Yes, a normal approximation is appropriate because both the sample size (n = 460) and the expected number of successes (460 × 0.16 = 73.6) are greater than 10.
We have,
In order to determine whether a normal approximation is appropriate, we need to check whether certain conditions are met.
One of these conditions is that the sample size n should be large enough, usually at least 30.
In this case,
We have a sample size of 460 which is large enough, so a normal approximation is likely to be appropriate.
However, we also need to make sure that the population size is much larger than the sample size so that the sampling is done with replacement.
If the population size is small relative to the sample size, then the sampling will be done without replacement, and we cannot use a normal approximation.
Now,
The sample size n = 460 and the expected number of successes:
= 460 × 0.16
= 73.6
This is greater than 10.
The expected number of failures.
= 460 × 0.84
= 386.4
This is also greater than 10.
Thus,
Yes, a normal approximation is appropriate because both the sample size (n = 460) and the expected number of successes (460 × 0.16 = 73.6) are greater than 10.
Learn more about normal approximation here:
https://brainly.com/question/24163530
#SPJ1
determine whether the following statement is true or false. if it is false, rewrite it as a true statement. if two events are independent, p(a|b)=p(b).A. TrueB. False, if events A and B are independent, then P (A and B) = P (A) * P (B)C. False, if events A and B are independent, then P (A and B) = 0 D. False, if events A and B are independent, then P (BIA) = P (A)
Answer: A is true, B is False, C is False and D is True.
Step-by-step explanation:
A. True. This statement is true by definition of independent events.
B. False. The correct statement is: If events A and B are independent, then P(A ∩ B) = P(A) * P(B). This is the definition of independent events.
C. False. If events A and B are independent, then P(A ∩ B) = P(A) * P(B). Since neither P(A) nor P(B) is necessarily zero, it follows that P(A ∩ B) is also not necessarily zero.
D. True. If events A and B are independent, then P(B|A) = P(B) and by rearranging the conditional probability formula, we get P(B ∩ A) = P(B|A) * P(A) = P(B) * P(A). Similarly, we can also show that P(A|B) = P(A), which means that P(B|A) = P(B) = P(A|B).
Learn more about probability here, https://brainly.com/question/25839839
#SPJ11
Compute the y-intercept if x-bar = 57, y-bar = 251, sx= 12, sy= 37 and r = 0.341. A)244.40 B)191.1 C)1.05
Answer:
C
Step-by-step explanation:
The y-intercept is approximately 191.1. The correct option is (B).
To compute the y-intercept, we need to use the equation of the regression line, which is:
y = a + bx
where a is the y-intercept, b is the slope, x is the independent variable (in this case, x-bar), and y is the dependent variable (in this case, y-bar).
The formula for the slope of the regression line is:
b = r * (sy/sx)
where r is the correlation coefficient, sx is the standard deviation of x, and sy is the standard deviation of y.
Substituting the given values, we get:
b = 0.341 * (37/12) = 1.05025
Now, we can use the formula for the y-intercept:
a = y-bar - b * x-bar
Substituting the given values, we get:
a = 251 - 1.05025 * 57 = 191.10925
Therefore, the y-intercept is approximately 191.1.
The answer is B) 191.1.
To know more about intercepts refer here :
https://brainly.com/question/14180189#
#SPJ11
I need help with this question
The correct equation for finding the value of d and the the distance between the sun and star is,
⇒ d = x cosФ
Given that;
Diagram for finding the distance between the sun and star.
Let us assume that, the distance between the sun and star is x
Now, We can formulate;
⇒ cos Ф = d / x
⇒ d = x cosФ
Therefore, The correct equation for finding the value of d and the the distance between the sun and star is,
⇒ d = x cosФ
Thus, Correct equation is,
⇒ d = x cosФ
Learn more about the angle visit:;
https://brainly.com/question/25716982
#SPJ1
need help in screenshot...
The solution to the expressions using laws of exponents are:
a) 625x⁴
b) a²²
c) m²¹m⁹
d) ¹/₂b²c⁻⁶
e) (m/n)²¹
How to use Laws of Exponents?Some of the laws of exponents are:
- When we multiply same bases, we retain the base the same and then add the exponents.
- When we raise a base with a power to another power, we keep the base the same and then multiply the exponents.
- When we divide same bases, we keep the base the same and subtract the denominator exponent from the numerator exponent.
a) (5x)⁴ = 5⁴x⁴
= 625x⁴
b) a³ * a¹⁷ * a²
= a³⁺¹⁷⁺²
= a²²
c) (m⁷/m⁻³)³
= m⁷*³m³*³
= m²¹m⁹
d) a⁰b⁷c⁻³/(2b⁵c³)
= ¹/₂b⁷⁻⁵c⁻³⁻³
= ¹/₂b²c⁻⁶
e) (m/n)¹² ÷ (n/m)⁻⁹
= (m/n)¹² * (m/n)⁹
= (m¹²/n¹²) * (m⁹/n⁹)
= (m/n)²¹
Read more about Laws of Exponents at: https://brainly.com/question/11761858
#SPJ1
___x + 2x + (-4 + 9)=___x + ____
pls help
The missing values are 7 and -4.
We have,
Combine like terms on the left side of the equation:
3x + 5 = ax + b
Since the equation holds for all values of x, we can substitute in a specific value of x and solve for the unknowns a and b.
Let's use x = 1:
3(1) + 5 = a(1) + b
Simplifying:
a + b = 8
Now let's use x = 2:
3(2) + 5 = a(2) + b
Simplifying:
2a + b = 11
We now have two equations with two unknowns:
a + b = 8
2a + b = 11
Subtracting the first equation from the second:
a = 3
Substituting into the first equation:
3 + b = 8
b = 5
Thus,
The missing values are 7 and -4:
Learn more about equations here:
https://brainly.com/question/3118662
#SPJ1
One inlet pipe can fill an empty pool in 16 hours, and a drain can empty the pool in 20 hours. How long will it take the pipe to fill the pool if the drain is left open? Express your answer as a reduced fraction. ____________ hours
It takes 80 hours to fill the pool when the drain is left open.
To solve this problem, we can consider the rates at which the inlet pipe and drain can fill and empty the pool, respectively.
The rate of the inlet pipe is 1 pool per 16 hours, which can be expressed as 1/16 pool per hour.
The rate of the drain is 1 pool per 20 hours, or 1/20 pool per hour.
When both the inlet pipe and drain are open, their rates add up. Therefore, the net rate at which the pool is being filled is:
1/16 - 1/20 = 5/80 - 4/80 = 1/80 pool per hour.
Know more about inlet pipe here:
https://brainly.com/question/15122557
#SPJ11
Find the discount or the sale price.
18. Find the discount on a $30 blouse that is on sale for
15% off.
19. Find the sale price of a $24 pair of sunglasses that is on sale
for 25% off.
Answer:
18. $4.50
19. $18
Step-by-step explanation:
18.
The discount is 15%.
The original price is $30.
The discount is 15% of $30.
To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by dividing the percent by 100.
15% of $30 = 15% × $30 = 0.15 × $30 = $4.50
19.
The discount is 25%.
The original price is $24.
The discount is 25% of $24.
To find a percent of a number, multiply the percent by the number. Change the percent to a decimal by dividing the percent by 100.
25% of $24 = 25% × $24 = 0.25 × $24 = $6
The discount is $6.
Now we subtract the amount of the discount, $6, from the original price.
$24 - $6 = $18
Answer: $18
a cookie manufacturer sells boxes of cookies that claim to weigh 16 ounces on the packaging. due to variation in the manufacturing process, the weight of the manufactured boxes follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.25 ounce. the manufacturer decides it does not want to sell any boxes with weights below the 1st percentile so as to avoid negative customer responses. what is the minimum acceptable weight, in ounces, of a box of cookies? round your answer to two decimal places.
Rounding to two decimal places, the minimum acceptable weight of a box of cookies is 15.42 ounces.
weight of the boxes of cookies follows a normal distribution with a mean of 16 ounces and a standard deviation of 0.25 ounces.
To find the minimum acceptable weight of a box of cookies, we need to find the value that corresponds to the 1st percentile of the normal distribution.
Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 1st percentile is approximately -2.33.
We can use the formula z = (x - μ) / σ, where x is the minimum acceptable weight, μ is the mean, and σ is the standard deviation, to solve for x.
Plugging in the values, we get:
-2.33 = (x - 16) / 0.25
Solving for x, we get:
x = -2.33 * 0.25 + 16 = 15.4175
Rounding to two decimal places, the minimum acceptable weight of a box of cookies is 15.42 ounces.
to learn more about deviation click here:brainly.com/question/31835352
#SPJ11
if n(t)=ce−λt, where c is some constant, what is dn(t)dt?
The derivative dn(t)/dt is: dn(t)/dt = c * e^(-λt) * -λ
So, dn(t)/dt = -λce^(-λt)
To find the derivative of n(t) = ce^(-λt) with respect to t, which is dn(t)/dt, follow these steps:
1. Identify the function n(t) = ce^(-λt) where c is a constant and λ is another constant.
2. Apply the chain rule for differentiation, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
So, we have:
dn(t)/dt = d(ce^(-λt))/dt = c * d(e^(-λt))/dt (since the constant c can be pulled out of the derivative)
Now, we need to find the derivative of the exponential function e^(-λt). Since it is a composite function, we'll use the chain rule again:
d(e^(-λt))/dt = e^(-λt) * d(-λt)/dt = e^(-λt) * -λ (because the derivative of -λt with respect to t is -λ)
Therefore, the derivative dn(t)/dt is:
dn(t)/dt = c * e^(-λt) * -λ
So, dn(t)/dt = -λce^(-λt).
To know more about derivatives refer here :
https://brainly.com/question/28672151#
#SPJ11
Which one is NOT an acceptable name for <1?
The option that is not an acceptable name for < 1 is D) improper.
How to define the digit ?This name properly refers to a numerical value that is less than one and denotes the decimal representation of a fractional quantity, with its numerator smaller than the denominator. Thus, this numerical denomination corresponds precisely to any number existing between zero and one.
Furthermore, it should be noted that this nomenclature exclusively applies exclusively to numbers below one, and not above it, since that would signify figures greater than one.
Find out more on acceptable names at https://brainly.com/question/17242320
#SPJ1
Options are:
A) negative
B) fraction
C) decimal
D) improper
if f(x)=x^2+2x then d/dx(f(lnx))=
Therefore, the derivative of f(lnx) with respect to x is 2ln(x)/x + 2/x.
To find d/dx(f(lnx)), we need to use the chain rule of differentiation.
Let's first find f(lnx):
f(lnx) = (lnx)^2 + 2(lnx)
Now, we can differentiate f(lnx) with respect to x:
d/dx(f(lnx)) = d/dx((lnx)^2 + 2(lnx))
To apply the chain rule, we need to find the derivative of the inside function, ln(x), with respect to x:
d/dx(lnx) = 1/x
Using the chain rule, we have:
d/dx(f(lnx)) = d/dx((lnx)^2 + 2(lnx))
= 2(lnx)(1/x) + 2(1/x)
Simplifying, we get:
d/dx(f(lnx)) = 2ln(x)/x + 2/x
To know more about derivative visit:-
https://brainly.com/question/25324584
#SPJ11
Kendra is training for a marathon she currently runs 22. 8 miles each saturday next week she willl incease he distance by 15%
Kendra is training for a marathon. Next week, Kendra will run 26.22 miles.
Kendra's current distance of running 22.8 miles each Saturday indicates a good level of endurance and fitness. However, to prepare for a marathon, she will need to gradually increase her running distance. Kendra has planned to increase her distance by 15% from her current distance. To calculate her new distance, we can use the following formula:
New distance = Current distance + (Percentage increase × Current distance)
Plugging in the values, we get:
New distance = 22.8 + (15% × 22.8) = 26.22 miles (rounded to two decimal places)
Kendra's new distance of 26.22 miles represents a significant increase from her current distance. It is important to note that Kendra should continue to gradually increase her running distance over time to avoid injury and improve her endurance. She can also incorporate other forms of exercise, such as strength training and cross-training, to complement her running and improve overall fitness. By following a well-rounded training plan, Kendra can increase her chances of successfully completing the marathon and achieving her fitness goals.
Learn more about training here
https://brainly.com/question/26270137
#SPJ11
Find the area of a horizontal cross section of a cylinder with a height of 34
centimeters and a circumference of about 131.88
centimeters. Use 3.14
for pie
Answer:
1384.74 square centimeters
Step-by-step explanation:
The area of a horizontal cross section of a cylinder is the same as the area of the circular base of the cylinder.
To find the area of the circular base of the cylinder, we first need to find the radius of the circle.
The formula for the circumference of a circle is C = 2πr, where r is the radius.
Given the circumference of the cylinder is 131.88 cm, and using 3.14 for π, we can use circumference formula to find the radius of the circular base:
[tex]\begin{aligned}C &= 2\pi r\\\\\implies 131.88 &= 2 \cdot 3.14 \cdot r\\\\131.88 &= 6.28 r\\\\\dfrac{131.88}{6.28} &= \dfrac{6.28 r}{6.28}\\\\21&=r\\\\r&=21\; \sf cm\end{aligned}[/tex]
Substitute the found value of r into the formula for the area of a circle to find the area of a horizontal cross section of the cylinder:
[tex]\begin{aligned}A &= \pi r^2\\\\A&=3.14 \cdot 21^2\\\\A&=3.14 \cdot 441\\\\A&=1384.74\;\sf cm^2\end{aligned}[/tex]
Therefore, the area of a horizontal cross section of the cylinder is approximately 1384.74 square centimeters.
Answer:
1384.74 cm²-------------------------
The circumference is given as 131.88 centimeters.
We know that the formula for the circumference is:
C = 2πr, where r is the radiusSo,
2πr = 131.88Solve for radius:
r = 131.88 / (2 × 3.14) = 21 cmUse the area formula:
A = πr²Substitute 21 cm for r and calculate the area:
A = 3.14 × 21² = 1384.74 cm²the card game euchre uses a deck with 32 cards: ace, king, queen, jack, 10, 9, 8, and 7 of each suit. suppose you choose one card at random from a well-shuffled euchre deck. what is the probability that the card is a jack, given that you are told it is a face card (jack, queen, or king of any suit)?
The probability of drawing a jack, given that we are told it is a face card, is 1/3 or approximately 0.33.There are 12 face cards in a well-shuffled euchre deck, comprising of 4 jacks, 4 queens, and 4 kings. The probability of drawing a face card from the deck is 12/32, or 3/8.
Now, we are asked to find the probability of drawing a jack, given that we already know the card is a face card. This can be calculated using conditional probability, which is the probability of an event occurring given that another event has already occurred.
The probability of drawing a jack given that the card is a face card can be represented as P(Jack | Face card). Using Bayes' theorem, we can calculate this probability as follows:
P(Jack | Face card) = P(Face card | Jack) * P(Jack) / P(Face card)
Here, P(Face card | Jack) represents the probability of drawing a face card given that the card is a jack, which is 1. P(Jack) represents the probability of drawing a jack from the deck, which is 4/32 or 1/8.
We already know that P(Face card) is 3/8.Substituting these values into the formula, we get:
P(Jack | Face card) = (1 * 1/8) / (3/8) = 1/3.
For such more questions on Probability:
https://brainly.com/question/24756209
#SPJ11
Julia takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut she makes is 7 inches long, and the length of the fabric is 5 inches. What is the fabric's width? If necessary, round to the nearest tenth.
inches
Answer:
4.9 inches
Step-by-step explanation:
c^2=a^2+b^2
7^2=5^2+b^2
b^2=7^2-5^2
b^2=24
b= square root of 24
=4.898979486
=4.9 inches
is being 2-edge-connected a transitive property? that is, if v and w are 2-edge-connected and w and y are 2 edge-connected, can you conclude that v and y are 2-edge-connected? prove your answer. you can use the fact that if there is a walk from vertex v to vertex w, then there is a path from vertex v to vertex w.
No, being 2-edge-connected is not a transitive property. Counterexamples can be constructed to show that the conclusion does not always hold.
For example, consider a graph with four vertices v, w, x, and y, where v and w are adjacent, as well as w and x, and x and y. In this case, v and w, and w and y are 2-edge-connected, but v and y are not 2-edge-connected since there is only one edge connecting them.
Thus, it can be concluded that being 2-edge-connected is not a transitive property, and counterexamples can be constructed to demonstrate this fact.
To learn more about graph click here:brainly.com/question/17267403
#SPJ11
A table of values for function A and the graph function B are shown. Create an equation for a third linear function with a rate of change that is between the rates of change for function A and function B
The equation for the third linear function is y = (3/4)x + 1/2
To find an equation for the third linear function with a rate of change between functions A and B, we need to find a slope that is greater than 3/4 but less than 3/4. One way to do this is to take the average of the slopes for A and B:
slope_avg = (3/4 + 3/4) / 2 = 3/4
Now that we have the slope for the third linear function, we can use any of the given points to find the y-intercept or constant term in the equation. Let's use the point (2, 2.5):
y = mx + b
2.5 = (3/4) * 2 + b
b = 2.5 - 3/2 = 1/2
Therefore, the equation for the third linear function is:
y = (3/4)x + 1/2
This equation has a slope that is between the slopes of functions A and B and passes through the point (2, 2.5).
To know more about equation here
https://brainly.com/question/10413253
#SPJ1
a number is stored in cell a1. write an excel formula that will square this number.
The value of an excel formula that will square this number is,
⇒ N²
We have to given that;
A number is stored in cell a1.
Hence, We can formulate;
Type = N² into the empty cell, in which N is a cell reference that contains the numeric value you want to square.
And, We also get;
To display the square of the value in cell A1 into cell B1,
We can type = A1² into cell B1.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs. Find the solution of the initial value problem: x" + 9x = 12 sin(3t), x(0) = x'(0) = 0 x(t) = Graph the solution to confirm the phenomenon of Pure Resonance
The solution to the initial value problem is x(t) = 4/27 sin(3t).
We have solved the initial value problem x" + 9x = 12 sin(3t), x(0) = x'(0) = 0 and graphed the solution to confirm the phenomenon of pure resonance.
First, we need to solve the differential equation x" + 9x = 12 sin(3t) using standard techniques from differential equations. We can begin by assuming a solution of the form x(t) = A sin(3t) + B cos(3t), where A and B are constants to be determined. Taking the first and second derivatives of x(t), we find
=> x'(t) = 3A cos(3t) - 3B sin(3t) and x''(t) = -9A sin(3t) - 9B cos(3t).
Substituting these expressions into the differential equation, we obtain
=> -9A sin(3t) - 9B cos(3t) + 9A sin(3t) + 9B cos(3t) = 12 sin(3t).
Simplifying, we get 0 = 12 sin(3t), which implies that sin(3t) = 0.
This has solutions at t = 0, pi/3, 2pi/3, pi, etc.
These are the resonant frequencies of the system, where the external force is in phase with the natural frequency of the system.
To find the constants A and B, we can use the initial conditions x(0) = 0 and x'(0) = 0. Substituting t = 0 into the expressions for x(t) and x'(t), we get A = 0 and B = 0.
Therefore, the solution to the initial value problem is x(t) = 4/27 sin(3t).
Now let's graph the solution to confirm the phenomenon of pure resonance. We can use a graphing calculator or software to plot the function x(t) = 4/27 sin(3t) over a suitable range of t. We can also graph the external force 12 sin(3t) to see how it compares to the motion of the system.
To know more about graph here
https://brainly.com/question/17267403
#SPJ4
the number of regions created when constructing a venn diagram with three overlapping sets is
The number of regions created when constructing a Venn diagram with three overlapping sets depends on the arrangement of the sets and their overlaps.
The number of regions created when constructing a Venn diagram with three overlapping sets is 8.
1. Draw three overlapping circles to represent the three sets.
2. Identify the distinct regions formed by the overlaps.
3. Count the number of distinct regions.
In a Venn diagram with three overlapping sets, you'll have these regions:
1. Only set A
2. Only set B
3. Only set C
4. Intersection of sets A and B
5. Intersection of sets A and C
6. Intersection of sets B and C
7. Intersection of set A, set B, and set C
8. The region outside all three sets
Thus, a total of eight regions are formed in a Venn diagram with three overlapping sets. However, in general, the formula for calculating the number of regions in a Venn diagram with three sets is 23 + 22, which equals 6. This means that there are six regions created when three circles overlap in a Venn diagram.
Learn more about Venn diagram:
brainly.com/question/29301560
#SPJ11
How can i show that p^(q-1) + q^(p-1) = 1 (mod pq)?
Step-by-step explanation:
you can just put in some values to check.
I actually used p =2 and q=3
the It will be
2^3-1 + 3^2-1 = 1 (mod 2×3)
2^2 +3^1 = 1 (mod 6)
4+3= 1 (mod6)
7= 1 (mod6)
which is true.
therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true
To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.
Therefore, we can write:
p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)
By the Chinese Remainder Theorem, we can combine these two equations to obtain:
p^(q-1) + q^(p-1) = 1 (mod pq)
Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).
Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)
Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)
Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))
Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)
In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)
To learn more about integer : brainly.com/question/15276410
#SPJ11
ASAP PLEASE!!!! A rectangular prism is made of stainless steel.
The prism measures 15 cm long, 10 cm wide, and 2 cm high.
The density of stainless steel is 7.9 g/cm³ what is the mass, in grams, of the prism?
The mass of the prism is 2370 g
How to determine the mass
The formula for calculating the volume of a rectangular prism is expressed as;
V = lwh
Such that the parameters are;
V is the volumew is the widthh is the height of the prismFrom the information given, we have that;
Volume = 15 × 10 × 2
Multiply the values, we get;
Volume = 300 cm³
The formula for density of the material is expressed as;
D = m/v
Where m is the mass and v is the volume
Substitute the values
m = 7. 9 × 300
Multiply the values
m = 2370 g
Learn about volume at: https://brainly.com/question/1972490
#SPJ1
the forward selection procedure starts with _____ independent variable(s) in the multiple regression model. question 7 options: a) one b) two c) all d) no
The forward selection procedure is a method of building a multiple regression model that involves starting with a single independent variable and gradually adding more variables based on their significance in improving the model's fit.
Therefore, the answer to this question is a) one, since the procedure starts with only one independent variable in the model.
The forward selection procedure is a popular method of model selection because it is relatively simple to implement and can lead to models that are both parsimonious and highly predictive.
However, it is important to use caution when interpreting the results of a forward selection procedure, as the final model may not be the best or most accurate representation of the data.
Other methods of model selection, such as backward elimination or stepwise regression, may be more appropriate in certain situations.
Know more about the forward selection procedure here:
https://brainly.com/question/31412178
#SPJ11
The line passing through the points a(-1,3l)andb(k,3)is parallel to the line whose equation is2y+3x=9 write the co-ordinates of a andb
The coordinates of point A are A(-1, 3l) and the coordinates of point B are B(k, 3), where k = 3l - (3/2).
To determine the coordinates of points A (-1, 3l) and B (k, 3) that lie on a line parallel to the line with the equation 2y + 3x = 9, we need to find the value of k for point B.
Given that the lines are parallel, they have the same slope. The equation 2y + 3x = 9 can be rewritten in slope-intercept form as y = -(3/2)x + 9/2, where the coefficient of x (-3/2) represents the slope of the line.
Since the lines are parallel, the slope of the line passing through points A and B should also be -3/2. Now we can find the value of k by substituting the coordinates of point A into the equation.
3l = -(3/2)(-1) + b
3l = (3/2) + b
3l - (3/2) = b
b = 3l - (3/2)
Know more about coordinates here:
https://brainly.com/question/16634867
#SPJ11
i need help please hurry.
The equation of height of each pyramid inside the cube is,
⇒ h = 2V / B
The equation that represent the volume of each pyramid is,
⇒ V = LWH / 3
The equation that represent the volume of each pyramid if the height of each pyramid is h and area of the base is B,
⇒ V = 1/3 (B × h)
Given that;
To find the formula for height and volume of pyramid.
Now, We know that;
The equation of height of each pyramid inside the cube is,
⇒ h = 2V / B
And, The equation that represent the volume of each pyramid is,
⇒ V = LWH / 3
And, The equation that represent the volume of each pyramid if the height of each pyramid is h and area of the base is B,
⇒ V = 1/3 (B × h)
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
This rectangular prism is made up of one-unit cubes. Find the
surface area of the rectangular prism
square units
Help me please
The surface area of the rectangular prism is 332 unit ²
What is surface area of prism?The area occupied by a three-dimensional object by its outer surface is called the surface area. Generally, the surface area of a prism is expressed as: SA = 2B + ph
Moreover, we can calculate the surface area of rectangular prism as;
SA = 2(lb + lh +bh)
l = 10 units
b = 4 units
h = 9 units
SA = 2(10×4 + 10×9 + 4×9)
SA = 2( 40+90+36)
SA = 2( 166)
SA = 332 units²
therefore the area of the prism is 332 unit ²
learn more about surface area of prism from
https://brainly.com/question/1297098
#SPJ1
You would like to purchase a home that is $216,000. What is the 20% down payment on the house?
The down payment is $43,200 on the house.
The 20% down payment on a $216,000 house is:
20% x $216,000
Let us convert the 20% to decimal value
To do this we have to divide 20 by 100
20/100=0.2
To find down payment multiply 0.2 with $216,000
0.2×216,000
= $43,200
Therefore, the down payment is $43,200 on the house.
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ1
Mr. Walker is hiking across Massachusetts he has three days to go 70 miles on the first day he works six hours at a speed of 4 mph on the second day he walked the same number of hours that speed was only 3 mph another day he worked eight hours to cover the remaining distance what was the speed on the third day
The speed on the third day was 3.5 mph.
To determine the speed on the third day, we need to find the total time Mr. Walker spent walking and the total distance he covered.
On the first day, he worked for 6 hours at a speed of 4 mph. Therefore, the distance covered on the first day is:
Distance = Speed * Time = 4 mph * 6 hours = 24 miles.
On the second day, he also worked for 6 hours at a speed of 3 mph. Therefore, the distance covered on the second day is:
Distance = Speed * Time = 3 mph * 6 hours = 18 miles.
To find the distance remaining after the first two days, we subtract the distances covered from the total distance:
Remaining distance = 70 miles - 24 miles - 18 miles = 28 miles.
On the third day, Mr. Walker worked for 8 hours to cover the remaining distance of 28 miles. Therefore, the speed on the third day is:
Speed = Distance / Time = 28 miles / 8 hours = 3.5 mph.
Know more about speed here:
https://brainly.com/question/28224010
#SPJ11
THE GCF OF 18 AND 36 AND ME 2. I AM A MULTIPLE OF 5. I AM GREATER THAN 18 LESS THAN 30. WHAT AM I?
The only number that fits these criteria is 25, which is a multiple of 5, greater than 18, and less than 30. The number is 25.
Supporting answer: To find the GCF (Greatest Common Factor) of 18 and 36, we need to find the largest number that can divide both 18 and 36 evenly. We can start by listing out the factors of 18 and 36:
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors of 18 and 36 are 1, 2, 3, 6, 9, and 18. The largest of these factors is 18, so the GCF of 18 and 36 is 18.
Next, we need to find a number that is a multiple of 5, greater than 18, and less than 30. The only number that fits these criteria is 25, which is a multiple of 5, greater than 18, and less than 30.
Therefore, the answer is 25.
Learn more about criteria here
https://brainly.com/question/1788910
#SPJ11
225,165 people visited Korina's website on Saturday. On Sunday, the number of visitors decreased by 1,000. How many people visited Korina's website on Sunday?
As the number of people visiting each day is the same 404 people visited on Sunday.
We have,
A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday and the number of people who visited on each day is the same.
As the number of visitors is same on each day and the total number of days is three each they the number of people visited is,
= (1212/3).
= 404.
So, On Sunday 404 visitors were there.
learn more about the unitary method here :
brainly.com/question/28276953
#SPJ1
complete question:
The water park had a total of 1,212 visitors on Friday, Saturday, and Sunday. If the same number of people visited each day, how many visitors were there on Sunday
