the given equation is
6x + 4y = 72
divide the equation by 2
3x + 2y = 36
3x + 2y - 36 = 0
compare with ax+by +c = 0
a = 3
b = 2
c = -36
x-intercept will be, -c/a = -(-36)/3 = 12
y intercept will be c/b = -36/2 = -18
Number 3.Light travels 1.9x10^5 kilometers per second.there are 6.4 x 10^5 seconds in one week .About how many kilometers does light travel.
helloo
from the question given, we have some variables
[tex]\begin{gathered} \text{speed}=1.9\times10^5\operatorname{km}\text{ /s} \\ \text{time}=6.4\times10^5s \\ \text{distance}=x \end{gathered}[/tex]now the formula for speed is given as
[tex]\begin{gathered} \text{speed}=\frac{\text{distance}}{\text{time}} \\ 1.9\times10^5=\frac{x}{6.4\times10^5} \\ x=(1.9\times10^5)\times(6.4\times10^5) \\ x=1.22\times10^{11}\operatorname{km} \end{gathered}[/tex]A cylinder has a height of 10 ft and a volume of 25,456 ft^3.The radius of the cylinder is approximately ___ feet.Round your answer to the nearest whole number.
From the question given, they provided us with the height,h = 10ft, and volume, V=25,456 cubic feet.
Thus, we have:
[tex]\begin{gathered} V=\pi\times r^2\times h \\ 25,456=\pi\times r^2\times10 \\ \frac{25,456}{10\pi}=r^2 \\ \text{Taking the value of }\pi\text{ as 3.142, we have:} \\ r^2=\frac{25,456}{10\times3.142} \\ r^2=810.1846 \\ r=\sqrt[]{810.1846} \\ r=28.46ft \end{gathered}[/tex]Hence, the radius of the cylinder is 28.46ft
Samuel is 10 years old. He moaned the neighbors lawn on Saturday and I and $40. It took him 2 hours come on the lawn in 2 hours to clean his room. How much money did Samuel earn an hour? A) $4.00B) $6.67C) $10.00D) 20.00
If he earned $40 in total and it took 4 hours to finish everything, he earns in an hour:
[tex]\frac{40}{4}=10[/tex]Answer: Samuel earns $10.00. Letter C.
Answer:
He got paid 10$ an hour. It does not say he gets paid for cleaning his room. Step-by-step explanation:10 x 4 = 40$
Step-by-step explanation:
The graph of g consists of two straight lines and a semi circle. Evaluate each
Given:
a)
[tex]\int ^1_0g(x)dx[/tex]Consider the shape included in the region from 0 to 1 of g(x).
The area is,
[tex]\int ^1_0g(x)dx=\frac{1}{2}\times1\times4=2[/tex]b) From x = to x = 6 includes the semi-circle. Its area is calculated as,
[tex]\int ^6_2g(x)dx=-\frac{1}{2}(\pi\times r^2)=-\frac{1}{2}(\pi\times2^2)=-2\pi=-6.28[/tex]Which two ratios are equivalent to 11/12?A. 4/5 and 12/13B. 22/24 and 33/36C. 22/33 and 33/34D. 23/24 and 35/36
Two ratios are equivalent if the division between them is equal to one. We need to look at the options to check for which these are true.
For A:
[tex]\frac{\frac{11}{12}}{\frac{4}{5}}=\frac{11}{12}\cdot\frac{5}{4}=\frac{55}{48}[/tex]Since the answer is different than one, this is not the correct option.
For B:
[tex]\frac{\frac{11}{12}}{\frac{22}{24}}=\frac{11}{12}\cdot\frac{24}{22}=\frac{264}{264}=1[/tex][tex]\frac{\frac{11}{12}}{\frac{33}{36}}=\frac{11}{12}\cdot\frac{36}{33}=\frac{396}{396}=1[/tex]Since the result of the division is one for both ratios, the correct option is "B".
Express - 345 asin simplest form, where m and n are integers.Enter the correct answer in the box.-345 =
As -345 is an integer, the simplest fraction form is:
[tex]\frac{-345}{1}[/tex]or -345/1 (m=-345, n=1).
If a bow requires 3/4 yards of lace how many bows can u make with 12 yards of lace
3/4 yards of a lace for each bow
for 12 yards of lace:?
Simply divide the 12 yards of lace by the lace required by each bow (3/4)
12 / (3/4) = 16 bows
Maggie graphed a scatter plot of the numberof hours she drove, t, and the number of milesshe traveled, d. She then found a trend line ofher data to be d = 45.5t + 8. What is thepredicted distance Maggie will travel # shedrives for 4 hours?A 182 milesB 372 milesC 364 milesD 190 milesWhat’s the answer ?
WE have the following:
[tex]d=45.5t+8[/tex]When t = 4
[tex]undefined[/tex]CAN SOMEONE HELP WITH THIS QUESTION?✨
The given function's f(t) = (t - 4)(t + 1)(t - 7), f-intercept is f(t) = 28 and the t-intercepts are t = - 1, 4, 7.
What are intercepts?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the y-axis of the coordinate system in analytic geometry using the widely used convention that the horizontal axis represents a variable x and the vertical axis represents a variable y. Therefore, x = 0 is satisfied at these sites. The x-intercept and y-intercept are the points where a line crosses each axis.
An intercept is a location where an axis and a graph intersect. The x-intercept is the name given to this particular one.
Put t = 0 in the function f(t) = (t - 4)(t + 1)(t - 7)
f(t)= (0-4)(0+1)(0-7)
f(t) = (-4)(1)(-7)
f(t) = 28
So, the f-intercept is (0,28)
Put f(t) = 0 to find t- intercepts
0 = (t-4)(t+1)(t-7)
So, t - 4 = 0
t = 4
For t + 1 = 0
t = -1
For (t - 7) = 0
t = 7
So, the t intercepts are t = -1, 4, 7.
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46 = -6t - 8 what is t
t=9,
1) Solving for t we have:
46 = -6t - 8 Add 8 to both sides
46+8 = -6t
54 = -6t Divide both sides by -6
9 = t Flipping it
t=9
2) So the Solution Set is S={9} for this equation.
Rational and Irrational Numbers make up the____ system.
We have the following:
Therefore, the answer is real numbers
I inserted a picture of the question answer choices E. 15 F.x
Recall that two terms are called like terms if they have the same variables with the same exponents, in simpler words, two terms are like terms if when adding them the result is a simplification of the sum.
Answer: 8 and 12, 1, and 15 are like terms.
Multiply the following polynomials. Once simplified, name the resulting polynomial. (x + 2) (4x^2 - 3x - 2)name:
The resulting polynomial consists of four terms , it is called a quadrinomial.
Find the standard deviation for the following wroup of data Hems, Round your answer to the nearest tenth for one decimal place), 7,9,11,14,15,16
The standard deviation of the groups of data is 3.3 .
The standard deviation is calculated using the formula [tex]{\displaystyle \sigma={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-{\mu }\right)^{2}}}}[/tex]
Where σ is the standard deviation.
x denotes the data of the population.
N is the size of the population.
μ is the mean of the population.
The given population is 7,9,11,14,15,16
Here N= 6
Mean (μ) = (7+9+11+14+15+16)÷6 = 72/6=12
Now we will put the values in the above equation to calculate the sd.
[tex]{\displaystyle \sigma={\sqrt {{\frac {1}{6}}\sum _{i=1}^{6}\left(x_{i}-{12 }\right)^{2}}}}[/tex]
Simplifying we get:
σ = √(64/6)
σ = 3.2659..
σ = 3.3
The standard deviation is a statistic that indicates the degree of volatility or dispersion in a set of numerical values.
A low standard deviation shows that possibly the values tend toward being close to the mean, sometimes referred to as the expected value of the set, whereas a large standard deviation suggests that the values are distributed over a wider range.
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a teacher performing a demonstration find that a piece of court displaces 23.5 ml of water . the piece of cork had a density of 5.7 grams. what is the density of the cork
We are asked to determine the density of the cork. To do that we will use the following formula:
[tex]D=\frac{m}{V}[/tex]Where:
[tex]\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}[/tex]The volume of the cork is the same as the volume that it displaced of water, therefore, we have:
[tex]V=23.5ml[/tex]Now, we substitute the values and we get:
[tex]D=\frac{5.7g}{23.5ml}[/tex]Solving the operations:
[tex]D=0.24\frac{g}{ml}[/tex]Therefore, the density of the cork is 0.24 g/ml.
ANSWER QUESTION 3 PHOTO ATTACHEDFAST REPLY = BETTER RATINGTHANK YOU!
Given
[tex]f(x)=xe^{7x}[/tex]Calculate the second derivative of f(x), as shown below
[tex]\begin{gathered} \Rightarrow f^{\prime}(x)=e^{7x}+7xe^{7x} \\ and \\ \Rightarrow f^{\prime}^{\prime}(x)=7e^{7x}+7(e^{7x}+7xe^{7x}) \\ \Rightarrow f^{\prime}^{\prime}(x)=14e^{7x}+49xe^{7x} \end{gathered}[/tex]Then, find the interval such that f''(x)>0 in order to find where f(x) is concave up,
[tex]\begin{gathered} 14e^{7x}+49xe^{7x}>0 \\ \Rightarrow2e^{7x}+7x*e^{7x}>0 \\ and \\ e{}^{7x}>0,x\in\Re \end{gathered}[/tex]Then,
[tex]\begin{gathered} 2e^{7x}>-7xe^{7x} \\ \Rightarrow2>-7x \\ \Rightarrow x>-\frac{2}{7} \end{gathered}[/tex]Therefore, f(x) is concave up when x in (-2/7, +infinite).
In the case of concavity down,
[tex]\begin{gathered} f^{\prime}^{\prime}(x)<0 \\ \Rightarrow2e^{7x}+7x*e^{7x}<0 \\ \Rightarrow2+7x<0 \\ \Rightarrow-\frac{2}{7}>x \end{gathered}[/tex]Thus, f(x) is concave down when x in (-infinite, -2/7).
The answer is the fifth and last option (top to bottom).
6(__+x)-8(-3+8x) = 30-58xfill in the blank
In this expression, we have the same value on the left side is equal to the same amount on the right side.
So, let's start operating it to simplify it
6(_+x) -8(-3+8x)=30-58x
6(_+x)+24-64x=30-58x
6( ) +6x +24 -64x =30 -58x
6( ) -58x+24=30-58x
6( )-58x +58x=30-24
6( ) =14 DIviding both sides by six
( ) =7/3
Testing:
6(7/3 +x) -8(-3+8x)=30-58x
14+6x +24 -64x =30-58x
38
Victor took a survey of high school students to see how many had part-time jobs last summer. The results of the survey are shown in the table. Compare theprobability that a student in the sophomore class had a part-time job to the probability that a student in the junior class had a part-time job.
Answer:
A sophomore is less likely than a Junior to have a job.
Explanation:
Given the table in the attached image.
The total number of sophomores is
[tex]35[/tex]The number of sophomores with a job is;
[tex]12[/tex]The probability that a sophomore had a job is;
[tex]P_S=\frac{12}{35}[/tex]The total number of Juniors is
[tex]37[/tex]The number of Juniors with a job is;
[tex]27[/tex]The probability that a Junior had a job is;
[tex]P_J=\frac{27}{37}[/tex]From the derived Probability, we can observe that the probability that a Junior had a job is greater than the probability that a Sophomore had a job.
[tex]P_J>P_S[/tex]Therefore, A sophomore is less likely than a Junior to have a job.
Multiply. Write the result in standard form.(2 + 1)(3^4 + 7 + 2)
To multiply polynomials, we use the distributive law
[tex]\begin{gathered} (2x+1)(3x^4+7x+2)=(2x+1)(3x^4)+(2x+1)(7x)+(2x+1)(2) \\ =2x(3x^4)+1(3x^4)+2x(7x)+1(7x)+2x(2)+1(2)_{} \\ =6x^5+3x^4+14x^2+7x+4x+2 \end{gathered}[/tex]The last part follows by the laws of exponentials, finally we combine like terms
[tex]\begin{gathered} 6x^5+3x^4+14x^2+7x+4x+2=6x^5+3x^4+14x^2+(7+4)x+2 \\ =6x^5+3x^4+14x^2+11x+2 \end{gathered}[/tex]Helpppppppp I can’t answer because I am bad at math
The magnitude of a number is the absoulute value of the number. Recall, the absolute value of a number is always positive. The absolute value of a is written as IaI
Hence,
magnitude of - 7.5 is 7.5
The correct option is D
Suppose 2' is a normally distributed random variable with ft = 10.3 and 0 = 3.8. For the following probability,draw an appropriate diagram, shade the appropriate region and then determine the value:P(9 <2 ≤ 14) = Note: Enter your answer up to 4 decimal places.
GIVEN
The following values are given:
[tex]\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}[/tex]SOLUTION
The z-score for the x values 9 and 14 can be calculated using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]For x = 9:
[tex]\begin{gathered} z=\frac{9-10.3}{3.8} \\ z=-0.34 \end{gathered}[/tex]For x = 14:
[tex]\begin{gathered} z=\frac{14-10.3}{3.8} \\ z=0.97 \end{gathered}[/tex]The probability can be calculated as follows:
[tex]P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:Therefore, the probability is given to be:
[tex]P(9\le x\le14)=0.4671[/tex]The probability is 0.4671.
Mariah needs to randomly select one of three groups of students to make their presentation first. Which simulation tools could she use in thissituation?O a bag containing 12 chips in three different colors, with four of each coloro a six-sided number cubea full standard deck of cardsa spinner divided evenly into four sections, with each section a different colorO two coins
the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Explanation:
number of groups of student = 3
We need to select one out of the three.
The option that can be used to simulate this choice is having 12 chips in three different colours. Each colour will have 4 each.
The 3 different colours represent the 3 different groups. While each 4 number of a colour represent the number of students in each group.
Hence, the correct answer is a bag containing 12 chips in three different colors, with four of each color (option A)
Two cards are drawn from a deck of 52 cards. The first card is replaced before drawing the second card. Find the probability that the first card is red and the second card is a 7
The probability that the first card is red and the second card is a 7 is 1/26.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the first card is a red and the second is a 7 = (number of red cards / total number of cards) x (number of 7 / total number of card)
Probability that the first card is a red and the second is a 7 = (26 / 52) x (4/52) = 1/26
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The sum of the two numbers is 133. Four times the smaller of the two numbers equals three times the greater number find the numbers using one variable.
The Solution:
Let the two number be x and y133-x (
Such that:
[tex]\begin{gathered} x<133-x \\ x=small\text{ number} \\ 133-x=larger\text{ number} \end{gathered}[/tex]So,
[tex]\begin{gathered} 4x=3(133-x) \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 4x=399-3x \\ \text{ Collect the like terms.} \\ 4x+3x=399 \\ 7x=399 \end{gathered}[/tex]Divide both sides by 7.
[tex]x=\frac{399}{7}=57[/tex]Therefore, the correct nswers are:
57 and 76
A bag of numbered lottery balls contains the numbers 1 through 50. What is the probability that a randomly selected ball will be a number that is not a multiple of 8? Give your answer as a simplified fraction.
A bag of numbered lottery balls contains he numbers 1 through 50.
One ball is selected at random.
From 50 balls, one ball can be selected in 50 different ways.
So, the total number of points in sample space is 50.
Let us consider the event that the number is a multiple of 8 be A.
There are six numbers between 1 o 50 which are multiple of 8.
Therefore, one ball can be selected from 6 balls in 6 different ways.
So, the number of points in sample space in favour of the event A is 6.
Therefore, by the classical definition of probability,
[tex]\begin{gathered} P(A)=\frac{6}{50} \\ =\frac{3}{25} \end{gathered}[/tex]Then, the probability that the selected number is not a multiple of 8 is
[tex]\begin{gathered} P(A^C)=1-P(A) \\ =1-\frac{3}{25} \\ =\frac{22}{25} \end{gathered}[/tex]So, the required probability is 22/25.
Select all of the constraints that apply to this situation $1.25x when x <12$12.00 + $0.75(x-12) when X_>12$1.25x when x _>120.75x when x >12$12.00 + $0.75x when x >12
We want to write expressions that describe the cost of the cookies. Let say we sell x cookies. If x is less than 12, then the cost per cookie is 1.25. So the cost of x cookies would be the product of this numbers, so it would be
[tex]1.25x,x<12[/tex]Note that when x=12 the cost should be 12. Also note that for each extra cookie, starting at 12, each cookie costs 0.75. If we buy x cookies , to calculate the extra cookies, with respect to 12, we simply substract 12 from x and we multiply it by 0.75. This would be
[tex]0.75\cdot(x\text{ -12)}[/tex]as this is an additional cost to the 12, we add 12 to this expression. THen we get
[tex]12+0.75\cdot(x\text{ -12)}[/tex]Note that for this expression, when x=12, we get that the expression becomes
[tex]12+0.75\cdot(12\text{ -12)=12}[/tex]THis means that the expression applies from 12 and on, so we have the followin inequality12
[tex]12+0.75\cdot(x\text{ -12), x}\ge12[/tex]Solve the system of two linear inequalities graphically,2y <&- 1618v 2 - 7x+56Step 1 of 3: Graph the solution set of the festlinear InequallyAnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawEnable ZoonpanChoose the type of boundary linesSolid (-) Dashed)Enter two points on the boundarytine:10Select the region you wish to be shaded:
Given
[tex]\begin{gathered} 2y<8x-16 \\ 8y\ge7x+56 \end{gathered}[/tex]The graph
Two boundary points
(0,7) (2,0)
Hi so some of the problems I don't know like I can't but I did do some problem by myself you can tell me whether it's correct
The symmetric property of equality, if AB = YU. then YU = AB
As per the symmetric property of equality,
if AB = YU. then YU = AB
As per the symmetric property of congurence,
∠H ≅ ∠K then ∠K ≅ ∠H
As per the reflexive property of congurence,
∠PQR ≅ ∠PQR
As per the distibutive property, multiplying the sum of two or more term by a number produces the same result as when each term is multiplied individually by the number and the products are added together.
3(x - 1) = 3x - 3
As per the substitution property one value can replace another value in an expression or equation and the value will remain the same.
If LM = 7, EF + LM = NP
Then EF + 7 = NP
Therefore, the above bits are done as per the property mentioned.
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find the area of the circle with a diameter of 8.6 ft
Given:
Diameter of the circle, d = 8.6 ft
To find the area of a circle, use the formula below:
[tex]undefined[/tex]Diameter of the circle, d
Type the correct answer in each box. Use numerals instead of words.The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.What is the surface area of the solid cone requiring paint to the nearest square centimeter?The surface area of the solid cone requiring paint rounded to the nearest whole number is square centimeters.
The surface area of a cone with diameter d and height h is given by:
[tex]A=\pi(\frac{d}{2})^2+\pi\cdot\frac{d}{2}\cdot\sqrt[]{h^2+(\frac{d}{2})^2}[/tex]For d = 5 cm and h = 11.4 cm, we have:
[tex]\begin{gathered} A=\pi(\frac{5}{2})^2+\pi\frac{5}{2}\sqrt[]{11.4^2+(\frac{5}{2})^2} \\ A=\frac{25}{2}\pi+\pi\frac{25}{2}\sqrt[]{129.96+\frac{25}{2}} \\ A=12.5\pi+12.5\cdot\pi\cdot\sqrt[]{142.46} \\ A\approx12.5\pi+12.5\cdot11.94\cdot\pi \\ A\approx508cm^2 \end{gathered}[/tex]