Answer:
Solution given:
[tex]x_{1},y_{1}=(8,-8)[/tex]
[tex]x_{2},y_{2}=(-1,-5)[/tex]
Now
Distance between them is:
d=[tex]\sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}[/tex]
d=[tex]\sqrt{(-1-8)²+(-5+8)²}=3\sqrt{10}[/tex]
Distance between them is [tex]\bold{3\sqrt{10}}[/tex]
Find the areas in that unit square PQRS, P(4,3), Q(4,1), S(-1,3), R(-1,1)
Answer:
Step-by-step explanation:
P(4,3), Q(4,1), S(-1,3), R(-1,1)
[tex]Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2} -y_{1})^{2}}\\\\PQ= \sqrt{(4-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-2)^{2}}\\\\\=\sqrt{4}\\\\=2 \ units\\\\\\QS=\sqrt{(-1-4)^{2}+(3-1)^{2}}\\\\=\sqrt{(-5)^{2}+(2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\ units\\\\\\SR =\sqrt{(-1-[-1])^{2}+(1-3)^{2}}\\\\=\sqrt{(-1+1)^{2}+(-2)^{2}}\\\\=\sqrt{0+4}\\\\= \sqrt{4}\\\\= 2 \\\\\\PR = \sqrt{(-1-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-5)^{2}+(-2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\\\\[/tex]
PQRS is a rectangle
Area= length *breadth
= 2 * √29
= 2√29 sq.units
Lionel sells to two groups of customers – 50% of its sales are to wholesalers and 50% to retailers. All sales to retailers are cash sales. Collections from wholesalers are follows: 75% in the month of sale and 25% in the month following sale. ii) 60% of direct material purchases are paid in cash in the month of purchase, and the balance is paid in the month following the purchase. iii) All other expenses are paid in the month incurred. iv) Manufacturing overhead includes monthly depreciation of $15,000. v) Sales: March, $320,000. vi) Purchases of direct materials: March, $175,000. vii) Other receipts: April – Donation received, $2,000 May – Sale of used office furniture, $4,000. viii) Other disbursements: May – Purchase of Ice Cream Mixer, $10,000. ix) Repays loan: April, $30,000. x) Cash balance on April 1, is expected to be $50,000.
Answer:
:D
Step-by-step explanation:
Cost of sales. Administrative expenses. Distribution costs. Property costs. Depreciation. [13]. Page 6. 6. © UCLES 2019. 9706/23/M/J/19.
In chapter 9, we discussed Confidence Interval methodology to draw conclusions about the difference in the brain size of the children with and without autism. Discuss a different methodology to conclude if there is any significant difference in the average brain size of the children with and without autism.
Answer:
Two sample t test
Step-by-step explanation:
The two sample t test can be used in the scenario described above, where two independent samples are obtained, we take a certain sample of children with autism and then another sample of children without autism. The number of children chosen for each sample should be random and could be of equal or unequal sizes. The mean and standard deviation of each of sample A and B are deternined and used to perform the analysis to determine if the mean of each sample are equal or not. This test is also called the WELCH T TEST
A random sample of 20 individuals who graduated from college five years ago were asked to report the total amount of debt (in $) they had when they graduated from college and the total value of their current investments (in $) resulting in the data set below.
Debt Invested
16472 37226
19048 33930
4033 66292
22575 24887
12020 44976
4731 59924
4571 59901
Which statement best describes the relationship between these two variables?
a. As college debt decreases current investment decreases.
b. College debt is not associated with current investment.
c. As college debt increases current investment decreases.
d. As college debt increases current investment increases.
Answer:
The answer is "Option c".
Step-by-step explanation:
Please find the complete question and its solution in the attached file.
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!
A sample of students was asked what political party do they belong. which of the following types of graphical display would be appropriate for the sample?
A. Stemplot.
B. Pie chart.
C. Scatterplot.
D. All of the above.
Answer:
B. Pie chart.
Step-by-step explanation:
In this question, the students are asked what political party they belong. The best display format would be one in which the graph can be divided into parts, or percents, according to the percentage of students belonging to each political party. The graph that best describes this, distributing a group into parts, is a pie chart, and thus, the correct answer is given by option b.
Scatterplot is used when two variables correlate together, that is, there is a relationship between them, which we don't have between the number, or proportion of students belonging to each political party. Stemplot are used when there is a high number of quantitative data, which we do not have here.
which of the following is a geometric sequence -3,3,-3,3... 11,16,21,26, ... 6, 13, 19, 24, ... -2,6,14,22, ...
Answer:
p and q are two numbers.whrite down an expression of
Each student at some college has a mathematics requirement M (to take at least one mathematics course) and a science requirement S (to take at least one science course). A poll of 150 sophomore students shows that: 60 completed M, 45 completed S, and 25 completed both M and S
Find the number of students who have completed
(a) At least one of the two requirements
(b) Exactly one of the two requirements
(c) Neither requirement.
all students = 150
M = 60
S = 45
M and S = 25
(a) At least one of the two requirements:
M or S = M + S - (M and S) = 60 + 45 - 25 = 80
(b) Exactly one of the two requirements:
(M or S) - (M and S) = 80 - 25 = 55
(c) Neither requirement:
(all students) - (M or S) = 150 - 80 = 70
probability that an individual has 20-20 vision is 0.16. In a class of 90 students, what is the mean and standard deviation of the number with 20-20 vision in the class? Round to the nearest thousandth.
A.
The mean is 90. The standard deviation is 1.1.
B.
The mean is 14.4. The standard deviation is 3.478.
C.
The mean is 90. The standard deviation is 1.2.
D.
The mean is 1.44
I WILL MARK BRAINLIEST:))
Please translate this expression into a verbal expression 4(5j+2+j). (5 points)
PLEASE HELP!!! I have been adding and multiplying many different ways however my answer are wrong. How do I go about solving the perimeter then?
Answer:
66 m
Step-by-step explanation:
First, lets add up the numbers you know. It should be:
16, 8, 17, and 7.
Add them all up, and you will get:
48.
For the last two sides, subtract 7 from 16 to get 9.
For the last slide, subtract 8 from 17 to get 9.
Add them all up, and get 66.
A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals
make up 3 percent of the town's population.
Part A
Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.
Answer:
p=c(1+r)^t so the population will be 4679.43424 or rounded to 4679
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
The exponential equation that represents the population of the town in terms of the number of years : [tex]p=4000 (1+0.4)^{t}[/tex]
What is an exponential equation?An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.
It is similar to the amount received after investing a certain amount compounded annually.
Given,
Initial population = 4000
Rate of increase = 4%
Let current population be p.
Let number of years passed be t.
The exponential equation will be: [tex]p=4000 (1+0.4)^{t}[/tex]
(The population of the town has grown exponentially. This means that:
Initial population = 4000
Population in year I = 4000 + 4% of 4000 = 4000(1 + 0.4)
Population in year II = 4000 + 4% of 4000(1 + 0.4) = 4000(1 + 0.4)(1+0.4)
and this goes on.)
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Directions: Find each missing measure
Answer:
Q9: x = 27, Q10: x = 17
Step-by-step explanation:
A line includes the points (0,2) and (1,6).
What is the equation of the line in slope-intercept form?
How do I do this equation
This question requires the manipulation of the Ideal Gas formula. By moving the variables around, you'll get :
V = nRT/P
n = PV/RT
Does anyone know this question?
Step-by-step explanation:
this is a relatively easy function. Just plug in the value for x
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
3 Lizzie buys 3 clocks for a total cost of £50 at a car boot sale.
She sells 2 of the clocks for £22 each and the other clock for £20
Lizzie thinks she has made a profit of over 30% of the cost of the clocks.
Answer:
28% She didn't make a profit over 30%
Step-by-step explanation:
She buys the clocks for 50 pounds
She sells them for 22 + 22 + 20 = 64 pounds.
The profit is 14 pounds
What's the % profit.
Profit % = 14/50*100 = 28%
She's not quite right.
Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) Pearson's coefficient of skewness of the data?
Unit sales for new product ABC have varied in the first seven months of this year as follows:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
What is the (population) standard deviation of the data?
Answer:
Coefficient of skewness = 0.5785
Population standard deviation = 88.154
Step-by-step explanation:
Given the data:
Month Jan Feb Mar Apr May Jun Jul
Unit Sales 314 285 158 482 284 310 281
Reordered data : 158, 281, 284, 285, 310, 314, 482
The population mean of the data :
Mean, μ = Σx / n = 2114 / 7 = 302
The median :
1/2(n+1)th term
n = 7
1/2(8)th term
Median = 4th term = 285
The population standard deviation, s :
s = √(Σ(x - μ)²/n)
s = √[(158-302)^2 + (281-302)^2 + (284-302)^2 + (285-302)^2 + (310-302)^2 + (314-302)^2 + (482-302)^2] / 7
s= √(54398 / 7)
s = √7771.1428
s = 88.154
The Pearson Coefficient of skewness :
[3(μ - median)] / s
3(302 - 285) / 88.154
3(17) / 88.154
51 / 88.154
= 0.5785
Camille bought a set of kitchen chairs discounted 25% off of the original price of $170. What was the dollar amount of discount of the set of chairs?
Answer:
$42.50
Step-by-step explanation:
All you have to do is simply multiply
170 x 0.25=$42.50
HELP PLEASE!!!
Can someone tell me what a constant of proportionality is?
Please add an example if you can!
Thanks!
Answer:
A number or number sentence that doesn't change
Step-by-step explanation:
Answer:
the constant of proportionality k, is the constant value of the ratio of two proportional quantities y and x
Step-by-step explanation:
k = y/x or y= kx
example : the cost of 20 books is rs. 180 how much will 15 books cost ?
a. rs. 125
b. rs. 130
c. rs. 135
d. rs. 140
answer is c. rs. 135
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
The probability of this event is represented by a value of 1.
Step-by-step explanation:
Probability of a certain event:
The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
This means that the probability of this event is represented by a value of 1.
How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.
Answer:
467 voters
Step-by-step explanation:
Given
See attachment for complete question
Required
Sample size at 95% confidence interval
From the attachment, we have:
[tex]p = 65\% = 0.65[/tex]
[tex]E = 4.33\% = 0.0433[/tex]
[tex]CL = 0.95[/tex]
[tex]\alpha = 0.05[/tex] i.e. 1 - CL
First, we calculate the critical level
At [tex]CL = 0.95[/tex] and [tex]\frac{\alpha}{2}[/tex]
[tex]z^* = 1.96[/tex] --- the critical level
So, we have:
[tex]n = p * (1 - p) * (\frac{z^*}{E})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (45.3)^2[/tex]
[tex]n = 0.65 * 0.35 * 2052.1[/tex]
[tex]n = 466.9[/tex]
[tex]n = 467[/tex] --- approximated
A town recently dismissed 5 employees in order to meet their new budget reductions. The town had 4 employees over 50 years of age and 16 under 50. If the dismissed employees were selected at random, what is the probability that no more than 1 employee was over 50
Answer:
0.7513 = 75.13% probability that no more than 1 employee was over 50
Step-by-step explanation:
The employees are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[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]
In this question:
4 + 16 = 20 employees, which means that [tex]N = 20[/tex]
4 over 50, which means that [tex]k = 4[/tex]
5 were dismissed, which means that [tex]n = 5[/tex]
What is the probability that no more than 1 employee was over 50?
Probability of at most one over 50, which is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,20,5,4) = \frac{C_{4,0}*C_{16,5}}{C_{20,5}} = 0.2817[/tex]
[tex]P(X = 1) = h(1,20,5,4) = \frac{C_{4,1}*C_{16,4}}{C_{20,5}} = 0.4696[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.2817 + 0.4696 = 0.7513[/tex]
0.7513 = 75.13% probability that no more than 1 employee was over 50
What is the median of the following set of values? 7, 21, 19, 15, 19, 14, 15, 19
The median of the following set of values is equals to 17.
What are median?Median represents the middle value of the given data when arranged in a particular order. The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
We are given that the median of the following set of values
7, 21, 19, 15, 19, 14, 15, 19
Line them up in order first.
7, 14, 15, 15, 19, 19, 19, 21
Here the middle value are 15 and 19.
The median is 15 and 19. OR 17,
Therefore, 15 + 19 = 34/2 which equals to 17.
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an amount of R3000, Is invested to three years at simple interest rate and it earned R905 interest. determine the simple interest rate at which the money was invested
Answer:
Step-by-step explanation:
P=R3000.00
T=3 years
SI=R905
SI=P\times R\times T\\R905=R3000\times \frac{r}{100}\times 3SI=P×R×T
R905=R3000×
100
r
×3
R905=\frac{R9000r}{100}R905=
100
R9000r
R905=\frac{R905}{R90}R905=
R90
R905
r=\frac{R905}{R90.}r=
R90.
R905
r=10.06\%r=10.06%
A cat is running away from a dog at a speed of 3m/s. originally, the distance between them was 48 meters. What should be the speed of the dog to catch with the cat in 1 minute?
Answer:
[tex]3.8\:\mathrm{m/s}[/tex]
Step-by-step explanation:
Use the formula [tex]d=rt[/tex] (distance is equal to rate/speed multiplied by time) to solve this problem.
We know that one minute is equal to 60 seconds. Therefore, the distance travelled by the cat in 1 minute is equal to [tex]d=3\cdot 60=180\text{ meters}[/tex].
To catch the cat, the dog needs to also cover an additional 48 meters, because the cat was initially 48 meters away from the dog and it ran away from the dog. Hence, the dog will need to cover [tex]180+48=228[/tex] meters in one minute.
Therefore, we have:
[tex]228=60r,\\r=\frac{228}{60}=\boxed{3.8\:\mathrm{m/s}}[/tex]
Answer:
[tex] \boxed{3.8 \: m/s} [/tex]
Explanation
The first step is to set the speed and the distance equal to the unknown rate of the dog.
3 m/s + 48 m = x m/60s.
Then substitute 60s in for both rates to get distance.
180m + 48m = x m/60
228m = 60x m
÷60 ÷60
3.8m = x m/s.
x = 3.8m/s
True/False Questions - one attempt tor each question
If f is a decreasing function on an interval, then f'(x) > 0 on that interval.
True
False
Submit Question
Answer:
False
Step-by-step explanation:
f'(x) would be a negative number. Hence less than zero.
DO THIS AND ILL MARK! PLEASE
Answer:
Sin = 7/25
Cos = 24/25
Tan = 7/24
Step-by-step explanation:
The ratio for sin is opposite/hypotenuse, cos is adjacent/ hypotenuse, and tan is opposite/ adjacent.
Find the distance between the two points in simplest radical form (−6, 1) and (−8,−4)