An equation can be defined as a mathematical statement in which two expressions are set equal to each other. In simple words, equations mean equality i.e. the equal sign. Since equations are all about “equating one quantity with another”,they are simply known as equation
Answer:
In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. ... For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Suppose a research company takes a random sample of 45 business travelers in the financial industry and determines that the sample average cost of a domestic trip is $1,192, with a sample standard deviation of $279. Construct a 98% confidence interval for the population mean (for domestic trip) from these sample data. Round your answers to 3 decimal places.
Answer:
98% confidence interval for the population mean =(1095.260,1288.740)
Step-by-step explanation:
We are given that
n=45
[tex]\mu=1192[/tex]
Standard deviation,[tex]\sigma=279[/tex]
We have to construct a 98% confidence interval for the population mean.
Critical value of z at 98% confidence, Z =2.326
Confidence interval is given by
[tex](\mu\pm Z\frac{\sigma}{\sqrt{n}})[/tex]
Using the formula
98% confidence interval is given by
[tex]=(1192\pm 2.326\times \frac{279}{\sqrt{45}})[/tex]
[tex]=(1192\pm 96.740)[/tex]
=[tex](1192-96.740,1192+96.740)[/tex]
=[tex](1095.260,1288.740)[/tex]
Hence, 98% confidence interval for the population mean (1095.260,1288.740)
The diagram below shows rectangle ABC is a midtsin of
BC, such that D,E and F are on the same line API AD
i = 53, 13" BE-sm
and DE 2 EF
84
2176
F
with reasons
3.1 Prove
AB - BF
3.2. Calculate AD
3.3 Complece. In are rigter angled A BEF, son 53, 13" - BE
Answer:
4x2+3=
Step-by-step explanation:
what number when multiplied by 5 is one third of the sum of 64 and 56?
Answer:
8
Step-by-step explanation:
Create an expression to model the situation. One can do this by simply rewriting the written expression in terms of numbers and variables. Use the variable (x) to represent the unknown value.
[tex]5(x)=\frac{1}{3}(64+56)[/tex]
Simplify this expression,
[tex]5(x)=\frac{1}{3}(64+56)\\5x=\frac{1}{3}(120)\\5x=40\\[/tex]
Use inverse operations to solve for (x),
[tex]5x=40\\x=8[/tex]
Pasagot po kasi d kopo alam
Answer:
ano po ba ga gawin jn? para masagutan ko po
Two vectors and are given by and . If these two vectors are drawn starting at the same point, what is the angle between them
Answer: hello your question is incomplete below is the complete question
The Two vectors; A = 5i + 6j +7k and B = 3i -8j +2k.
answer;
angle = 102°
Step-by-step explanation:
multiplying the vectors
A.B = |A| * |B|* cosθ
hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )
= 15 - 48 + 14 /(√25+26+29) * (√9+64+4)
= -0.206448454
θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°
If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)
Answer:
a) The bullet hits the ground after 64 seconds.
b) The bullet hits the ground 113,511.7 feet away.
c) The maximum height attained by the bullet is of 16,384 feet.
Step-by-step explanation:
Equations of motion:
The equations of motion for the bullet are:
[tex]x(t) = (v_0\cos{\alpha})t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]
In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.
Initial speed of 2048 ft/s at an angle of 30o to the horizontal.
This means that [tex]v_0 = 2048, \alpha = 30[/tex].
So
[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]
(a) After how many seconds will the bullet hit the ground?
It hits the ground when [tex]y(t) = 0[/tex]. So
[tex]1024t - 16t^2 = 0[/tex]
[tex]16t^2 - 1024t = 0[/tex]
[tex]16t(t - 64) = 0[/tex]
16t = 0 -> t = 0 or t - 64 = 0 -> t = 64
The bullet hits the ground after 64 seconds.
(b) How far from the gun will the bullet hit the ground?
This is the horizontal distance, that is, the x value, x(64).
[tex]x(64) = 1773.62(64) = 113511.7[/tex]
The bullet hits the ground 113,511.7 feet away.
(c) What is the maximum height attained by the bullet?
This is the value of y when it's derivative is 0.
We have that:
[tex]y^{\prime}(t) = 1024 - 32t[/tex]
[tex]1024 - 32t = 0[/tex]
[tex]32t = 1024[/tex]
[tex]t = \frac{1024}{32} = 32[/tex]
At this instant, the height is:
[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]
The maximum height attained by the bullet is of 16,384 feet.
Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.
Answer:
Step-by-step explanation:
B looks like it would work.
You add speeds * time when you are travelling in opposite directions.
I don't know why you would add or subtract 1 as in A and C
120 * t = 540
t = 540/120
t = 4.5 hours.
So after 4.5 hours they are 540 miles apart.
Answer:
b
Step-by-step explanation:
Check out the attachment and help me out please!!!
Answer:
20
Step-by-step explanation:
4 + 2 + 5 + 4 + 0 + 1 + 1 + 3 = 20
Multiply 25 x 47 x 3
Instruction
Active
Identifying a Graphical Solution
Try it
Which represents the solution of x2 + y2 > 16 and y? < 4x?
HE
of
64
N
2
2
N-
4
2
4
Answer: The Third Graph/ C
Step-by-step explanation:
Calculate the number of ways to form a set of three distinct items such that no two of the selected items are in the same row or same column
Answer:
1200
Explanation:
Order does not matter, if we said xyz order, it would still not make a difference if it was zyx or yzx hence we use the combination formula:
nCr = n! / r! * (n - r)!
where n= total number of items
r= number of items chosen at a time
Combinations are used when the order of events do not matter in calculating the outcome.
We calculate using the formula:
(30×20×12)÷3!=1200
There are therefore 1200 ways for the three distinct items to not be in same row or column
help
Does this graph represent a function? Why or why not?
A- no because it fails the vertical line test
B- yes because it passes the vertical line test
C-yes because it passes the horizontal line test
D- no because it fails the horizontal line test
Answer: No, it fails the vertical line test.
Step-by-step explanation:
In the xy-plane, the slope of the line y = mx − 4 is
less than the slope of the line y = x − 4. Which of the
following must be true about m?
[Show Workings}
I will give brainlist to the person with the right
If the slope of the line y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.
The general formula for calculating an equation of a line is expressed as:
[tex]y = mx + b[/tex] where:
m is the slope of the line
Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:
[tex]mx=1x\\[/tex]
Divide through by x
[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]
Hence the slope of the line y = x - 1 is 1.
According to the question, since we are told that the slope of the line
y = mx − 4 is less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement
Learn more about the slope of a line here: https://brainly.com/question/16949303
Answer:
Step-by-step explanation:
What value of b will cause the system to have an infinite number of solutions?
V = 6x + b
-3 x + 1/2 V = -3
Answer:
-6
Step-by-step explanation:
V = 6x + b
1/2 V -3 x = -3
V - 6x = -6
V - 6x = b
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.8 millimeters and a standard deviation of 0.07 millimeters. Find the two diameters that separate the top 8% and the bottom 8%. These diameters could serve as limits used to identify which bolts should be rejected. Round your answer to the nearest hundredth, if necessary.
Answer:
5.70 < X < 5.89
Step-by-step explanation:
Z = ±1.40507156
z = (x - μ)/σ
1.40507156 = (x - 5.8)/.07
5.70 < X < 5.89
Multiply (x2 + 3x + 5)(2x2 - 2x + 1).
A. 2A - 6x2 + 5
B. 3x2 + x + 6
C. 2A + 4x2 + 5x2 - 7x + 5
D. 2x4 + 8x3 + 17x2 + 13x+5
Lucian was hiking through a field directly toward his car, which was parked on a long, straight road perpendicular to his path, when he came to a swamp. He turned 55 degrees to the right and hiked 3 miles in that direction to reach the road. How far did he need to walk down the road to reach his car? (Please include a labeled diagram so step by step solution is easy to follow).
A real estate agent has 12 properties that she shows. She feels that there is a 30% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling no more than 2 properties in one week. Round your answer to four decimal places.
Answer:
0.2528 = 25.28% probability of selling no more than 2 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A real estate agent has 12 properties that she shows.
This means that [tex]n = 12[/tex]
She feels that there is a 30% chance of selling any one property during a week.
This means that [tex]p = 0.3[/tex]
Compute the probability of selling no more than 2 properties in one week.
2 or less sold, which is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138[/tex]
[tex]P(X = 1) = C_{12,1}.(0.3)^{1}.(0.7)^{11} = 0.0712[/tex]
[tex]P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0138 + 0.0712 + 0.1678 = 0.2528[/tex]
0.2528 = 25.28% probability of selling no more than 2 properties in one week.
PLEASE HELP! Don’t know how to solve this or where to start. I tried multiplying and dividing but still got the wrong answer. How do I solve this problem?
Answer:
306 square meters.
Step-by-step explanation:
Divide the shape into 2 rectangles.
Lets do the one that is sticking to the top first.
The area is 6 * 15, which is 90.
Lets do the second rectangle. The area is:
27 * 8, which is 216.
Add them all up (90 + 216), which is 306.
Answer:
306m²
Step-by-step explanation:
Split the shape into two rectangles with the accureate lengths
The top-most of the two rectangles with length 6m and width 15m:
6 x 15 = 90 m² (area of rectangle A)
The bottom rectangle:
27(full length) x 8m(full width) = 216m²
Add the two areas together for the full shape
216 + 90 = 306m²
Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 30% of the time, three events 20% of the time, two events 15% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for less than three events each month. P (x < 3) = 2 Find the expected number of events Javier volunteers in a month. 3.6 It is given that x must be below a certain value, which limits the rows to use in the PDF table. What is the sum of the probabilities of those rows?
Answer:
[tex]P(x < 3) = 25\%[/tex]
[tex]E(x) = 3[/tex]
Step-by-step explanation:
The given parameters can be represented as:
[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]
Solving (a): P(x < 3)
This is calculated as:
[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3
So, we have:
[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]
[tex]P(x < 3) = 25\%[/tex]
Solving (b): Expected number of events
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]
[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]
[tex]E(x) = 340\%[/tex]
Express as decimal
[tex]E(x) = 3.40[/tex]
Approximate to the nearest integer
[tex]E(x) = 3[/tex]
Is AFGH ~ AJKL? If so, identify the similarity postulate or theorem that
applies.
G
K
10
6
30°
30°
Н
A. Similar - SAS
B. Cannot be determined
C. Similar - SSS
D. Similar - AA
Answer: B. Cannot be determined
Explanation:
We can't use SAS since we don't have two pairs of proportional sides. We only know one pair of sides. This also rules out SSS as well since we'd need 3 pairs of proportional sides.
We can't use AA because we don't have two pairs of congruent angles.
Currently, we simply don't have enough information to determine if the triangles are similar or not.
What is the most specific name for a quadrilateral with one pair of parallel sides?
A. trapezoid
B. rectangle
C. parallelogram
D. quadrilateral
help me pls
Answer:
C: parallelogram
Step-by-step explanation:
Area of composite shapes ?
Answer: 58
Step-by-step explanation: you add them all together
Its 108 the other answer is the perimeter not the area.
19. In a random sample of 250 students, we found that 75 work out 4 or more times a week. Find the 95% confidence interval for the proportion of students who work out 4 or more times a week.
Answer:
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
In a random sample of 250 students, we found that 75 work out 4 or more times a week.
This means that [tex]n = 250, \pi = \frac{75}{250} = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.2432[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 1.96\sqrt{\frac{0.3*0.7}{250}} = 0.3568[/tex]
The 95% confidence interval for the proportion of students who work out 4 or more times a week is (0.2432, 0.3568).
If BC = 8.3, CD - 6,7, and AD = 11.6, find AB to the nearest tenth.
Answer:
ab=14.4
Step-by-step explanation:
This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6. Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6. Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
Step-by-step explanation:
Lets consider the unknown number as x
according to the question,
6-x= 5(x+2)
6-x= 5x+10
-x-5x=10-6
-6x=4
x=4/-6= 2/-3
x= -2/3
hope this helps
please mark me as brainliest.
Answer:
Step-by-step explanation:
Plato!! Answer: -4
Hope this helped
Twice the difference of a number and 6
Answer:
2x=6. I think friend it is correct.
Answer:
2(×-6)
Step-by-step explanation:
Correct me if im wrong thanks ●~●
If 4x³+kx²+px +2 is divisible by x²+ α prove that kp=8.
Answer:
Attached images
It was just easier for me this way.
Let me know in comments if you have questions.
Step-by-step explanation:
answer please I’m dying from math
Answer:
[tex]\huge\boxed{\text{D)} \ 15x^4 + 2x^3 - 8x^2 - 22x - 15}[/tex]
Step-by-step explanation:
We can solve this multiplication of polynomials by understanding how to multiply these large terms.
To multiply two polynomials together, we must multiply each term by each term in the other polynomial. Each term should be multiplied by another one until it's multiplied by all of the terms in the other expression.
We can do this by focusing on one term in the first polynomial and multiplying it by all the terms in the second polynomial. We'd then repeat this for the remaining terms in the second polynomial.Let's first start by multiplying the first term of the first polynomial, [tex]3x^2[/tex], by all of the terms in the second polynomial. ([tex]5x^2+4x+5[/tex])
[tex]3x^2 \cdot 5x^2 = 15x^4[/tex] [tex]3x^2 \cdot 4x = 12x^3[/tex] [tex]3x^2 \cdot 5 = 15x^2[/tex]Now, we can add up all these expressions to get the first part of our polynomial. Ordering by exponent, our expression is now
[tex]\displaystyle 15x^4 + 12x^3 + 15x^2[/tex]Now let's do the same with the second term ([tex]-2x[/tex]) and the third term ([tex]-3[/tex]).
[tex]-2x \cdot 5x^2 = -10x^3[/tex] [tex]-2x \cdot 4x = -8x^2[/tex] [tex]-2x \cdot 5 = -10x[/tex] Adding on to our original expression: [tex]\displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 10x[/tex] [tex]-3 \cdot 5x^2 = -15x^2[/tex] [tex]-3 \cdot 4x = -12x[/tex] [tex]-3 \cdot 5 = -15[/tex] Adding on to our original expression: [tex]\displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 15x^2 - 10x - 12x - 15[/tex]Phew, that's one big polynomial! We can simplify it by combining like terms. We can combine terms that share the same exponent and combine them via their coefficients.
[tex]12x^3 - 10x^3 = 2x^3[/tex] [tex]15x^2 - 8x^2 - 15x^2 = -8x^2[/tex] [tex]-10x - 12x = -22x[/tex]This simplifies our expression down to [tex]15x^4 + 2x^3 - 8x^2 - 22x - 15[/tex].
Hope this helped!
The circumference of a circle is 14 inches. Find the circle's radius and diameter.
Please help :)
