Answer:
5x - 4y = 20
Step-by-step explanation:
First find slope
(5- -10)/(8- -4) = 15/12 = 5/4
(y - 5) = 5/4 (x - 8), multiply everything by 4 so you don't have fractions
4y - 20 = 5x - 40
5x - 4y = 20
How do you solve this?
Answer:
.75 teaspoons per ounce
Step-by-step explanation:
Take the number of teaspoons and divide by the number of ounces
10.5 / 14
.75 teaspoons per ounce
3. Match each staternent with an expression that could be used to find the price
p+ 0.3p
0.7p
e. 85% more than the original time
f 15% less time than the original
g. 85% time decrease
h, 15% time increase
17p
p-07p
I
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expres
find the amount of money in his bank? Let "m" represent the original
Answer:
3a) 30% more than original price
b) 70% of the original price
c) 17times the original price
d) 70% less than original price
e) t + 0.85t
f) t - 0.15t
g) t - 0.85t
h) t + 0.15t
4. The expression that can be used to find the amount of money in his bank = m + 0.25m
Question:
3. Match each statement with an expression that could be used to find the price.
'The expressions for a to d were not stated in the question'.
a) p+ 0.3p
b) 0.7p
c) 17p
d) p-07p
'From e to h, we were not told what to determine'.
Write the expression in terms of time
e. 85% more than the original time
f. 15% less time than the original
g. 85% time decrease
h. 15% time increase
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original.
Step-by-step explanation:
let original price = p
a) p+ 0.3p = p + 30% of p
30% more than original price
b) 0.7p = 70% of p
= 70% of the original price
c) 17p = 17 × p
= 17times of the original price
d) p-0.7p = p - 70% of p
= 70% less than original price
Let original time = t
e) 85% more than the original time = t + 85%of t
= t + 0.85t
f) 15% less time than the original time = t - 15% of t
= t - 0.15t
g) 85% time decrease = t - 85% of t
= t - 0.85t
h) 15% time increase = t + 15% of t
= t + 0.15t
4. Since "m" represent the original amount in Hus piggy bank
An increase of 25% = original amount + 25% of original amount
= m + 25% of m
'Of' means multiplication
= m + 0.25 ×m
= m + 0.25m
= 1.25m
The expression that can be used to find the amount of money in his bank = m + 0.25m
Which graph has the parent function 1/x?
Answer:
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
Step-by-step explanation:
A rational function is described as the fraction of polynomials, where the denominator has degree of at least 1 .
Or it can be said that there must be a variable in the denominator.
The general form of a rational function is:
[tex]\text{Rational Function}= f(x)=\frac{p(x)}{q(x)}[/tex]
In this case the parent function provided is: [tex]f(x)=\frac{1}{x}[/tex].
The function is rational.
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
The graph is attached below.
calculate the middle between -4 and 5
Answer:
eight (8)
Step-by-step explanation:
-3,-2,-1,0,1,2,3,4
The notation f:S→T denotes that f is a function, also called a map , defined on all of a set S and whose outputs lie in a set T . A function f:S→T is injective if for all x,y∈S , f(x)=f(y) implies that x=y . Alternatively: a function is injective if we can uniquely recover some input x based on an output f(x) . What functions are injective?
Answer:
There are many. Two examples are
[tex]f(x) = x, \\f(x) = x^3[/tex]
Step-by-step explanation:
There are many examples. The simplest is
1 -
[tex]f(x) = x[/tex]
It is trivial that
[tex]\text{if \,\,\,\,} f(x) = f(y) \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]
2 -
[tex]f(x) = x^3[/tex]
That function is injective as well.
[tex]\text{if \,\,\,\,} x^3 = y^3 \,\,\,\,\,\text{then} \,\,\,\,\, x=y[/tex]
An example of a function that is NOT injective is
[tex]f(x) = x^2[/tex]
Notice that
[tex]f(-2) = (-2)^2 = 2^2 = 4[/tex]
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
Kristen wants to buy a Persian cat. She takes out a loan for $500 for one year. The bank charges
her an annual simple interest rate of 8%.
a. How much will she have to pay back at the end of the 1 year?
b. How much interest does she have to pay?
Answer:
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
Step-by-step explanation:
Simple interest for any amount p is given by
SI = p*r*t/100
where r is the annual rate rate of interest
t is the time
____________________________________________
Given
p= $500 (loan taken)
r = 8%
t = 1 year
SI = 500*8*1/100 = 40
Thus, $40 is the interest charged in a year.
Total money paid at the end of one year = loan taken + interest charged
= $500 + $40
= $540
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).
Answer:
8.55 days for a decay rate parameter of 8.1% per day
Step-by-step explanation:
Assuming a decay rate parameter of 8.1% per day
the general equation for radioactive decay is;
N = N₀e^(-λt)
x - decay constant (λ) - rate of decay
t- time
N - amount remaining after t days , since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2
N₀ - amount initially present
substituting the values
N₀/2 = N₀e^(-0.081t)
0.5 = e^(-0.081t)
ln (0.5) = -0.081t
-0.693 = -0.081t
t = 0.693 / 0.081 = 8.55
half life of substance is 8.55 days
The original price of a mountain bike was reduced by $125.
If p= the mountain bike's original price in dollars, which algebraic expression
represents the reduced price?
Answer:
p-125
Step-by-step explanation:
p represents the original price, which was reduced by 125. therefore, the reduced price is represented by the algebraic expression p-125
Answer: p - 125
Step-by-step explanation: Here, notice that the value that we don't know is the mountain bike's original price in dollars.
Since the original price of the mountain bike was reduced by $125,
we take away 125 from our variable, which is p.
So we have p - 125.
Find the radius of a circle given that the area is three times its circumference
Answer:
Radius of the circle = 6 units
Step-by-step explanation:
Let the radius of the circle be r
According to the given condition:
Area of the circle = 3 times the circumference of the circle
[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]
help pls take your time..
Answer:
As [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex] and as [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]
Step-by-step explanation:
Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards minus infinity).
As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)
Select and place the symbol that will make the statement true |-a| |a|
Answer:
|-a|=|a|
Step-by-step explanation:
The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.
Therefor this is how we can solve this.
|-a| __ |a|
a __ a
a=a
0.580 80 repeating as a simplified fraction
Answer:
979
Step-by-step explanation:
Answer:
115/198
Step-by-step explanation:
khan
Identify the domain of a radical function with an odd index.
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
Answer:
1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean
2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?
The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.
So
Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.
2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
We have that:
[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]
This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{164000 - 168000}{4000}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
what is the answer to -9x = -27
Answer:
x = 3
Step-by-step explanation:
9x = 27
Divide both sides by 9,
x = 27/9 which on factorization of the numerator is written as
x = 9 x 3/9 = 3
Calculation 2: Exponent Or Index Method
9x = 27
Since 9 = 3² and 27 = 3³, the given equation takes the form
3² x = 3³
This gives
x = 3³ ÷ 3² = 3³¯² [using the formula a^m ÷ a^n = a^(m-n)]
= 3¹ = 3 (since the first power of a number is the number itself)
9 x 1 = 9
9 x 2 = 16
9 x 3 = 279 x 4 = 36
We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,
x = 3
hope this helped!
What’s the correct answer for this question?
Answer:
68°
Step-by-step explanation:
Angle IJK is 112
Opposite angles of a quadrilateral inscribed in a circle add up to 180°
So
m<IHK = 180-112
m<IHK = 68°
Which of the following rational numbers is greater than 5/17 but less than 6/17.
Answer:
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
Step-by-step explanation:
As mention in the question number is
[tex]\frac{5}{17}\ < \frac{6}{17} \\multiply\ both\ side\ by\ 10\ in\ numerator\ and\ denominator\ we\ get \\\frac{50}{170} <\frac{60 }{170}\\[/tex]
Therefore the number is :
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
8+8?
Pls help will mark you or whatever
Answer:
8+8=16
Step-by-step explanation:
Lets say you have 8 apples and your friend gives you 8 more apples. So, you count 9,10,11,12,13,14,15,16 which was 8 times.
Hope this helps.
What is the formula to find the area of a triangle
Answer:
A= 1/2bh
Step-by-step explanation:
(how its supposed to be said: Area= one half base times height)
:)
Answer:
(1) As a simple definition, a triangle is a two-dimensional figure that has 3 sides (and 3 angles as well).
(2) A triangle as shown in attached picture has the area that is typical calculated by the multiplication of half of base and height.
A = (1/2) x Base x Height
Base can be a particular side of triangle
Height is the perpendicular line segment between the opposite vertex of selected base and that base.
Hope this helps!
:)
Which answer is equivalent to the equation shown below?
7c = 49
A.log7 c = 49
B.c = log49 7
C.logc49 = 7
D.c = log7 49
Answer:
D.
Step-by-step explanation:
The base of a log is also the base of an exponent. So 7 to the c power, our 7 would be the base. To find c, we simply just do log base 7 of 49, which comes out to be 2.
In a large population, 64% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal to 4 places.
Answer:
0.9940
Step-by-step explanation:
P(at least 1) = 1 − P(zero)
P(at least 1) = 1 − (1 − 0.64)⁵
P(at least 1) = 1 − (0.36)⁵
P(at least 1) = 0.9940
The probability that at least one of them has been vaccinated is 0.9939.
What is binomial distribution?
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.
For the given situation,
Number of people vaccinated = 64% = 0.64
The formula of binomial distribution is
[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]
Here x is the number of successes, x ≤ 1
n is the number of trials, n = 5
p is the probability of a success on a single trial, p = 0.64 and
where, [tex]nC_{x}=\frac{n!}{x!(n-x)!}[/tex]
The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]
[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]
⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]
⇒ [tex]P(X=0)= 0.0060[/tex]
Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]
⇒ [tex]P(X \leq 1)=1-0.0060[/tex]
⇒ [tex]P(X \leq 1)=0.9939[/tex]
Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.
Learn more about binomial distribution here
https://brainly.com/question/27939234
#SPJ3
What’s the correct answer for this?
Answer:
C
Step-by-step explanation:
Measure of Arc FED = 51+79
= 130°
Since the measures of arcs and angles are the same
Hence
<FED = 130°
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P0=6, and the population after 8 weeks is P8=86 Find an explicit formula for the beetle population after n weeks.
After how many weeks will the beetle population reach 236?
Answer:
The number of weeks it will take for the beetle population to reach 236 is 28.75.
Step-by-step explanation:
If a quantity starts at size P₀ and grows by d every time period, then the
quantity after n time periods can be determined using explicit form:
[tex]P_{n} = P_{0} + d \cdot n[/tex]
Here,
d = the common difference, i.e. the amount that the population changes each time n is increased by 1.
In this case it is provided that the original population of beetle was:
P₀ = 6; (week 0)
And the population after 8 weeks was,
P₈ = 86
Compute the value of d as follows:
[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]
Thus, the explicit formula for the beetle population after n weeks is:
[tex]P_{n}=P_{0}+8n[/tex]
Compute the number of weeks it will take for the beetle population to reach 236 as follows:
[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]
Thus, the number of weeks it will take for the beetle population to reach 236 is 28.75.
In the diagram below, AB is parallel to CD. What is the value of x?
А. 150
В. 60
С. 120
D. 30
Answer:
x=150 because these are supplementary angles
Consider the function y=f(x)=3x. The values of f(1/2) and f(1/4), rounded to the nearest hundredth, are_______ and__________ , respectively.
Answer:
f(1/2)=1.5
f(1/4)=0.75
Please help me with this question!!!
Answer:
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
Step-by-step explanation:
Using Euler's formula, this can be written as ...
x^2 = 9·e^(i5π/6)
Then the square roots are ...
x = (±√9)e^((i5π/6)/2) = ±3e^(i5π/12)
Of course, multiplying by -1 is the same as adding 180° to the angle.
The square roots are ...
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
1/4x - 2/5 =39 someone please answer this question thx
Answer:
157.6
Step-by-step explanation:
Use PEMDAS! In this rule, it is stated that we should always add/subtract before multiplying/dividing. Also, whatever you do on one side of an equation, you do to another. Therefore, in order to get rid of the -2/5, add 2/5 so we can get rid of it. We also (according to the rule), have to add it to the other side in order to balance out. So add the 2/5 to 39. Then the other side is now 39.4. Now we have to get x by itself. Divide both sides by 1/4 (or multiply by 4 on both sides) in order to get x=157.6
Plastic knives are sold in packs of 15 for 32p. Plastic forks are sold in packs of 12 for 43p. Sam wants to buy the same number of forks as knives. What is the least amount of money Sam will be able to spend?
Step-by-step explanation:
Find the lowest common multiple of 15 and 12.
Which is 60.
15×4=60 so 32x4=£1.28
12x5=60 so 43x5=£2.15
2.15+1.28= £3.43
Suppose that the operations manager of a nose mask packaging delivery service is
contemplating the purchase of a new fleet of trucks. When
packages are efficiently stored in the trucks in preparation for delivery, two major constraints
have to be considered. The weight in pounds and volume in cubic feet for each item. Now
suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard
deviation of 3.9 pounds. In addition suppose that the average volume for each of these
packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the
variation of the weight and volume?
Answer:
Coefficient of variation (weight) = 15%
Coefficient of variation (volume) = 25%
Step-by-step explanation:
Let's begin by listing out the given information:
Population = 200, Average weight = 26 lb,
standard deviation (weight) = 3.9 lb,
Average volume = 8.8 ft³,
standard deviation (volume) = 2.2 ft³
Based on the data given, the manager will have to make a deduction by comparing the relative scatter of both variables due to the different units of measuring weight (pounds) and volume (cubic feet).
To compare the variation of the weight and volume, we use the coefficient of variation given by the formula:
Coefficient of Variation = (Standard deviation ÷ Mean) * 100%
⇒ [tex]C_{v}[/tex] = (σ ÷ μ) * 100%
For weight
σ = 3.9 lb, μ = 26 lb
[tex]C_{v}[/tex] (weight) = (3.9 ÷ 26.0) * 100% = 15%
[tex]C_{v}[/tex] (weight) = 15%
For volume
σ = 2.2 ft³, μ = 8.8 ft³
[tex]C_{v}[/tex] (volume) = (2.2 ÷ 8.8) * 100% = 25%
[tex]C_{v}[/tex] (volume) = 25%
∴ the relative variation of the volume of the package is greater than that of the weight of the package