Solve: x - 1 < 3 help me plssss

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.

Answer:

f(1/2)=1.5

f(1/4)=0.75

Answer:

9.52% probability of getting both candies green

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the candies are selected is not important. They are also selected without replacement. So we use the combinations formula to solve this question.

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]

Find the probability of getting both candies green

Desired outcomes:

2 green, from a set of 5. So

[tex]D = C_{5,2} = \frac{5!}{2!3!} = 10[/tex]

Total outcomes:

2 from a set of 4+5+6 = 15. So

[tex]T = C_{15,2} = \frac{15!}{2!13!} = 105[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{10}{105} = 0.0952[/tex]

9.52% probability of getting both candies green

Answer:

The expression is 4x² and coefficient is 4.

Step-by-step explanation:

All have the same variables, x², so you add up together :

[tex] 1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2} [/tex]

[tex] = 4 {x}^{2} [/tex]

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

Answer:

  For each hour that Michelle drove, she traveled an additional 50 miles.

Step-by-step explanation:

The point (0, 350) tells you Michelle's trip is 350 miles long. The point (7, 0) tells you she completed it in 7 hours. The point (6, 50) on the graph tells you she has 50 miles remaining of the original 350 after 6 hours.

True: for each hour Michelle drove, she traveled an additional 50 miles.

Answer:

B. For each hour that Michelle drove, she traveled an additional 50 miles.

Step-by-step explanation:

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.

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

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!

:)

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.

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 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!

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

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]

Answer:

x=150 because these are supplementary angles

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

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.

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.

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.

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)

Answer:

Step-by-step explanation:

let s note a and b

x = ap+b

we can write two equations

(1) 300=3a+b

(2) 450=1.5a+b

multiply by 2 the (2) we got

900 =3a+2b

minus (1) it gives

900 - 300 = 3a+2b-3a-b = b

so b = 600

and from (1) it gives 3a = 300-600 = -300

so a = -100

then

x=-100p+600

thanks

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°

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°

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

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°))

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

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

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

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.

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

Answer:

979

Step-by-step explanation:

Answer:

115/198

Step-by-step explanation:

khan

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]