Calvin owns a toy store. He can spend at most $200 on restocking cars and dolls. A doll costs $6.50, and a car costs $8.00. Let x represent the number of cars, and let y represent the number of dolls. Identify an inequality for the number of toys he can buy. Then identify the number of dolls Calvin can buy if he buys 10 cars.
Answers
Solution:
Given that;
Calvin owns a toy store. He can spend at most $200 on restocking cars and dolls. A doll costs $6.50, and a car costs $8.00.
Let x represent the number of cars, and let y represent the number of dolls.
The maximum amount Calvin can spend is
[tex]8x+6.50y\leq200[/tex]If he buys 10 cars, the maximum number of dolls is
[tex]\begin{gathered} 8x+6.50y\leq200 \\ 8(10)+6.50y\leq200 \\ 6.50y\leq200-80 \\ 6.50y\leq120 \\ y\leq\frac{120}{6.50} \\ y\leq18.46153 \\ y\leq18\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the answer is
[tex]8x+6.50y\leq200;\text{ no more than 18 dolls}[/tex]Related Questions
Simplify: 7⁵÷2⁸[tex] {7}^{5} \div {2}^{8} [/tex]what does this =
Answers
Answer:
[tex]65\frac{167}{256}[/tex]Explanation:
Given the expression:
[tex]{7}^5\div{2}^8[/tex]We can rewrite this as:
[tex]\begin{gathered} \frac{7^5}{2^8}=\frac{16807}{256} \\ =65\frac{167}{256} \end{gathered}[/tex]O MEASUREMENT Choosing metric measurement units Fill in the blanks below with the correct units. (a) Kevin's classroom is about 7 ? (b) It took about 190? ✓wide. of water to fill the bathtub. (c) Omar has a cellular phone. Its mass is about 100 ?
Answers
For question a. both options measure the correct thing, however, it is unreal to think that Linda could use only 20 milliliters to wash her car. Therefore, the correct answer is liters
For question b., same as with question a., all options measure the correct thing, distance, but it is unreal to think that a mountain is only 3 millimeters, centimeters, or meters high. Therefore, the correct answer is kilometers.
For question c., same as the last two questions, both options measure the correct thing, mass. However, it is unreal to think that a dog weights only 6 grams, therefore, the correct option is kilograms
Trigonometric Identities Find the area of each triangle to the nearest tenth
Answers
We will have the following:
1.
[tex]\begin{gathered} A=(10)(12)\frac{sin(55)}{2}\Rightarrow A=60sin(55) \\ \\ \Rightarrow A\approx49.1 \end{gathered}[/tex]So, the area of the first triangle is approximately 49.1 ft^2.
2.
[tex]\begin{gathered} A=(18.5)(25)\frac{sin(20)}{2}\Rightarrow A=231.25sin(20) \\ \\ \Rightarrow A\approx79.1 \end{gathered}[/tex]So, the area of the second triangle is approximately 79.1 in^2.
Evaluate sine, cosine, and tangent at the following value. Use the reference angle, θ′, and write your answer in exact form: 41π/6
Answers
Let us find the reference angle:
[tex]\begin{gathered} \frac{41}{6}\pi\Rightarrow\frac{41}{6}\cdot\frac{2}{2}\pi=\frac{41}{12}\cdot2\pi=(3+\frac{5}{12})2\pi \\ \frac{41}{6}\pi\Rightarrow\frac{5}{6}\pi \end{gathered}[/tex]Now, let us to calculate the sine and cosine of this angle:
[tex]\begin{gathered} \sin (\frac{5}{6}\pi)=\sin (150\degree)=0.5 \\ \cos (\frac{5}{6}\pi)=\cos (150\degree)=\sqrt[]{1-\sin ^2(\frac{5}{6}\pi)}=\sqrt[]{1-0.5^2}=\sqrt[]{\frac{3}{4}}=\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]From this, we have:
[tex]\begin{gathered} \sin (\frac{41\pi}{6})=\frac{1}{2} \\ \cos (\frac{41\pi}{6})=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]And because:
[tex]\tan (\theta)=\frac{\sin (\theta)}{\cos (\theta)}[/tex]we can calculate:
[tex]\tan (\frac{41\pi}{6})=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}}=\frac{1}{2}\cdot\frac{2}{\sqrt[]{3}}=\frac{\sqrt[]{3}}{3}[/tex]From the solution developed above, we are able to summarize the solution as:
[tex]\begin{gathered} \sin (\frac{41\pi}{6})=\frac{1}{2} \\ \\ \cos (\frac{41\pi}{6})=\frac{\sqrt[]{3}}{2} \\ \\ \tan (\frac{41\pi}{6})=\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]6. Given a circle with a radius of 3 and a reference triangle of 45°. What are the sine andcosine of the angle?
Answers
Answer:
[tex]\begin{gathered} sine(45)=\frac{\sqrt{2}}{2} \\ cosine(45)=\frac{\sqrt{2}}{2} \end{gathered}[/tex]Step-by-step explanation:
The hypotenuse of a reference triangle that lies on the unit circle is the radius of the unit circle. Therefore, if it has a radius of 3 and a reference triangle of 45 degrees.
Remember that sine and cosine are represented by the following equations:
[tex]\begin{gathered} sin(angle)=\frac{opposite}{hypotenuse} \\ cos(angle)=\frac{adjacent\text{ }}{hypotenuse} \end{gathered}[/tex]Now, for the following circle and the reference triangle:
[tex]\begin{gathered} \text{ sin\lparen45\rparen=}\frac{opposite}{3} \\ \text{ opposite=3*sin\lparen45\rparen} \\ opposite=\frac{3\sqrt{2}}{2} \\ \\ \text{ cos\lparen45\rparen=}\frac{\text{ adjacent}}{3} \\ \text{ adjacent=}\frac{3\sqrt{2}}{2} \end{gathered}[/tex]Hence, for the sin and cosine:
[tex]\begin{gathered} sine(45)=\frac{\sqrt{2}}{2} \\ cosine(45)=\frac{\sqrt{2}}{2} \end{gathered}[/tex]Question 3 (1 point) Choose the answer. Replace ? with =, >, or < to make the statement true 164 +12? 4 + 24 ÷ 2
Answers
By simplifying the expression, we will see that the correct symbol is ">"
164 + 12 > 4 + 24/2
Which symbol should we use?
Here we have the expression:
164 + 12 ? 4 + 24/2
First, let's simplify both sides to see what we get:
164 + 12 = 174 + 2 = 176
4 + 24/2 = 4 + 12 = 16
So now we want a symbol that compares 176 and 16, obviously, 176 is larger, then we can write the inequality:
176 > 16
Then the correct symbol is ">"
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Sam deposited $500 into a savings account that earns4% simple interest for 3 years.
Answers
ok
I = 500 x 0.04 x 3
I = 60
Earnings = $60
Total money = 500 + 60
= $560
1. Given R (7,-1), B(-3,-6), plot the points and trace the figure Part A a determine the lengths of each side (round to the nearest hundredth).prat B Determine the perimeter.
Answers
Given the points, we graph it as follows:
A. We determine the lengths of each side using the following expression:
[tex]d=\sqrt[]{(X)^2+(Y)^2_{}}[/tex]Here X & Y are the x & y-components from the directional vectors made from the points given.
Now, using the points we find the following directional directional vectors:
[tex]RA=(3-7,-6+1)\Rightarrow RA=(-4,-5)[/tex][tex]AB=(-3-3,-6+6)\Rightarrow AB=(-6,0)[/tex][tex]BE=(-3+5,-6-4)\Rightarrow BE=(2,-10)[/tex][tex]RE=(-5-7,4+1)\Rightarrow RE=(-12,5)[/tex]Now, we will determine the lengths of each side:
[tex]d_{RA}=\sqrt[]{(-4)^2+(-5)^2}\Rightarrow d_{RA}=\sqrt[]{41}[/tex][tex]d_{AB}=\sqrt[]{(-6)^2+(0)^2}\Rightarrow d_{AB}=6[/tex][tex]d_{BE}=\sqrt[]{2^2+(-10)^2}\Rightarrow d_{BE}=2\sqrt[]{26}[/tex][tex]d_{RE}=\sqrt[]{(-12)^2+5^2}\Rightarrow d_{RE}=13[/tex]So, the lengths of each side are:
Side RA = 6.40 units.
Side AB = 6 units.
Side BE = 10.20 units.
Side RE = 13 units.
B. The approximate perimeter is:
6.40 + 6 + 10.20 + 13 = 55.4
So, its perimeter is approximately 55.4 units.
Wordblank:linear equation, parallel, slope, y intercept VocabularyChoose the best term from the box to complete each definition.1. The value of m in the equation y = mx + b represents the____2. When lines are the same distance apart over their entire lengths, theyare ____3. The___is the value b in the equation y = mx +b.4. A ____is a relationship between two variables that gives astraight line when graphed.
Answers
EXPLANATION
Given the equation y=mx+b
The value of m in the equation y=mx + b represents the slope.
When lines are the same distance apart over their entire lengths, they are parallel.
The y-incercept is the value b in the equation y=mx + b.
A linear function is a relationship between two variables that gives straight line when graphed.
Hello, I would be grateful If you could help me with that question
Answers
Answer:
11 1/9%
Explanation:
First, calculate the number of grams gained.
[tex]1000-900=100\text{ gms}[/tex]Next, find the profit percentage of the goods.
[tex]\begin{gathered} \text{ Profit Percentage}=\frac{\text{ Grams Gained}}{\text{ Actual Measure Used}}\times100 \\ =\frac{100}{900}\times100 \\ =11\frac{1}{9}\% \end{gathered}[/tex]The profit percentage is 11 1/9%.
Six times the sum of a number and eight is 30. Find the number.
Answers
Let the unknown number be "x".
Let's break apart the word problem.
• "The sum of a number and eight" can be written as
[tex]x+8[/tex]• Six times "the sum of a number and eight" can be written as:
[tex]6(x+8)[/tex]• All of this is equal to 30, so we can write the final equation:
[tex]6(x+8)=30[/tex]With the help of a little algebra, we can solve for "x" (the unknown number). The steps are shown below:
[tex]\begin{gathered} 6(x+8)=30 \\ 6x+48=30 \\ 6x=30-48 \\ 6x=-18 \\ x=-\frac{18}{6} \\ x=-3 \end{gathered}[/tex]The number is - 3hello I have a few problems I need help with
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*We have that GH & G'H will be congruent, that since G was rotated about H and not scaled(1).
*We have that AB and A'B' have the same length and are perpendicular(1).
*We have that they should match when <1 is congruent with <2 and AB is congruent with AD(3).
Andy needs to create an open topped box to carry a catapult to school for physics class. He uses a piece of cardboard that is 40 inches by 50 inches to make the box, and plans to cut out square corners of measure x inches. What is the maximum possible volume of the box?
Answers
Hello there. To solve this question, we'll have to remember some properties about maximizing volumes of boxes.
Let's start by drawing the situation:
In the left, we have the cardboard piece that was 40 inches by 50 inches, then on the right we have it after cutting the square corners of measure x inches.
Now, we create a box by closing the walls:
The measures of the cardboard piece after having been cut the corners are 40 - 2x and 50 - 2x, while after in the box format, its height is equal to x.
Therefore, the total volume of the box is given by:
[tex]x\cdot(50-2x)\cdot(40-2x)=4x^3-180x^2+2000x[/tex]To maximize this function, we take its derivative and find the roots of the polynomial:
[tex](4x^3-180x^2+2000x)^{\prime}=12x^2-360x+2000[/tex]Taking its roots, we get:
[tex]\begin{gathered} 12x^2-360x+2000=0 \\ \\ x=\frac{360\pm\sqrt[]{360^2-4\cdot12\cdot2000}}{2\cdot12}=\frac{360\pm40\sqrt[]{21}_{}}{24}=15\pm5\sqrt[]{\frac{7}{3}} \end{gathered}[/tex]In this case, we got two values, but only one of them will maximize this function.
Taking the second derivative of the function, we get:
[tex](4x^3-180x^2+2000x)^{\prime\prime}=24x-360[/tex]Plugging the values in, we get:
[tex]\begin{gathered} 24\cdot\frac{360+40\sqrt[]{21}}{24}-360=40\sqrt[]{21} \\ \\ 24\cdot\frac{360-40\sqrt[]{21}}{24}-360=-40\sqrt[]{21} \end{gathered}[/tex]And the value such that f''(x) < 0 will be the value that gives us the maximum volume of the box.
Plugging it into the expression for the volume, we finally get:
[tex]\begin{gathered} 4\cdot\mleft(15-5\sqrt[]{\frac{7}{3}}\mright)^3-180\cdot\mleft(15-5\sqrt[]{\frac{7}{3}}\mright)^2+2000\cdot\mleft(15-5\sqrt[]{\frac{7}{3}}\mright) \\ \\ \\ 3000+\frac{7000\sqrt[]{21}}{9}=\text{Maximum volume} \end{gathered}[/tex]This maximum volume is approximately equal to 6564 cubic inches.
what is 25.60 with a tip of 20 percent
Answers
First, calculate what is 20% of 25.60 equal to.
To do so, just multiply 25.60 times 0.20:
[tex]25.60\cdot0.20=5.12[/tex]Add the tip of 5.12 to the original quantity of 25.60:
[tex]25.60+5.12=30.72[/tex]Therefore, 25.60 with a tip of 20 percent, is 30.72
I don’t understand this at all. Could you break it down for me?
Answers
Vertical angles are the angles opposite each other when two lines cross.
Let's see which angle forms a "X" with ∠EOD:
So, ∠COF is "vertical" with ∠EOD.
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#7When 2 angles add up to 90 degrees, we say that they are complementary angles.
Since ∠POF + ∠FOB = 90, then ∠POF is complementary to ∠FOB.
═══════════════════════════════════════════════
#8∠BOC + ∠AOC is a straight angle (straight line).
A straight angle is 180 degrees.
So, we can write,
[tex]\angle BOC+\angle AOC=180\degree[/tex]We know ∠BOC = 150, so ∠AOC will be,
[tex]\begin{gathered} 150\degree+\angle AOC=180\degree \\ \angle\text{AOC}=180-150 \\ \angle\text{AOC}=30\degree \end{gathered}[/tex]═══════════════════════════════════════════════
#9From the diagram, we can see that ∠EOA and ∠FOB are vertical angles. Thus, they are equal.
Since ∠EOA = 37,
∠FOB = 37
Now, from the diagram, we can see,
∠FOA + ∠FOB = 180 [since they are straight line]
Now, we can easily find ∠FOA:
[tex]\begin{gathered} \angle FOA+\angle FOB=180 \\ \angle\text{FOA}+37=180 \\ \angle\text{FOA}=180-37 \\ \angle\text{FOA}=143\degree \end{gathered}[/tex]═══════════════════════════════════════════════
#10Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.
For example,
∠1 and ∠2 are adjacent angles.
From our diagram,
∠HGO is adjacent to ∠EGH
From the diagram above, we see that G is the common vertex and GH is the common side.
Thus,
∠HGO is adjacent to ∠EGH
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#11From the diagram, we see that ∠EGH and ∠HGO fall in a straight line. So, they add up to 180 degrees.
[tex]\angle\text{EGH}+\angle\text{HGO}=180[/tex]Given,
∠HGO = 128,
Let's find ∠EGH:
[tex]\begin{gathered} \angle\text{EGH}+\angle\text{HGO}=180 \\ \angle\text{EGH}+128=180 \\ \angle\text{EGH}=180-128 \\ \angle\text{EGH}=52\degree \end{gathered}[/tex]Given,
[tex]\angle\text{EGH}\cong\angle\text{DOB}[/tex]We can say:
[tex]\angle\text{DOB}=52\degree[/tex]═══════════════════════════════════════════════
#12From the figure, we see that ∠EOA + ∠EOD + ∠DOB = 180 degrees [straight line].
Given,
∠EOA = 67
∠DOB = 29
We can solve for ∠EOD:
[tex]\begin{gathered} \angle EOA+\angle EOD+\angle DOB=180 \\ 67+\angle\text{EOD}+29=180 \\ 96+\angle\text{EOD}=180 \\ \angle\text{EOD}=180-96 \\ \angle\text{EOD}=84\degree \end{gathered}[/tex]═══════════════════════════════════════════════
#13When 2 angles add up to 180 degrees, we say that they are supplementary angles.
Given,
∠AOD + ∠DOB = 180
We can say that ∠AOD is supplementary to ∠DOB.
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#14Since ∠COF is congruent to ∠DOF and fall is a straight line, we can say that they are each 90 degrees.
Thus, FO and CD will be perpendicular to each other.
So, we can say,
FO is perpendicular to CD
═══════════════════════════════════════════════
#15
Given,
∠COP = 72 and ∠POF = 31, we have:
We want to know the measure of ∠EOD.
Let's see below:
We see that ∠COF and ∠EOD are vertical angles.
Vertical angles are equal.
So,
∠EOD = ∠COP + ∠POF
∠EOD = 72 + 31
∠EOD = 103°
'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-
Answers[tex]\begin{gathered} 6.\angle\text{COF} \\ 7.\text{Complementary} \\ 8.\angle\text{AOC}=30\degree \\ 9.\angle\text{FOA}=143\degree \\ 10.\angle\text{HGO} \\ 11.\angle\text{DOB}=52\degree \\ 12.\angle\text{EOD}=84\degree \\ 13.Supplementary \\ 14.Perpendicular \\ 15.\angle\text{EOD}=103\degree \end{gathered}[/tex]
Finding Slope and Graphing Equations of Lines Part 1 Directions: find the slope of the line passing through the given points. Then tell whether the line rises, falls, is horizontal, or is vertical. Show all work. 1.) (8, 15) and (12, -1) 2.) (5,-2) and (2,-2) 3.) (9, -3) and (-6,4) 4.) (4, 5) and (21,5)
Answers
The slope of a line is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex]1: (8, 15) and (12, -1)
[tex](x_1,y_1)=(8,15)\text{ and }(x_2,y_2)=(12,-1)[/tex]So the slope is
[tex]m=\frac{-1-15}{12-8}=\frac{-16}{4}=-4[/tex]Since the slope is negative, the line falls.
2: (5,-2) and (2,-2)
[tex](x_1,y_1)=(5,-2)\text{ and }(x_2,y_2)=(2,-2)[/tex]So the slope is
[tex]m=\frac{-2-(-2)}{2-5}=\frac{-2+2}{-3}=\frac{0}{3}=0[/tex]Since the slope is 0, the line is a flat horizontal line.
3: (9, -3) and (-6,4)
[tex](x_1,y_1)=(9,-3)\text{ and }(x_2,y_2)=(-6,4)[/tex]So the slope is
[tex]m=\frac{4-(-3)}{-6-9}=\frac{4+3}{-15}=-\frac{7}{15}[/tex]Since the slope is negative, the line falls.
4: (4, 5) and (21, 5)
[tex](x_1,y_1)=(4,5)\text{ and }(x_2,y_2)=(21,5)[/tex][tex]m=\frac{5-5}{21-4}=\frac{0}{17}=0[/tex]Since the slope is 0, the line is a flat horizontal line.
Find the inverse of the matrix8 2 -4 -5if it exists
Answers
The inverse (A^-1) of a matrix A is :
From the problem, we have :
a = 8, b = 2, c = -4 and d = -5
Using the formula above :
Simplify the fraction and multiply it inside the matrix.
The answer is :
John wants to choose 4 of his friends to go to Disneyland with him. If he has 15 friends, in howmany ways can he choose 4 of them?
Answers
In this case, the order does not matter and we can not replace it.
Hence, we need to use a combination for this case.
The equation is given by:
[tex]nCx=\frac{n!}{x!(x-n)!}[/tex]Where n represents the total number of friends and x represents the number of the group.
Then,
n = 15 friends
x = choose 4 of them
Replacing:
[tex]15C4=\frac{15!}{4!(15-4)!}[/tex]Simplify:
[tex]\begin{gathered} 15C4=\frac{15!}{4!11!} \\ 15C4=1365 \end{gathered}[/tex]Hence, Jhon can choose them 1365 ways.
The correct answer is option d.
I need to know the answer and how to solve this
Answers
Explanation
when a line intersect a pair of parallel lines, diverse angles are formed
As we can see, angles 1 and angle 2 are supplementary , ( the sum equal 180)
the same for angles 3 and 4,
also angle1 is congruent to angle 3
[tex]m\angle1=m\angle3\text{ Eq(1)}[/tex]
and
angle 3 and 4 are supplementary ,so
[tex]\begin{gathered} m\angle3+m\angle4=180 \\ \text{replace m}\angle4=115 \\ m\angle3+115=180 \\ \text{subtract 115 in both sides} \\ m\angle3+115-115=180-115 \\ m\angle3=65 \\ m\angle3=m\angle1=65 \end{gathered}[/tex]I hope this helps you
Deon is on his way home in his car. He has driven 24miles so far, which is one-half of the way home. What is the total length of his drive?
Answers
Given:
a.) He has driven 24miles so far, which is one-half of the way home.
Let's compute the total length that he must drive.
[tex]\text{ 24 }\div\text{ }\frac{1}{2}\text{ = }\frac{\text{24}}{1}\text{ x }\frac{2}{1}[/tex][tex]\text{ = }\frac{48}{1}\text{ = 48}[/tex]Therefore, the answer is 48 miles.
Trini plans to order 48 cupcakes for her best friend's birthday party. She searched online for pricingand the average per cupcake was $2. Instead she bought two boxes of cake mix, some frosting, cupcakeliners and 48 gold eatable hearts to put on top of the cupcakes. She spent a total of $12, went homeand baked the cupcakes. How much did she save?
Answers
How much she saved = what she planned to spend - how much she actaully spent
how much she planned to spend => $48 x 2(average amount per cup cake) = $96
amount spent = $12
Amount saved = $96 - $ 12 =$84
The ratio of 6 inches to 3 feet expressed in simplest form is 1/6
Answers
First, convert feet to inches by multiplying them by 12.
So, 3 feet = 36 inches.
Now find the ratio of 6 inches to 36 inches.
[tex]\frac{6}{36}=\frac{1}{6}[/tex]Thus, the ratio is 1/6.
can some one help me !
Answers
In linear equation,568.4983 is price after sales tax .
What are instances of linear equations?
Ax+By=C represents a two-variable linear equation in its standard form. A standard form linear equation is, for instance, 2x+3y=5.Finding both intercepts of an equation in this form is rather simple (x and y).When resolving systems of two linear equations, this form is also incredibly helpful.A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.a bicycle listed price = 523.96
sales tax rate = 8.5%
= 523.96 * 8.5 %
= 44.5383
bicycle price with sales tax = 568.4983
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The cost of a bicycle to a store owner was $550, and she sold the bicycle for $1150Step 3 of 3: What was her percent of profit based on selling price? Follow the problem-solving process and round your answer to thenearest hundredth if necessary.
Answers
So,
If she sold the bicycle for $1150 and the cost for her to buy it was $550, the profit can be found if we substract:
[tex]\begin{gathered} 1150-550 \\ =600 \end{gathered}[/tex]Now, the percent of profit can be found if we divide the last result by the cost:
[tex]\frac{600}{550}=1.09[/tex]Or, 1.09*100 = 109%.
find the line that passesthrough (2, 4) and (5,-4)
Answers
Line equation in slope and intercept form:
y = mx + b
slope = m = (y2 - y1)/(x2 - x1)
In this case:
m = (-4 - 4)/(5 -2) = -8/3
m = -8/3
Using the first point in the line equation we will find the value of b:
y = mx + b
b = y - mx
b = 4 - (-8/3)(2) = 4 - 16/3 = (12 - 16)/3 = -4/3
b = -4/3
Answer:
y = (-8/3)x - 4/3
simplify variable 0.8x-0.2x-5
Answers
The value of variable x is 25/3 ≈ 8.3
Given equation:
0.8x - 0.2x - 5 = 0
0.8x - 0.2x = 5
take x as common on left hand side
x(0.8 - 0.2) = 5
x(0.6) = 5
divide 0.6 on both sides
x(0.6)/0.6 = 5/0.6
x = 5/0.6
x = 5/6/10
x = 5*10/6
x = 50/6
x = 25/3 ≈ 8.3
Therefore the value of variable x is 25/3 ≈ 8.3
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Convert the polar coordinate, ( 9,(9,5713to a rectangular coordinate, (Ex, Ey).x=[ Select ]V[ Select ]y= [Select][ Select ]
Answers
Given data:
The given polar coordinate is (9, 5π/3).
The expression for the x- coordinate is,
[tex]\begin{gathered} x=9\cos (\frac{5\pi}{3}) \\ =9\times\frac{1}{2} \\ =4.5 \end{gathered}[/tex]The expression for the y-coordinate is,
[tex]\begin{gathered} y=9\sin (\frac{5\pi}{3}) \\ =-7.7942 \\ \approx-7.79 \end{gathered}[/tex]Thus, the caretesian coordinate is (+4.5, -7.79).
a 2-pound bag of cherries cost $11.20. what is the price per ounce
Answers
Given data:
The given cost of 2-pound is C=$11.20.
The given cost can be express as,
2-pound=$11.20
2(16 ounce)=$11.20
1 ounce =$11.20/32
=$0.35
Thus, the price of 1 ounce is $0.35.
A chemical company makes two brands of antifreeze. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze. In order to obtain 60 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?First brand Second brand
Answers
Given the word problem, we can deduce the following information:
1. The first brand is 35% pure antifreeze, and the second brand is 60% pure antifreeze.
2. The chemical company intended to obtain 60 gallons of a mixture that contains 45% pure antifreeze.
To determine the amount in gallons of each brand of antifreeze, we first let:
x= the amount of 35% pure antifreeze
60-x= the amount of 60% pure antifreeze
Based on the given information, our equation would be:
[tex]0.35x+0.60(60-x)=0.45(60)[/tex]Next, we get the value of x:
[tex]\begin{gathered} 0.35x+0.60(60-x)=0.45(60) \\ \text{Simplify and rearrange} \\ 0.35x+36-0.6x=27 \\ -0.25x+36=27 \\ 0.25x=36-27 \\ 0.25x=9 \\ x=\frac{9}{0.25} \\ \text{Calculate} \\ x=36\text{ gallons} \end{gathered}[/tex]Then, we plug in x=36 into 60-x:
[tex]60-x=60-36=24\text{ gallons}[/tex]Therefore,
First brand = 36 gallons
Second brand = 24 gallons
Answer question 55.51 These 15 ages of students at an after-schoolevent are in order from least to greatest.6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18What is the Minimum number of this data?A 1B 3C7D 651
Answers
Given:
Given the data set
6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18
Required: Interquartile range
Explanation:
Sample size is n = 15.
First, arrange the data set in ascending order.
6, 6, 6, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 18
Compute the quartiles Q1 and Q3.
[tex]\begin{gathered} Q_1=(\frac{n+1}{4})^{t\text{h }}\text{ term} \\ =(\frac{15+1}{4})^{th}\text{ term} \\ =4^{th}\text{ term} \\ =7 \end{gathered}[/tex][tex]\begin{gathered} Q_3=(\frac{3(n+1)}{4})^{th}\text{ term} \\ =(\frac{3(15+1)}{4})^{th}\text{ term} \\ =12^{th}\text{ term} \\ =13 \end{gathered}[/tex]The interquartile range is
[tex]\begin{gathered} IQR=Q_3-Q_1 \\ =13-7 \\ =6 \end{gathered}[/tex]Final Answer: The interquartile range of the given data set is 6.