
According to the z table, the value will be
[tex]\begin{gathered} P(x<96)=P(z<1.2)=0.8849 \\ P(x<96)=88.49\% \end{gathered}[/tex]Hence, 88.49% of the randomly selected firms will earn less than $96.
So the probability will be 0.8849.
Final answer -
The final answer is 0.8849 or 88.49%.The problem is:The area of a square picture frame is 55 square inches. Find the length of one side of the frame. explain.Part A. Part B To the nearest whole inch. To the nearest 10th of an inch
Part A
area = 55 in²
The area of a square is given by:
area = side x side
So
55 in² = side x side
55 in² = side²
Taking the square root of both sides of the equation we get:
√55 in² = side
7 in = side
Part B
side = 7.4 in
Solve the following quadratic equation using the quadratic formula in the picture: Problem: -3y^2 - 2y - 6 = 0
The given equation is,
[tex]-3y^2-2y-6=0[/tex]Here, a = -3, b = -2, c = -6. Therefore, y can be calculated as,
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{2\pm\sqrt[]{4-(4)(-3)(-6)}}{-6}=-\frac{1\pm\sqrt[]{-68}}{3} \\ =\frac{-1+\sqrt[]{68}}{3},\frac{-1-\sqrt[]{68}}{3} \end{gathered}[/tex]