Up: How Many?If the hexagon is one whole, how many one-thirds (3s) are in 12/3?Explain how the model shows the problem and thesolution.How many 1/3 are in 1 and 2/3?
so we have to divide 5/3 by 1/3
[tex]\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}\cdot\frac{3}{1}=5[/tex]so there are 5 1/3's in 1 2/3
Simplify the rational expression. 16b2+40b+25/4b+5 Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).
Given the rational expression;
[tex]\frac{16b^2+40b+25}{4b+5}[/tex]We shall begin by factorizing the numerator as follows;
[tex]\begin{gathered} 16b^2+40b+25 \\ \text{Note that the coefficient of b}^2\text{ is greater than 1} \\ \text{Therefore we shall multiply the constant by the coefficient of b}^2 \\ \text{That gives us;} \\ 16\times25=400 \\ We\text{ shall now use the sum-product method, which is;} \\ \text{The factors of the constant 400} \\ S\text{hall also sum up to the coefficient of b } \\ \text{These factors are +20, +20} \\ \text{Therefore;} \\ 16b^2+40b+25\text{ becomes;} \\ 16b^2+20b+20b+25 \\ \text{Factorize by groups of two and we'll have} \\ 4b(4b+5)+5(4b+5) \\ \text{This becomes;} \\ (4b+5)(4b+5) \end{gathered}[/tex]The rational expression now becomes;
[tex]\frac{(4b+5)(4b+5)}{(4b+5)}[/tex]m varies directly with n. Determine m when n=8 and k= 16
We have that m varies directly with n, then:
[tex]m=kn[/tex]now, if n =8 and k=16, then:
[tex]\begin{gathered} m=(16)(8)=128 \\ m=128 \end{gathered}[/tex]therefore, m = 128
Part A: Solve the following equation: 8 + 2(x - 3) = 3x - 3
We need to solve the following equation:
[tex]8+2(x-3)=3x-3[/tex]First we distribute the product in the left side:
[tex]\begin{gathered} 8+2(x-3)=3x-3 \\ 8+2x-6=3x-3 \end{gathered}[/tex]Then we pass all the terms with an x to the left side and all the constant terms to right side:
[tex]\begin{gathered} 8+2x-6=3x-3 \\ 2x-3x=6-3-8 \\ -x=-5 \\ x=5 \end{gathered}[/tex]So the answer is x=5.
A line has the equationFind the equation of a parallelline passing through (3,2).Y=1/3x-5
Answer:
y = 1/3x + 1
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be founded using the following:
[tex]y-y_1=m(x-x_1)[/tex]If the line is parallel to y = 1/3x - 5, the line will have the same slope. Since the slope of y = 1/3x - 5 is 1/3 because it is the value beside the x, the slope of our line is also 1/3
Then, replacing m by 1/3 and (x1, y1) by (3, 2), we get:
[tex]y-2=\frac{1}{3}(x-3)[/tex]Finally, solve for y:
[tex]\begin{gathered} y-2=\frac{1}{3}(x)-\frac{1}{3}(3) \\ y-2=\frac{1}{3}x-1 \\ y-2+2=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]Therefore, the equation of the line is:
y = 1/3x + 1
A university class has 29 students: 14 are psychology majors, 9 are history majors, and 6 are nursing majors. The professor is planning to select two of thestudents for a demonstration. The first student will be selected at random, and then the second student will be selected at random from the remaining students.What is the probability that the first student selected is a psychology majorand the second student is a history major?Do not round your intermediate computations. Round your final answer to three decimal places.
from the question given:
14 psychology majors
9 history major
6 nursing major
there are 29 total students
The probability that thr first student selected at random is a psychology major is 14/29
The probability that the second student selected at random from the remaining students is a history major is 9/28
The probability that the first student chosen is psychology major a a
You need to ride an average of at least 35 miles per day for five consecutive days toqualify for a cross-country biking expedition. The distances (in miles) of your rides in thefirst four days are 45, 33, 27, and 26. What distances on the fifth day will allow you toqualify for the competition?
We are to maintain a constant mean distance of ( d-avg ) to qualify for the cross-country biking expedition.
The qualification for the expedition is to rirde an average distance of:
[tex]d_{avg}\text{ }\ge\text{ 35 miles each for 5 consecutive day }[/tex]We are already on target for 4 days. For which we covered a distance ( d ) for each day:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Day 1:}}\text{ 45 miles} \\ \text{\textcolor{#FF7968}{Day 2:}}\text{ 33 miles} \\ \text{\textcolor{#FF7968}{Day 3:}}\text{ 27 miles} \\ \text{\textcolor{#FF7968}{Day 4: }}\text{26 miles} \end{gathered}[/tex]We are to project how much distance we must cover atleast on the fifth day ( Day 5 ) so that we can qualify for the expedition. The only condition for qualifying is given in terms of mean distance traveled over 5 days.
The mean value of the distance travelled over ( N ) days is expressed mathematically as follows:
[tex]d_{avg}\text{ =}\sum ^N_{i\mathop=1}\frac{d_i}{N}[/tex]Where,
[tex]\begin{gathered} d_i\colon Dis\tan ce\text{ travelled on ith day} \\ N\colon\text{ The total number of days in consideration} \end{gathered}[/tex]We have the data available for the distance travelled for each day ( di ) and the total number of days in consideration ( N = 5 days ). We will go ahead and used the standard mean formula:
[tex]d_{avg}\text{ = }\frac{d_1+d_2+d_3+d_4+d_5}{5}[/tex]Then we will apply the qualifying condtion to cover atleast 35 miles for each day for the course of 5 days.
[tex]\frac{45+33+27+26+d_5}{5}\ge\text{ 35}[/tex]Then we will solve the above inequality for Day 5 - (d5) as follows:
[tex]\begin{gathered} d_5+131\ge\text{ 35}\cdot5 \\ d_5\ge\text{ 175 - 131} \\ \textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}} \end{gathered}[/tex]The result of the above manipulation shows that we must cover a distance of 44 miles on the 5th day so we can qualify for the expedition! So the range of distances that we should cover atleast to qualify is:
[tex]\textcolor{#FF7968}{d_5\ge}\text{\textcolor{#FF7968}{ 44 miles}}[/tex]All covered distances greater than or equal to 44 miles will get us qualified for the competition!
A right rectangular prism has length 3 3 ft, width 13 ft, and height 23 ft. 1 You use cubes with fractional edge length ft to find the volume. How many cubes are there for each 3 of the length, width, and height of the prism? Find the volume. How many cubes are there for each of the length, width, and height of the prism? cubes, the width has The length has cubes, and the height has cubes.
First, we need to convert the mixed numbers into fractions
[tex]3\frac{1}{3}=\frac{3\cdot3+1}{3}=\frac{10}{3}\text{ ft}[/tex][tex]1\frac{1}{3}=\frac{1\cdot3+1}{3}=\frac{4}{3}\text{ ft}[/tex][tex]2\frac{1}{3}=\frac{2\cdot3+1}{3}=\frac{7}{3}\text{ ft}[/tex]To find how many cubes fit on the length, we need to divide 10/3 by 1/3, as follows:
[tex]\frac{\frac{10}{3}}{\frac{1}{3}}=\frac{10}{3}\cdot3=10[/tex]To find how many cubes fit on the width, we need to divide 4/3 by 1/3, as follows:
[tex]\frac{\frac{4}{3}}{\frac{1}{3}}=\frac{4}{3}\cdot3=4[/tex]To find how many cubes fit on the height, we need to divide 7/3 by 1/3, as follows:
[tex]\frac{\frac{7}{3}}{\frac{1}{3}}=\frac{7}{3}\cdot3=7[/tex]Then, the length has 10 cubes, the width has 4 cubes, and the height has 7 cubes.
The volume of each cube is:
[tex]V=a^3=(\frac{1}{3})^3=\frac{1}{27}ft^3[/tex]The number of cubes that fit in the rectangular prism is: 10x4x7 = 280. Therefore, the volume of the prism is
[tex]280\cdot\frac{1}{27}=\frac{270+10}{27}=\frac{270}{27}+\frac{10}{27}=10\frac{10}{27}ft^3[/tex]17) A father gave $500 to his two sons. He gave x dollars to one son. Which of the following expressions correctly shows the amount he gave to the other son . *
Total amount given by father = $500
He gave an amount of $x to his first son
then father will left with $500- $x amount
So, He will pay an amount of (500-x) to his other son
Answer : d) 500 - x
On a coordinate plane, point J is located at (-1, units, from point J to point K? 2) and point K is located at (8, 10). What is the distance, in Enter your answer in the space provided.
The expression for the distance between two coordinates are express as :
[tex]\text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substitute the values of the coordinates:
[tex]\begin{gathered} (x_1,y_1)=(-1,-2) \\ (x_2,y_2)=(8,10) \end{gathered}[/tex][tex]\begin{gathered} \text{ Distance=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Distance}=\sqrt[]{(8-(-1))^2+(10-(-2))^2} \\ \text{Distance}=\sqrt[]{(8+1)^2+(10+2)^2} \\ \text{Distance}=\sqrt[]{9^2+12^2} \\ \text{Distance}=\sqrt[]{81+144} \\ \text{Distance}=\sqrt[]{225} \\ \text{Distance}=15\text{ unit} \end{gathered}[/tex]So, distance between two points (-1,-2) & (8,10) is 15
Answer : Distance between two points (-1,-2) & (8,10) is 15.
Think about a real-life situation that would create a real-world system of inequalities. Write the situation as a word problem, and provide the system of inequalities.
Word Problem
Dalion goes to the store to get the new promo ice-cream that costs $2 per scoop. The total amount of money with Dalion is $30.
Write an inequality for the number of scoops that Dalion can get.
Let the number of scoops that Dalion can get be x.
If Dalion gets x scoops of ice cream, the price = x × 2 = 2x dollars
But we know that the cost of x scoops of ice cream cannot exceed the total amount of money with Dalion, that is, $30.
So,
2x dollars has to be less than or equal to $30. In mathematical terms, the equation is
2x ≤ 30
Hope this Helps!!!
Not understanding what they want and how they get to it
SOLUTION
The image below shows the solution
what is the sum(add) of 2.31 and .21
what is the sum(add) of 2.31 and .21
we have
2.31+0.21=2.52
Remember that
2.31=2+0.31
so
2+0.31+0.21=2+0.52=2.52
Hello did i do the graph right ? i needed to only plot my image
Given:-
[tex](10,10),(1,5),(10,7),(5,7),(1,8),(7,7)[/tex]To find:-
Plot the given points.
The graph of the given points is,
11) Find the Constant of proportionality (k) from the equations below.
Direct variation is in the form
y = kx
a y = 7x the constant k is 7
b y = 12x the constant k is 12
c y = 1/2x the constant k is 1/2
d y = -4x the constant k is -4
2) 58, 67, 44, 72, 51, 42, 60, 46, 69Minimum :Maximum :Q,Q2:Q,
Given the following data set:
58, 67, 44, 72, 51, 42, 60, 46, 69
First, we will arrange the data in order from the least to the greatest.
42, 44, 46, 51, 58, 60, 67, 69, 72
The minimum = 42
The maximum = 72
Q2 = the median of the data = the number that in the middle
As the set has 9 data, so, the median will be the data number 4
Q2 = 58
To find Q1 and Q3 , the data will be divided into two equal groups
(42, 44, 46, 51), 58, (60, 67, 69, 72)
Q1 = the median of the first group = (44+46)/2 = 45
Q3 = the median of the second group = (67+69)/2 = 68
So, the answer will be:
Minimum : 42
Maximum : 72
Q1 : 45
Q2 : 58
Q3 : 68
1. Which one does not belong *O y=(x+4)(x-6)O y=2x²-88-24O y=x2+5x-25O y=x®+3x?-10x-24
y=x®+3x?-10x-24
Given the fact that all options but the last one are quadratic equations. The only one that does not belong is the last one y=x®+3x?-10x-24 for this one resembles a linear equation whose highest coefficient is above 3x.
For:
a) y=(x+4)(x-6) is the same as y= x² -2x+24
b) y=2x²-88-24
c) y=x²+5x-25
d) y=x®+3x?-10x-24
Hi! I am having trouble with A assignment called "TIME TO SHOP!" I just need answers.
The total item price is $265.50 while the total price with sales tax inclusive is $282.76
Here, we want to determine the sales price of each of the individual items, the total price of all and the appropriate sales tax
To get the price of each, we find the discount off the price of each
Mathematically, that would be;
[tex]\text{Price - (discount percentage }\times\text{ price)}[/tex]We follow through each of the chosen items as follows
1) Blu-Ray player
[tex]\begin{gathered} 42-(12\text{ percent of 42)} \\ =\text{ 42-(}\frac{12}{100}\text{ }\times\text{ 42)} \\ =\text{ 42- 5.04 = \$36.96} \end{gathered}[/tex]2) Jeans
[tex]\begin{gathered} 18.50-(20\text{ percent of 18.50)} \\ =\text{ 18.5 - }(\frac{20}{100}\times18.50) \\ =\text{ \$14.80} \end{gathered}[/tex]3) Set of Books
[tex]\begin{gathered} 15-(15\text{ percent of 15)} \\ =\text{ 15-(}\frac{15}{100}\times15) \\ =\text{ \$12.75} \end{gathered}[/tex]4) Sneakers
[tex]\begin{gathered} 39.5-(32\text{ percent of 39.5)} \\ =\text{ 39.5 - (}\frac{32}{100}\text{ }\times\text{ 39.5)} \\ \\ =\text{ \$26.86} \end{gathered}[/tex]5) Cell Phone
[tex]\begin{gathered} 199-(12.5\text{ percent of 199)} \\ 199-(\frac{12.5}{100}\times\text{ 199)} \\ =\text{ \$174.125} \end{gathered}[/tex]Now, we proceed to get the total of all the items
This is simply obtainable by adding up all the calculated prices
Mathematically, that would be;
174.125 + 26.86 + 12.75 + 14.8 + 36.96 = 265.495
This is a total of $265.50
Now, we want to calculate the total price with the value of the sales tax inclusive
Mathematically, that would be;
[tex]\begin{gathered} \text{Total price + (sales tax percentage of Total price)} \\ =\text{ 265.50 + (}\frac{6.5}{100}\text{ }\times\text{ 265.5)} \\ \\ =\text{ 282.7575 } \\ =\text{ \$282.76} \end{gathered}[/tex]Estimate the amount of money he will have after paying these bills each month
First, add all those bills.
[tex]undefined[/tex]Find the surface area of the following composite figure. 12 ft 32 ft 10 ft 10 ft A. 1480 sq. feet B. 1620 sq. feet C. 1720 sq. feet D. 1820 sq feet
prism area
[tex]\begin{gathered} SA=2lw+2lh+2wh \\ SA=2(10\times10)+2(10\times32)+2(10\times32) \\ SA=2(100)+2(320)+2(320) \\ SA=200+640+640 \\ SA=1480 \end{gathered}[/tex]then, pyramid area
[tex]\begin{gathered} SA=l(2\times ap+l) \\ SA=10(2\times12+10) \\ SA=10(24+10) \\ SA=10(34) \\ SA=340 \end{gathered}[/tex]therfore, area of the figure
[tex]SA=1480+340=1820[/tex]answer: D. 1820 sq feet
2. A certain elevator can hold a maximum weight of 2,800 pounds. This total is determined by estimating the average adult weight as 200 pounds and the average child weight as 80 pounds. Write an inequality that represents this situation, then graph it on the coordinate plane below. Determine a combination of children, c, and adults, a, that can safely ride the elevator.
Let's begin by listing out the given information
Elevator Max weight (e) = 2000 lb
Each adult's weight (a) = 200 lb
Each child's weight (c) = 80 lb
Our inequality is given by:
[tex]200a+80c\le2000-----1[/tex]We will proceed to find the combination of people that can safely ride the elevator
[tex]\begin{gathered} 200a+80c\le2000 \\ \text{If there are 5 a}dults,\text{ we have:} \\ 200(5)+80c\le2000 \\ 1000+80c\le2000 \\ 80c\le2000-1000 \\ 80c\le1000 \\ c\le12.5(\text{that's 12 }children) \\ \text{If there are 8 a}dults,\text{ we have:} \\ 200(8)+80c\le2000 \\ 80c\le2000-1600 \\ 80c\le400 \\ c\le5(\text{5 }children) \end{gathered}[/tex]Evaluate. 10/16 divided by 5/16
2
Explanation
Let's remember the rule to divide two fractions
[tex]\begin{gathered} \frac{a}{b}\text{ divided by }\frac{c}{d} \\ \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc} \end{gathered}[/tex]so,
calculate by applying the formula
[tex]\begin{gathered} \frac{10}{16}\text{ divided by }\frac{5}{16} \\ \frac{\frac{10}{16}}{\frac{5}{16}}=\frac{10\cdot16}{5\cdot16}=\frac{10}{5}=2 \end{gathered}[/tex]therefore, the result is 2
I hope this helps you 2
b) The slope of a line is 3. The line contains the points (-1,8), and (x, 2).Then x =
The slope between two points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Plugging the values of the points given and the slope we have that:
[tex]\begin{gathered} \frac{2-8}{x-(-1)}=3 \\ \frac{-6}{x+1}=3 \\ 3(x+1)=-6 \\ x+1=-\frac{6}{3} \\ x+1=-2 \\ x=-2-1 \\ x=-3 \end{gathered}[/tex]Therefore x=-3
this one is super hard
we have the expression
[tex]d\log a+\log c[/tex]Apply property of log
[tex]d\log a+\log c=\log (a^d\cdot c)[/tex]Cuanto es : Siente mas que cuatro veces un número igual a 13?
Respuesta:
O número es 1.5
Explicacion paso-a-paso:
No sabemos cual o número, entonces o llamamos de x.
Siente mas que cuatro veces un número
7 + 4x
Igual a 13:
7 + 4x = 13
4x = 13 - 7
4x = 6
x = 6/4
x = 1.5
O número es 1.5
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 8 cm. 5 cm. 9 cm. 4 cm. 10 cm. Surface Area: cm2
Solution
Step 1
State the number of shapes in the figure
The shape is made up of
2 triangles
and
3 rectangles
Step 2
State an expression for the area of a triangle and find the area of the triangle
[tex]\text{The area of a triangle ( A}_1)\text{ = }\frac{1}{2}\times base\text{ }\times height[/tex]Where the base = 10cm
height = 4cm
The area of the triangle after substitution is
[tex]\begin{gathered} A_1=\frac{1}{2}\times10\times4 \\ A_1=20cm^2 \end{gathered}[/tex]Since there are two triangles total area of the triangles = 2 x 20 = 40cm²
Step 3
State the expression for the area of a rectangle
[tex]\text{Area of a rectangle = Length }\times width_{}[/tex]Where
For rectangle 1
length = 8cm
width = 9cm
Area of rectangle 1 after substitution = 8 x 9 = 72cm²
For rectangle 2
length = 10cm
width= 9cm
Area of rectangle 2 after substitution = 9 x 10 = 90cm²
For rectangle 3
length = 5cm
wiidth = 9cm
Area of rectangle 3 after substitution = 9 x 5 = 45cm²
Step 4
Find the total area of the shape
[tex]\text{Total surface area of the shape = 45 +90 +}72+40=247cm^2[/tex]Therefore the surface area of the shape = 247cm²
If you are selling your house with a local realtor who requires a 5 Pete cent commission fee what can you expect to pay the realtor of your house sells for 170,000
Let f(-1)=16 and f(5) = -8a. Find the distance between these pointsb. Find the midpoint between these pointsc. Find the slope between these points
We are given the following information
f(-1) = 16 and f(5) = -8
Which means that
[tex](x_1,y_1)=(-1,16)\text{and}(x_2,y_2)=(5,-8)[/tex]a. Find the distance between these points
Recall that the distance formula is given by
[tex]d=\sqrt[]{\mleft({x_2-x_1}\mright)^2+\mleft({y_2-y_1}\mright)^2}[/tex]Let us substitute the given points into the above distance formula
[tex]\begin{gathered} d=\sqrt[]{({5_{}-(-1)})^2+({-8_{}-16_{}})^2} \\ d=\sqrt[]{({5_{}+1})^2+({-24_{}})^2} \\ d=\sqrt[]{({6})^2+({-24_{}})^2} \\ d=\sqrt[]{36^{}+576^{}} \\ d=\sqrt[]{612} \end{gathered}[/tex]Therefore, the distance between these points is √612 = 24.738
b. Find the midpoint between these points
Recall that the midpoint formula is given by
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Let us substitute the given points into the above midpoint formula
[tex]\begin{gathered} (x_m,y_m)=(\frac{-1_{}+5_{}}{2},\frac{16_{}+(-8)_{}}{2}) \\ (x_m,y_m)=(\frac{-1_{}+5}{2},\frac{16_{}-8}{2}) \\ (x_m,y_m)=(\frac{4}{2},\frac{8}{2}) \\ (x_m,y_m)=(2,4) \end{gathered}[/tex]Therefore, the midpoint of these points is (2, 4)
c. Find the slope between these points
Recall that the slope is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex]Let us substitute the given points into the above slope formula
[tex]m=\frac{-8-16}{5-(-1)}=\frac{-24}{5+1}=\frac{-24}{6}=-4[/tex]Therefore, the slope of these points is -4.
What is the equation of the line? −x−2y=4x + 2y = 4−x+4y=2x−4y=2
We can write the line equation as:
[tex]y=mx+b[/tex]And to find the values of the coefficients 'm', and 'b', we can use the intercepts(where the line cuts the x and y axis) on the graph. Looking at the graph, we have the following interceptions:
[tex]\lbrace(0,2),(4,0)\rbrace[/tex]Plugging those values in our equation, we have:
[tex]\begin{cases}2=b \\ 0=4m+b\end{cases}\Rightarrow4m=-2\Rightarrow m=-\frac{1}{2}[/tex]Writing the line equation in slope intercept form, we have the following:
[tex]y=-\frac{1}{2}x+2[/tex]Rewriting this equation:
[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ \Rightarrow\frac{1}{2}x+y=2 \\ \Rightarrow x+2y=4 \end{gathered}[/tex]And this is our final answer. The line equation is
[tex]x+2y=4[/tex]
Reason quantitatively. The two rectangles shown
are similar. What is the value of x
Two shapes are similar if the ratio of the lengths of their corresponding sides are equal.
Both shapes given in the question are rectangles, therefore, one pair of opposite sides is longer than the other.
We can find the ratio for the bigger rectangle since it has all the values complete and then compare this ratio to the smaller rectangle to find the value of the unknown side.
The ratio of the longer side to the shorter side for the bigger rectangle is
[tex]\begin{gathered} \frac{16}{2} \\ =8 \end{gathered}[/tex]Therefore, for the smaller rectangle, the ratio of the longer side to the shorter side is
[tex]\frac{4}{x}=8[/tex]Solving for x, we have
[tex]\begin{gathered} x=\frac{4}{8} \\ x=0.5 \end{gathered}[/tex]The value for x is 0.5.