Answer:
D
Step-by-step explanation:
to determine the relationship between these two lines you have to find the slope.
=> if they have the same slope ,then they are parallel.
=> if they have negative inverse slope relative to each other ,then they are perpendicular.
=> if the slope for both equations is neither of the above cases ,then the two equations are neither parallel nor perpendicular.
so if we divide the first equation by 3 which is the commen factor for the whole equation and arrange it in the form y=mx +b it would give us y =5x +4. and since the two have the same slope which is 5 ,then we can conclude they are parallel lines.
tommy starts walking from school to home at the same time that his dad starts walking home to school the both depart at 300pm tommy is walking at a speed of 1.35meters pr second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time wil they meet
Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
Given that:-
Tommy starts walking from school to home at the same time that his dad starts walking home to school they both depart at 300pm Tommy is walking at a speed of 1.35meters per second and his dad is walking at a speed of 1.65 meters per second. the distance between home and school is 720 meters at what time will they meetThe time will be calculated by using the relative speed concept.
Relative speed = Speed of father - Speed of Tommy
Relative speed = 1.65 - 1.35
Relative speed = 0.3 meter per second
Relative speed = Distance / Time
0.3 = 720 / Time
Time = 720 / 0.3
Time = 2400 seconds = 2400/ 60 = 40 minutes
We know that both departed at 3 pm they will meet at 3:40 pm.
Therefore Tommy and his father will meet after 2400 seconds or 40 minutes. So they will meet at 3:40 pm.
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The student council members are selling tickets to a school performance. Tickets are $10 for adults, a, and $5 for students, s, and they expect that twice as many students as adults will attend. Their goal is to earn $1500 from ticket sales.
Answer:
How about 100 adults and 100 students?
Step-by-step explanation:
Could you respond?
Select the correct answer from each drop-down menu.
Consider these account options. Then complete the statement.
• Account 1 compounds annually at a rate of 3.00%.
• Account 2 compounds monthly at a rate of 3.25%.
• Account 3 compounds weekly at a rate of 3.10%.
• Account 4 compounds daily at a rate of 3.15%.
Account
yields the highest annual interest rate at
The account that yields the highest annual interest rate is account 2.
Which account yields the highest annual interest rate?
In order to determine the account that yields the highest interest, the effective annual interest has to be calculated. The effective annual interest is the interest rate that an account actually earns when compounding is accounted for.
Effective annual rate = (1 + APR / m ) ^m - 1
M = number of compounding
Account 2: (1 + 0.0325/12)^12 - 1 = 3.3%
Account 3 : (1 + 0.0310 / 52)^52 - 1 = 3.15%
Account 4: (1 + 0.0315 /365)^365 - 1 = 3.2%
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Question 16 (5 points) What's the volume of a cube with a side length of 3 inches? O27 cubic inches O 12 square inches O 12 cubic inches O27 square inches
Answer:
27 cubic inches
Step-by-step explanation:
A cube by definition has all the side lengths equal to each other. Kind of like how a square has all equal sides, except with a cube, there's depth. So the volume of the cube would be the width*length*depth, but since the width=length=depth, you only need one side, and you just cube it, or raise it to the third power. So you have the equation: [tex]A=(3\text{ inches})^3=27\text{ inches}^3[/tex] which is read as 27 cubic inches
You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree. What is the angle of elevation to the location of the kite? Show your work finding the angle of elevation and state the measure of the angle. You are flying a kite and have let out 30 feet of string but it got caught in an 8ft tree . What is the angle of elevation to the location of the kite ? Show your work finding the angle of elevation and state the measure of the angle . PLEASE SHOW ALL WORK !!!
Answer:
use a sin cos tan calculator.
Step-by-step explanation
on calculator
2nd tan
tan x = 30/8
there's ur answer
Find the surface of the rectangular solid
Answer: 80.28 square feet
Step-by-step explanation:
[tex]2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28[/tex]
URGENT! PLS ANSWER QUICK!!!!!!!!
Which best describes the relationship between the line that passes through the points (9, –5) and (5, –2) and the line that passes through the points (–4, –2) and (–8, 1)?
Since the lines have the same slopes, hence they are parallel lines
How to determine the relationship between linesWe can determine the relations by knowing the slopes of the line
For the line with coordinates (9, –5) and (5, –2)
Slope = -2+5/5-9
Slope = -3/4
For the line with coordinates (–4, –2) and (–8, 1)
Slope = 1+2/-8+4
Slope = -3/4
Since the lines have the same slopes, hence they are parallel lines
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What is the approximate area of a circle with a radius of 10 in?
[tex]\huge\boxed{\textsf{A.}\ 78.5\ \text{in}^2}[/tex]
Correction to your question text: diameter, not radius.
The area of a circle is given by:
[tex]A=\pi r^2[/tex]
The radius is half of the diameter.
[tex]A=\pi\cdot\left(\dfrac{10}{2}\right)^2[/tex]
Substitute and solve.
[tex]\begin{aligned}A&=\pi\cdot\left(\frac{10}{2}\right)^2\\&=\pi\cdot5^2\\&=\pi\cdot25\\&\approx\boxed{78.5}\end{aligned}[/tex]
{f(x)=2x+1 g(x)=x2+2x−8
The value of g(x) = 2[f(x)]² - 1 is g(x) = 8x² + 8x + 1
How to find a function?f(x) = 2x+1
Find
g(x) = 2[f(x)]² - 1
Hence,
g(x) = 2[2x + 1]² - 1
g(x) = 2[4x² + 4x + 1] - 1
g(x) = 8x² + 8x + 2 - 1
g(x) = 8x² + 8x + 1
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Which of the following are solutions to the equation below?
Check all that apply.
x²-2x-24 = 0
Answer:
[tex]x=6, x=-4[/tex]
Step-by-step explanation:
1) Let's solve this quadratic equation by factorizing. We need to find two numbers that multiply to -24 and add up to -2 simultaneously. If we pull out the factors of -24, two of them will be -6 and 4, which multiply to -24 as well as add up to -2.
3) Write [tex]-2x[/tex] as a sum.
[tex]x^2-6x+4x-24=0[/tex]
Now, we can factor them out by grouping.
[tex]x^2-6x+4x-24=0\\x(x-6) + 4(x-6)=0[/tex]
Since, [tex]x -6[/tex] is common in both of the factors, we only take one of the [tex]x -6[/tex] along with [tex]x[/tex] and [tex]4[/tex] and all equated to 0.
[tex](x-6)(x+4) = 0[/tex]
Solve for x: [tex]x-6=0[/tex]
[tex]x=0+6\\x=6[/tex]
Solve for x: [tex]x+4=0[/tex]
[tex]x=0-4\\x=-4[/tex]
Therefore, our solutions to this quadratic equation are [tex]x=6, x=-4[/tex].
The numbers 1 through 15 are written on cards. One card is chosen at random. Event A is choosing a
multiple of 5. Event B is choose an even number. What is the probability of choosing a number that
is not a multiple of 5?
Step-by-step explanation:
the probability is always the number of desired cases over the number of all possible cases.
in our situation we have 15 cards.
that is the total possible cases when a random card is chosen.
how many desired cases do we have ?
a number NOT a multiple of 5.
how many are there ?
it is easier to say how many numbers there are being a multiple of 5 : 5, 10, 15
so, 3 numbers out of the 15 are multiple of 5.
that means
15 - 3 = 12 numbers of the 15 are NOT multiples of 5.
so, the probability to draw a card that is not a multiple of 5 is
12/15 = 4/5 = 0.8
the information about event B and even numbers is irrelevant for the question.
Complete the table of inputs and outputs for the given function. F(x)= -5(x+7)
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the function f(x) = -5(x + 7)
When x = -2; f(-2) = -5(-2 + 7) = -25
When x = -1; f(-1) = -5(-1 + 7) = -30
When x = 0; f(0) = -5(0 + 7) = -35
When x = 1; f(1) = -5(1 + 7) = -40
When x = 2; f(2) = -5(2 + 7) = -45
The table of inputs that satisfy the given function is (-2, 25), (-1, -30), (0, 35), (1, -40) and (2, -45).
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What set of transformations could be applied to rectangle ABCD to create A″B″C″D″? 'Rectangle formed by ordered pairs A at negative 4, 2, B at negative 4, 1, C at negative 1, 1, D at negative 1, 2. Second rectangle formed by ordered pairs A double prime at 2, negative 4, B double prime 1, negative 4, C double prime at 1, negative 1, D double prime at 2, negative 1. Reflected over the x‒axis and rotated 180° Reflected over the y-axis and rotated 180° Reflected over the x‒axis and rotated 90° counterclockwise Reflected over the y-axis and rotated 90° counterclockwise
The set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°
What is reflection?"It is a geometric transformation where all the points of an object are reflected on the line of reflection."
For the given question,
The Rectangle ABCD is formed by ordered pairs A at (-4, 2), B at (-4, 1), C at (-1, 1), D at (-1, 2)
The Rectangle A″B″C″D″ is formed by ordered pairs A" at (-4, -2), B" at (-4, -1), C" at (-1, -1) and D" at (-1, -2)
We can observe that the coordinates of ABCD are of the form (-x, y) where x, and y, are positive numbers
The form of the ordered pair of the vertices of the A″B″C″D″ will be (-x, -y)
The coordinates of the point (-x, y) after a reflection over the y-axis would be of the form (x, y)
And after rotation of 180°, the coordinates would be (-x -y).
Hence, the set of transformations that could be applied to ABCD, to create A″B″C″D″ is a reflection over the y-axis, followed by a rotation of 180°.
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Use the Divergence Theorem to evaluate
Integral of (9x + 2y + z2) dS
where S is the sphere
x2 + y2 + z2 = 1.
The value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
How to evaluate the integral?The expression is given as:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS[/tex]
[tex]x^2 + y^2 + z^2 = 1[/tex]
Rewrite the integral as:
[tex]\int\limits^{}_s {9x + 2y + z*z} \, dS[/tex]
As a general rule, we have:
[tex]\int\limits^{}_s {Px + Qy + R*z} \, dS[/tex]
By comparison, we have:
P = 9
Q = 2
R = z
By the divergence theorem, we have:
F = Pi + Qj + Rk
So, we have:
F = 9i + 2j + zk
Differentiate
F' = 0 + 0 + 1
F' = 1
The volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
Where:
r = F' = 1
So, we have:
[tex]V = \frac{4}{3}\pi (1)^3[/tex]
Evaluate
[tex]V = \frac{4}{3}\pi[/tex]
This means that:
[tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
Hence, the value of the integral is [tex]\int\limits^{}_s {9x + 2y + z^2} \, dS = \frac{4}{3}\pi[/tex]
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The length of a rectangle is four times its width. The perimeter is 100 cm. What is the number of square centimeters in the area of the rectangle?
let width be 'x'
according to the question,
length = 4x
perimeter = 100 cm
we know ,
perimeter of rectangle = 2(l+b)
100= 2(4x+x)
100= 10x
x= 10
then length = 4x = 4×10= 40
and , area of rectangle = l×b
= 40 × 10 = 400
area of rectangle is 400cm
Answer:
Step-by-step explanation:
let width=x
length=4x
2(x+4x)=100
2×5x=100
x=100/10=10
width=10 cm
length=4×10=40 cm
area=l×b=40×10=400 cm²
HELP PLSSS WILL GIVE BRAINLIEST PLSSSS
Houa works at an electronics store as a salesperson. Houa earns a 4% commission on the total dollar amount of all phone sales she makes, and earns a 5% commission on all computer sales. Houa had $600 more in computer sales than in phone sales and earned a total of $129 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Houa made and the dollar amount of computer sales she made. Define the variables that you use to write the system.
One of the two equations required in the system of equations needed to determine the dollar amount of phone and computer sales Houa made is y = x + 600.
How do we write the system of equations?Let x represents the dollar amount of phone sales Houa made, and y represents the dollar amount of computer sales she made.
Therefore, a system of equations that could be used to determine x and y can be written as follows:
y = x + 600 ........................................................... (1)
0.04x + 0.05y = 129 ......................................... (2)
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Determine if the following relations are functions. If not, explain.
Answer:
Graph 3 represents a function
Graph 4 is not a function
Step-by-step explanation:
By definition :
A function is a rule or law which relates all the elements of one set with some UNIQUE element of another set.
Which means that from a given value of the input x, there will be only one value of y in a function f(x) = y
Graphically it would represent that for a given point x , there would only be one value of y corresponding to that x.
In graph 4, we can see that for one x, there exists two values of y.
Example : at x = 5, we have y=5 AND y= -5; which is not possible in case of a function.
help me solve this need help asap
Answer:
(-5-5x)/(4x+3
Step-by-step explanation:
Replace x with y to get (-3y-5)/(4y+5). Solve for y to get (-5-5x)/(4x+3).
A man walks to a coffee shop which is 4 km from his house in 20 minutes. Again, he walks to another shop at the same rate, and the total distance covered by him is 10 km in 50 minutes. What is his speed between the coffee shop and the other shop?
a. 10 km/hr
b. 8 km/hr
c. 12 km/hr
d. 6 km/hr
Answer:
c. 12km/hr
Step-by-step explanation:
Speed = distance/time
Coffee shop: Divide distance traveled by time taken to get the speed in km/min, then convert minutes to hours, and finally simplify to calculate the speed in km/hr
4km/20min * 60min/1hr = 240km/20hr = 12km/1hr = 12km/hr
Other shop: Same task, in the question it already says he is traveling at the same rate so this is only useful to check your answer
10km/50min * 60min/1hr = 600km/50min = 12km/1hr = 12km/hr
Find the next term in the following number pattern: 1, 16, 81, 256, 625, ____
Help!
The parallel circuit works if one connector works or both work.
Suppose that connectors work independently of each other and, further,
the probability of each component working is 0.84 and 0.72 respectively. What is the probability the parallel circuit works?
Now A and B are independent
Both connectors must work together to make the parallel circuit work
P(A and B)
P(A)*P(B)(0.84)(0.72)0.6048Connectors be C1 and C2
P(C1)=0.84P(C2)=0.72We need P(C1.C2)
Note the formula
For independent events
[tex]\boxed{\sf P(AB)=P(A)P(B)}[/tex]
[tex]\\ \tt{:}\dashrightarrow P(C1C2)=P(C1)P(C2)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.84(0.72)[/tex]
[tex]\\ \tt{:}\dashrightarrow 0.6[/tex]
Need help please with number 2!!!
Answer:
Step-by-step explanation:
Consider the equation y = 12 – 3x.
Which of the following is a graph of this equation?
Answer:
second graph
Step-by-step explanation:
looking at the y intercept. 12 is y int
Answer:
Second line
Step-by-step explanation:
our equation rearranged is y=-3x+12
meaning that y-intercept is 12, that is where the line cuts the y axis
we find that the second line cuts the y axis around that 12 therefore it is the most relevant line here
Need help with number 9 and number 10
Answer:
9. 3 acute angles
10: a) Acute Isosceles
b) Acute Scalene
Step-by-step explanation:
9: Sum of Interior angle theorem: Sum of the interior angles of a Triangle = 180°
An Acute angle is a angle that is less than 90°
the sum of the two acute angles must be less than 180°
The base angles of an isosceles triangle are congruent.
So For example,
the base angles of the isosceles are ∠1 and ∠2
Lets make the three angle measure closer:
if ∠1 = 46° then ∠2 also have to be 46° and ∠3 = 88°
all three angle are less than 90° and two angles are congruent.
I need help with this please
There are 36 possible combinations that can occur when 2 dice are rolled. For the sake of this question, we'll count instances where dice 1 = 3/dice 2 = 2 and dice 1 = 2/dice 2 = 3.
Now, let's think about all of the possible ways a total of 5 could be rolled.
1 + 4
2 + 3
3 + 2
4 + 1
That's 4 possibilities to roll a total of 5 out of 36 possible outcomes.
4 / 36 = ? / 180
---Now, we need to use a proportion in order to figure out the possibilities out of 180.
36x = 720
x = 20
If you rolled a pair of fair dice 180 times, you would expect to roll a total of 5, 20 times.
Hope this helps!
6. The length of the minor arc AB of a circle, centre O, is 2π cm and the length of the major arc is 22π cm. Find:
a) the radius of the circle
b) the acute angle AOB.
Answer:
a) 24 [cm]; b) 30°.
Step-by-step explanation:
a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];
b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:
m(∠AOB)=360*(1/12)=30°.
solve for x
A:10 B:14.5 C:20 D:6÷3
By applying Cathetus theorem, the value of x is equal to 10 units.
How to determine the value of x?In order to determine the value of x, we would apply Cathetus theorem (leg rule), which states that each leg of a right-angled triangle is the geometric mean that's directly proportional between the hypotenuse and the part of the hypotenuse that's directly below the leg.
In this context, we have:
x² = m × a
x² = (21 + 4) × 4
x² = 25 × 4
x² = 100
x = √100
x = 10 units.
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Points out
1.00
P Flag
question.
Instructions: Given the preimage and image, find the dilation scale factor. Use the forward slash (i.e.
"/") for all fractions (e.g. -1/2 is the same as
-6 -5
Scale Factor:
5
J'
-3 -2 -1
P
KT
3
T
4
5 6
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Dilation is the increase or decrease in size of a figure by a scale factor.
The scale factor of the image = K'T'/KT = 1/2 ÷ 1 = 1/2
The dilation scale factor used to form polygon K'T'P'J' from polygon KTPJ is 1/2
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Firm X is a monopolist with marginal cost of $37/unit. If elasticity of demand is -9, use the markup formula to determine the price Firm X should charge to maximize profit.
Step-by-step explanation:
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The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 11 mL. Suppose that 12 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.
What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
If a single randomly selected individual is observed, find the probability that this person consumes is between 59.3 mL and 61.2 mL.
For the group of 12 pancake eaters, find the probability that the average amount of syrup is between 59.3 mL and 61.2 mL.
For part d), is the assumption that the distribution is normal necessary? YesNo
Using the normal distribution and the central limit theorem, we have that:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 60, \sigma = 11, n = 12, s = \frac{11}{\sqrt{12}} = 3.1754[/tex].
Hence:
The distribution of X is [tex]X \approx N(60,11)[/tex].The distribution of [tex]\bar{X}[/tex] is [tex]\bar{X} \approx (60,3.1754)[/tex].The probabilities are given by the p-value of Z when X = 61.2 subtracted by the p-value of Z when X = 59.3, hence, for a single individual:
X = 61.2:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{61.2 - 60}{11}[/tex]
Z = 0.11
Z = 0.11 has a p-value of 0.5398.
X = 59.3:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{59.3 - 60}{11}[/tex]
Z = -0.06
Z = -0.06 has a p-value of 0.4761.
0.5398 - 0.4761 = 0.0637.
0.0637 = 6.37% probability that a single person consumes between 59.3 mL and 61.2 mL.
For the sample of 12, we have that:
X = 61.2:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{61.2 - 60}{3.1754}[/tex]
Z = 0.38
Z = 0.38 has a p-value of 0.6480.
X = 59.3:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59.3 - 60}{3.1754}[/tex]
Z = -0.22
Z = -0.22 has a p-value of 0.4129.
0.6480 - 0.4129 = 0.2351 = 23.51% probability that the sample mean of the consumption of 12 people is between 59.3 mL and 61.2 mL. Since the sample size is less than 30, a normal distribution has to be assumed.
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