the initial population of a town is 16,237 and it grows with a doubling time of 24 years. what will the popluation be in 2 years.

We know that t is the number of hours Isabel worked as a tutor, and that she worked for a total of 93 hours. This means that the number of hours she worked as a waitress is 93 - t hours.

Now, for each of the t hours she worked as a tutor, she earned $8, so the total amount Isabel earned from that job is 8t dollars.

For each of the 93 - t hours Isabel worked as a waitress, she earned $9, so the amount she earned from her job as a waitress is 9(93 - t) dollars.

Therefore, the total amount she earned is 8t + 9(93 - t) dollars. This can be simplified to 837 - t dollars.

Answer:

50*0.4*45=900cm²

Answer:

[tex]B'(x,y) = (0,-2)[/tex]

Step-by-step explanation:

Given

The attached grid

Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]

Required

Determine the coordinates of B'

First, we have to write out the coordinates of B

[tex]B(x,y) = (-5,0)[/tex]

Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]

[tex]B(x,y) = (-5,0)[/tex] becomes

[tex]B'(x,y) = B(x+5,y-2)[/tex]

Substitute -5 for x and 0 for y

[tex]B'(x,y) = (-5+5,0-2)[/tex]

[tex]B'(x,y) = (0,-2)[/tex]

Answer:

a =7.5

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2  where a and b are the legs and c is the hypotenuse

a^2 + 10 ^2 = 12.5^2

a^2 + 100  =156.25

Subtract 100 from each side

a^2 = 56.25

Take the square root of each side

sqrt(a^2) = sqrt( 56.25)

a =7.5

Answer:

B. The set is linearly independent because at least one of the vectors is a multiple of another vector.

Step-by-step explanation:

A set of n vector of length n is linearly independent if the matrix with these vectors as column has none of zero determinant. The set of vectors is dependent if the determinant is zero. In the given question the vectors have no zero determinants therefore it is linearly independent.

Answer:

(A) the selling price is $20 per yards, and the expected yards to be sold is 10,000 yards

the derivative f'(20) is negative, which means the fabric producing company will sell 350 fewer yards when selling price is $20 per yard

(B) = R'(20) = $3000

∴the company will get extra $3000 revenue when selling price is $20 per yard

Step-by-step explanation:

A. given that

f(20)= 10,000

f'(20)= -350(first derivative)

the selling price is $20 per yards, and the expected yards to be sold is 10,000 yards

the derivative f'(20) is negative, which means the higher the price, it wil reduce the number of yards to be sold making it 350 fewer yards

(B) R(p) = p f(p)

f(20)= 10,000

f'(20)= -350(first derivative)

R(p) = p f(p)

differentiate with respect to p, using product rule

R'(p) = p f' (p) + f(p) (first derivative)

where p = 20

R'(20) = 20 f' (20) + f(20)

R'(20) = 20(-350) + 10,000

R'(20) = -7000 + 10,000

R'(20) = $3000

∴ the revenue is increasing by $3000 for every selling sold yard and increase in price per yard

Answer:

Margin of Error = ME =± 5.2592

Step-by-step explanation:

In the given question n= 20 < 30

Then according to the central limit theorem z test will be applied in which the standard error will be  σ/√n.

Sample Mean = μ = 64

Standard Deviation= S= σ = 12

Confidence Interval = 95 %

α= 0.05

Critical Value for two tailed test for ∝= 0.05 = ±1.96

Margin of Error = ME = Standard Error *Critical Value

ME = 12/√20( ±1.96)=

ME    = 2.6833*( ±1.96)= ± 5.2592

The standard error for this test is σ/√n

=12/√20

=2.6833

Answer: y=3

Step-by-step explanation:

To solve the equation, we want to get the same terms onto the same side and solve.

y+3=-y+9                 [add y on both sides]

2y+3=9                    [subtract 3 on both sides]

2y=6                        [divide 2 on both sides]

y=3

Answer:

y=3

Step-by-step explanation:

Answer:

x= 1.75

Step-by-step explanation:

Answer:

1.75 = x?

Step-by-step explanation:

Answer:

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Step-by-step explanation:

To identify outliers the interquartile range of the dataset can be used

Outliers can be identified as data values that are

- greater than Upper Q 3 plus 1.5 (IQR)

- less than Upper Q 1 minus 1.5 (IQR)

Using the interquartile range concept, it is found that:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

----------------------------

[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]

Thus:

The interquartile range​ (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.

A similar problem is given at https://brainly.com/question/14683936

Answer:

2 is the only even prime number

Answer:

2

Step-by-step explanation:

2 is the only even prime number. There is no even prime number other than 2. Prime numbers are the numbers which can only be divided by 1 and the number itself.

Answer:

x=2

Step-by-step explanation:

12-10=2

Answer:

x=2

Step-by-step explanation:

10=12-x

Subtract 12 from each side

10-12 = 12-12-x

-2 =-x

Multiply by -1

2 = x

Answer: The investment will be 6314 after 9 years.

Step-by-step explanation:

Formula to calculate the accumulated amount in t years:

[tex]A=P(1+r)^t[/tex], whereP= principal amount, r= rate of interest ( in decimal)

Given: P = $4,625

r= 3.52% = 0.0352

t= 9 years

Then, the accumulated amount after 9 years would be:

[tex]A=4625(1+0.0352)^9\\\\=4625(1.0352)^9\\\\=4625(1.36527)\approx6314[/tex]

Hence, the investment will be 6314 after 9 years.

Answer:

a) CI = ( 148,69 ; 243,31 )

b) n = 189

Step-by-step explanation:

a)  If the Confidence Interval is 95 %

α = 5 %     or   α = 0,05     and   α/2  = 0,025

citical value for α/2  =  0,025     is    z(c) = 1,96

the  MOE   ( margin of error is )  

1,96* s/√n

1,96* 163,7/ √46

MOE =  47,31

Then  CI  =  196 ± 47,31

CI = ( 148,69 ; 243,31 )

CI look very wide ( it sems that if sample size was too low )

b) Now if s (sample standard deviation) is 175, and we would like to have only 50 ppm width with Confidence  level 95 %, we need to make

MOE = 25 = z(c) *  s/√n

25*√n = z(c)* 175

√n   =  1,96*175/25

√n  = 13,72

n = 188,23

as n is an integer number we make n = 189

Explanation:

Two points on this line are (0,1) and (2,0)

Use the slope formula

m = (y2-y1)/(x2-x1)

m = (0-1)/(2-0)

m = -1/2

The negative slope means the line goes downhill as you move from left to right.

Answer:

You can use your graphing calculator to find the answer.

Go to STAT, then TESTS, and hit "1: Z-Test..."

Make sure it is set to Stats, then for mu0, do 70; for standard deviation, do 9; for mean, you do 62; for sample size, you do 19. For mu, you do not equal to mu0. Then you hit "Calculate".

You then get a z-value (critical value) of -3.874576839, and a p-value of 0.00010685098.

This means that...

We reject the null hypothesis that the average height of lodgepole pines in Yellowstone is 70 feet because p = 0.0001 is less than the significance level of alpha = 0.01. There is sufficient evidence to suggest that the mean height of lodgepole pines in Yellowstone is NOT equal to 70 feet.

Hope this helps!

Answer:

16 km

Step-by-step explanation:

Given:

Distance from Washington to Stamford = distance from Washington to Salem + distance from Salem to Stamford = 10.3 km + 11.9 km = 22.2 km

Distance from Washington to Oakdele = 6.2 km

Required: the difference between the distance from Washington to Stamford and from Washington to Oakdele

Solution:

Distance from Washington to Stamford = 22.2 km

Distance from Washington to Oakdele = 6.2 km

The difference = 22.2 km - 6.2 km = 16 km

Therefore, from Washington, it is 16 km farther to Stamford than to Oakdele.

Answer:

The probability that Pat will pass the exam is 0.02775.

Step-by-step explanation:

We are given that exam consists of 100 true-false questions. Pat plans to guess the answer to each question without reading it.

If a grade on the exam is 60% or more, Pat will pass the exam.

Let X = grade on the exam by Pat

The above situation can be represented through binomial distribution such that X ~ Binom(n = 100, p = 0.50).

Here the probability of success is 50% because there is a true-false question and there is a 50-50 chance of both being the correct answer.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]100 \times 0.50[/tex] = 50

and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]

                                                                  = [tex]\sqrt{100 \times 0.50 \times (1-0.50)}[/tex]

                                                                  = 5

So, X ~ Normal([tex]\mu=50, \sigma^{2} = 5^{2}[/tex])

Now, the probability that Pat will pass the exam is given by = P(X [tex]\geq[/tex] 60)

         P(X [tex]\geq[/tex] 60) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{60-50}{5}[/tex] ) = P(Z [tex]\geq[/tex] 2) = 1 - P(Z < 2)

                                                       = 1 - 0.97725 = 0.02275

Hence, the probability that Pat will pass the exam is 0.02775.

Answer:

a. P(0 < z < 3.00) =  0.4987

b. P(0 < z < 1.00) =  0.3414

c. P(0 < z < 2.00) = 0.4773

d. P(0 < z < 0.79) = 0.2852

e. P(-3.00 < z < 0) = 0.4987

f. P(-1.00 < z < 0) = 0.3414

g. P(-1.58 < z < 0) = 0.4429

h. P(-0.79 < z < 0) = 0.2852

Step-by-step explanation:

Find the area under the standard normal probability distribution between the following pairs of​ z-scores.

a. z=0 and z=3.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 3.00) = 0.9987

Thus;

P(0 < z < 3.00) = 0.9987 - 0.5

P(0 < z < 3.00) =  0.4987

b. b. z=0 and z=1.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 1.00) = 0.8414

Thus;

P(0 < z < 1.00) = 0.8414 - 0.5

P(0 < z < 1.00) =  0.3414

c. z=0 and z=2.00

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 2.00) = 0.9773

Thus;

P(0 < z < 2.00) = 0.9773 - 0.5

P(0 < z < 2.00) = 0.4773

d.  z=0 and z=0.79

From the standard normal distribution tables,

P(Z< 0) = 0.5  and P (Z< 0.79) = 0.7852

Thus;

P(0 < z < 0.79) = 0.7852- 0.5

P(0 < z < 0.79) = 0.2852

e. z=−3.00 and z=0

From the standard normal distribution tables,

P(Z< -3.00) = 0.0014  and P(Z< 0) = 0.5

Thus;

P(-3.00 < z < 0 ) = 0.5 - 0.0013

P(-3.00 < z < 0) = 0.4987

f. z=−1.00 and z=0

From the standard normal distribution tables,

P(Z< -1.00) = 0.1587  and P(Z< 0) = 0.5

Thus;

P(-1.00 < z < 0 ) = 0.5 -  0.1586

P(-1.00 < z < 0) = 0.3414

g. z=−1.58 and z=0

From the standard normal distribution tables,

P(Z< -1.58) = 0.0571  and P(Z< 0) = 0.5

Thus;

P(-1.58 < z < 0 ) = 0.5 -  0.0571

P(-1.58 < z < 0) = 0.4429

h. z=−0.79 and z=0

From the standard normal distribution tables,

P(Z< -0.79) = 0.2148  and P(Z< 0) = 0.5

Thus;

P(-0.79 < z < 0 ) = 0.5 -  0.2148

P(-0.79 < z < 0) = 0.2852

Answer:

The probability that the insurer pays at least 1.44 on a random loss is 0.18.

Step-by-step explanation:

Let the random variable X represent the losses covered by a flood insurance policy.

The random variable X follows a Uniform distribution with parameters a = 0 and b = 2.

The probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b\\\\\Rightarrow f_{X}(x)=\frac{1}{2}[/tex]

It is provided, the probability that the insurer pays at least 1.20 on a random loss is 0.30.

That is:

[tex]P(X\geq 1.2+d)=0.30\\[/tex]

⇒

[tex]P(X\geq 1.2+d)=\int\limits^{2}_{1.2+d}{\frac{1}{2}}\, dx[/tex]

                [tex]0.30=\frac{2-1.2-d}{2}\\\\0.60=0.80-d\\\\d=0.80-0.60\\\\d=0.20[/tex]

The deductible d is 0.20.

Compute the probability that the insurer pays at least 1.44 on a random loss as follows:

[tex]P(X\geq 1.44+d)=P(X\geq 1.64)[/tex]

                        [tex]=\int\limits^{2}_{1.64}{\frac{1}{2}}\, dx\\\\=|\frac{x}{2}|\limits^{2}_{1.64}\\\\=\frac{2-1.64}{2}\\\\=0.18[/tex]

Thus, the probability that the insurer pays at least 1.44 on a random loss is 0.18.

Answer:

c. -13/4.

d. -13/3.

Step-by-step explanation:

c. f(3/2) = (1/2)(3/2) - 4

= 3 / 4 - 4

= 0.75 - 4

= -3.25

= -3 and 1/4

= -13/4.

d. f(-2/3) = (1/2)(-2/3) - 4

= -2/6 - 4

= -1/3 - 4

= -1/3 - 12/3

= -13/3.

Hope this helps!

Answer:

Step-by-step explanation:

shape D

Answer:

D.

Step-by-step explanation:

Well congruent means same size and same shape.

a) rectangle

This shape is a rectangle where as the given shape is a parallelogram.

This is not congruent to the given shape.

b) Parallelogram

This may be a parallelogram but it is too wide,

Hence, it is not congruent.

c) Rectangle

This is not a parallelogram,

Hence, this s not congruent

d) Parallelogram

This is a parallelogram with the same size just not in the same place but it is still congruent.

Thus, answer choices D. is the correct answer.

Answer:

Step-by-step explanation:

[tex]f(x) = 4 {e}^{x} [/tex]

[tex]f(2) = 4 {e}^{2} [/tex]

[tex]f(2) = 4 \times 7.389[/tex]

[tex]f(2) = 29.6[/tex]

( Approximately 30)

Hope this helps..

Good luck on your assignment..

Answer:

approximately 30

Step-by-step explanation:

[tex]f(x)=4e^x[/tex]

Put x as 2 and evaluate.

[tex]f(2)=4e^2[/tex]

[tex]f(2)=4(2.718282)^2[/tex]

[tex]f(2)= 29.556224 \approx 30[/tex]

Answer:

23+15i

Step-by-step explanation:

(-3+2i) (-3-7i)

multiply -3 w (-3+2i) and multiply -7i w (-3+2i)

9-6i+21i-14i^2

combine like terms

9+15i-14i^2

i squared is equal to -1 so

9+15i-(14x-1)

9+14+15i

23+15i

hope this helps :)

Answer:

New height= 41.4 inches

Second new height= 36inches

Step-by-step explanation:

Height is assumed to be 36 inches

If it increases by 15%.

15%= 0.15

It's new height =( 36*0.15) +36

New height= 5.4+36

New height = 41.4 inches

This expression (36*0.15) is the expression of adding 15% to the height.

So if the 15% is taken away again , height= 41.4-(36*0.15)

Height= 41.4-5.4

Height= 36 inches

Answer:

$1137

Step-by-step explanation:

Solution:-

We will define the random variable as follows:

                       X: Monthly social security (OASDI) payments

The random variable ( X ) is assumed to be normally distributed. This implies that most monthly payments are clustered around the mean value ( μ ) and the spread of payments value is defined by standard deviation ( σ ).

The normal distribution is defined by two parameters mean ( μ ) and standard deviation ( σ ) as follows:

                       X ~ Norm ( μ , σ^2 )

We will define the normal distribution for (OASDI) payments as follows:

                       X ~ Norm ( μ , 116^2 )

We are to determine the mean value of the distribution by considering the area under neat the normal distribution curve as the probability of occurrence. We are given that 1/4 th of payments lie above the value of $1214.87. We can express this as:

                      P ( X > 1214.87 ) = 0.25

We need to standardize the limiting value of x = $1214.87 by determining the Z-score corresponding to ( greater than ) probability of 0.25.

Using standard normal tables, determine the Z-score value corresponding to:

                     P ( Z > z-score ) = 0.25 OR P ( Z < z-score ) = 0.75

                     z-score = 0.675

- Now use the standardizing formula as follows:

                     [tex]z-score = \frac{x - u}{sigma} \\\\1214.87 - u = 0.675*116\\\\u = 1214.87 - 78.3\\\\u = 1136.57[/tex]

Answer: The mean value is $1137

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57

Answer:

The 10th term is -524,288

Step-by-step explanation:

The general format of a geometric sequence is:

[tex]a_{n} = r*a_{n-1}[/tex]

In which r is the common ratio and [tex]a_{n+1}[/tex] is the previous term.

We can also use the following equation:

[tex]a_{n} = a_{1}*r^{n-1}[/tex]

In which [tex]a_{1}[/tex] is the first term.

The common ratio of a geometric sequence is the division of the term [tex]a_{n+1}[/tex] by the term [tex]a_{n}[/tex]

In this question:

[tex]a_{1} = 2, a_{2} = -8, r = \frac{-8}{2} = -4[/tex]

10th term:

[tex]a_{10} = 2*(-4)^{10-1} = -524288[/tex]

The 10th term is -524,288

Answer:

x = 300

n = 410

p' = 0.7317

[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]

Step-by-step explanation:

From the given information;

the objective is to answer the following:

(i) Enter an exact number as an integer, fraction, or decimal.

Mean x = 300

(ii) Enter an exact number as an integer, fraction, or decimal.

Sample size n = 410

(iii) Round your answer to four decimal places.

Sample proportion p' of the drivers who always claimed they buckle up is :

p' = x/n

p' = 300/410

p' = 0.7317

Which distribution should you use for this problem? (Round your answer to four decimal places.)

P' _ ( , )

The normal distribution is required to be used because we are interested in proportions and the sample size is large.

Let consider X to be the random variable that follows a normal distribution.

X represent the number of people that always claim they buckle up

∴

[tex]P' \sim Normal (\mu = p' , \sigma = \sqrt{\dfrac{p(1-p)}{n}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(1-0.7317)}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.7317(0.2683)}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{\dfrac{0.19631511}{410}})[/tex]

[tex]P' \sim Normal (\mu = 0.7317, \sigma = \sqrt{4.78817341*10^{-4}})[/tex]

[tex]\mathbf{P' \sim Normal (\mu = 0.7317, \sigma = 0.02188)}[/tex]

Answer:

(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

First graph in top row is the answer.

Step-by-step explanation:

The given function is, f(x) = x⁴ - 4x³ + x² + 6x

For zeros of the given function, f(x) = 0

x⁴ - 4x³ + x² + 6x = 0

x(x³ - 4x² + x + 6) = 0

Therefore, x = 0 is the root.

Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]

                                      = {±1. ±2, ±3, ±6}

By substituting x = -1 in the polynomial,

x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)

                           = 1 + 4 + 1 - 6

                           = 0

Therefore, x = -1 is also a root of this function.

For x = 2,

x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)

                           = 16 - 32 + 4 + 12

                           = 0

Therefore, x = 2 is a root of the function.

For x = 3,

x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)

                           = 81 - 108 + 9 + 18

                           = 0

Therefore, x = 3 is a root of the function.

x = 0, -1, 2, 3 are the roots of the given function.

In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.

From these points, first graph in top row is the answer.