A local farmer had a mouse problem in his barn. He estimated there were about 800
mice to start with. He adopted some cats and noticed that the number of mice was
decreasing by 8%/wk. The graph models the number of mice x weeks after the
farmer adopted the cats.
Identify and interpret the key features of the exponential function modeled in terms
of this situation!

Answer: Carol's Thrift shop rate of change = $4.99/item

Wilma's Child Care rate of change is $7.50/hr

Step-by-step explanation:

Carol's Shop: equation of the line is in y=mx + b form, where m = slope = rate of change = $4.99/item

Wilma's slope = (y2 - y1) / (x2 - x1) = (15-0)/ (2-0) = $7.5/hr

Wilma's has the greater rate of change

Answer: 25*tan(35°)

Step-by-step explanation: For this problem, since the triangle is a right triangle, you must use the formula, tangent(Ф) = opposite/adjacent. In this case, Ф = 35 degrees. The side opposite to the angle Ф is x, and the side adjacent to Ф is 25. Therefore,

tangent(35°) = x/25

After multiplying the 25 over,

x = 25*tan(35°)

Answer:

-54

Step-by-step explanation:

8(-9)=-72

6(-3)=-18

-72+(-18)=-54

-Hope this helped

Answer:

There are 80 lunch items altogether.

Step-by-step explanation:

If the ratio of hotdogs to hamburgers is 10:30 then all we have to do is multiply the whole ratio by 2 to get 20:60.

So it there are 20 hotdogs and 60 hamburgers then there are 80 lunch items altogether because 20+60=80.

;)

According to the given dot plot, the striking deviation is at the value of 4, making the correct answer option C: 4.

What is the striking deviation?

A striking deviation is a noticeable or significant difference or deviation from the norm or expected value in a data set. It refers to an observation or value that stands out from the others due to its higher frequency, magnitude, or significance. In statistics, striking deviations can be identified through various measures, such as standard deviation, variance, or graphical representation, such as dot plots or box plots.

To determine the striking deviation in the given dot plot, we need to look for the value with a noticeably larger number of dots compared to the others. We can do this by comparing the frequency of dots for each value. From the given graph, we can see that the frequency of dots at 4 is significantly higher than the other values. This means that 4 has a higher occurrence or significance in the data set compared to the other values.

Therefore, the striking deviation is at the value of 4, making the answer option C: 4.

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Answer:

15.13 units

Step-by-step explanation:

The equation of line passes through the points (2, 0) and (0, -1) will be;

⇒ y = 1/2 x - 1

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (2, 0) and (0, -1).

Now,

Since, The equation of line passes through the points (2, 0) and (0, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

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

m = - 1 / - 2

m = 1 / 2

Thus, The equation of line with slope 1 / 2 is,

⇒ y - 0 = 1 / 2 (x - 2)

⇒ y = 1/2 x - 1

⇒ y = 1/2 x - 1

Therefore, The equation of line passes through the points (2 , 0) and

(0, - 1) will be;

⇒ y = 1/2 x - 1

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The conversion of 41.98km to centimeters is gotten as; 4198000 cm

We are dealing with units conversion here and in this concept it involves converting from unit to the other using a standard conversion ratio.

Now, we are given the value as 41.98 km. However, we want to convert this value from kilometers to centimeters. The conversion ratio is;

1 kilometer = 100000 centimeters

Thus, using the conversion ratio above, we can say that;

41.98 km = (41.98 * 100000)/1

= 4198000 cm

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A graph of the line that passes through the points (3, -7) and (-3, 5) is shown in the image attached below. Also, the equation of this line is y = -2x - 1.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, the points on the line include the following:

Substituting the given points into the formula, we have;

Slope, m = (5 - (-7))/(-3 - 3)

Slope, m = (5 + 7)/(-6)

Slope, m = 12/-6

Slope, m = -2

At point (3, -7), a linear equation for the line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

y + 7 = -2(x - 3)

y + 7 = -2x + 6

y = -2x + 6 - 7

y = -2x - 1

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Step-by-step explanation:

because

ST = QR = 16

that means that also the distance from the center point is the same.

in other words :

UC = VC

therefore,

2x = 5x - 9

0 = 3x - 9

9 = 3x

x = 3

The pair of numbers that would be in the columns, considering the proportional relationship, is given as follows:

20 would be in the column for 2, and 60 would be in the column for 6.

A proportional relationship is a special linear function, with intercept having a value of zero, in which the output variable is obtained with the multiplication of the input variable and the constant of proportionality k, as shown as follows:

y = kx

The table is extended to represent more equivalent ratios for 2:6, hence the constant of the relationship is given as follows:

k = 6/2 = 3.

Hence the equation is:

y = 3x.

The values given by each column are given as follows:

When x = 20, the numeric value of the relationship is of:

y = 3 x 20 = 60.

Hence the first option is correct.

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Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.

Suppose we have 2 positive integers, a and b, then:

gcd (a, b) = the greatest common divisor = common prime factors of a and b

lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b

In the given problem:

gcd (a, b) = 15

prime factorization of 15:

15 = 3 x 5

Hence,

a = 3 x 5 x ....

b = 3 x 5 x ....

lcm (a, b) = 90

prime factorization of 90:

90 = 3 x 5 x 2 x 3

Therefore the possible pairs of a and b are:

Combination 1:

a = 3 x 5 = 15

b = 3 x 5 x 2 x 3 = 90

Combination 2:

a = 3 x 5 x 2 = 30

b = 3 x 5 x 3 = 35

We can conclude the two integers are 15 and 90 or 30 and 45.

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Answer:

y = - [tex]\frac{3}{5}[/tex] x + 8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{5}[/tex] , then

y = - [tex]\frac{3}{5}[/tex] x + c ← is the partial equation

to find c substitute (5, 5 ) into the partial equation

5 = - 3 + c ⇒ c = 5 + 3 = 8

y = - [tex]\frac{3}{5}[/tex] x + 8 ← equation of line

The instance has a mean of 1834 and a standard deviation of 231.2, respectively.

Given data;

A comparison of typical earnings for different professions can be found in the international average salary income database. The information is acquired from publications and reports that were obtained directly from governmental organizations, like the US Bureau of Labor Statistics or the ILO. Consider being informed that the standard deviation of the income of computer programmers in Canada is $458.60 and that a computer programmer in Canada making $2,063.30 has a z-score of 0.50 in comparison to other programmers in Canada. Consequently, the typical pay for computer programmers in Canada is. Assume you are also informed that the mean wage for computer programmers in Portugal is $1,387.40 and that a computer programmer in Portugal who earns $1,387.40 has a z-core of 2.00 in comparison to other computer programmers in Portugal is $925.

Since, the salaries are relative and we know that the z-score is given by;

z = X - μ / σ

0.50 = 2063.30 - μ / 458.60

μ = 2063.30 - 229.3

μ = 1834

As, the salaries are relevant so;

2 = 1387.40 - 925 / σ

σ = 462.4/2

σ = 231.2

Hence, the mean and standard deviation of the case is 1834 and 231.2 respectively.

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The relationship has a constant of proportionality of 38/39

From the question, the given parameters are

Variable 1 = 9/6

Variable 2 = 19/13

The above parameters can be represented as the following points

(x, y) = (9/6, 19/13)

The constant of proportionality of the points is then calculated as

k = y/x

Substitute the known values in the above equation

So, we have the following equation

k = (19/13)/(9/6)

Evaluate the quotient

So, we have

k = 38/39

Hence, the constant of proportionality is 38/39

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Answer:

7 :D

Step-by-step explanation:

Lets go step by step!

When we do something to one side, we must do it to the other!

2x - 5 < 9

2x - 5 + 5 < 9 + 5

2x < 14

2x/2 < 14/2

x < 7

Your answer is 7 :D

Have an amazing day!

Please rate and mark brainliest!

Answer:

x=7

Step-by-step explanation: Okay so,

2x−5=9

First, you take the 5 and add it to the 9:

2x=9+5=

2x=14

Then you divide 2x by 2 and what you do to one side you do to the other, so you also divide 14 by 2:

2x/2=14/2=

x=7

Hope this helps!

The original price for the television is $883.51

A store will discount an item by a percent of the original price.

Given that, a store is having a sale on televisions, all televisions are on sale for 15% off, a customer buys a television for $750.99.

Let the original price be x

x*(100-15)% = 750.99

x = 750.99*100/85

x = 883.51

Hence, the original price for the television is $883.51

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The linear equation of the table is, t = -5/3a +19

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

y = mx + c

where

y = dependent variable

m = slope

x = independent variable

c = y - intercept

Here we have the table with the values of t and the value of a.

Now, we need to find the linear equation for this table.

In order to find the linear equation, we need the values of slope and the y intercept values.

To find the value of slope we have to take two point from the given table.

They are (6,9) and (9,4).

Now, apply the value on the slope formula, then we get,

m = (4 - 9) / (9 - 6)

m = -5/3

Now, we have to use the slope m and the point (6,9), to find the value of y intercept,

Then we get the value of c as,

9= -5/3(6)+c

9=-10+c

c=19

Therefore, the linear equation of the table is, t = -5/3a +19

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The length of side BC is 15.6 cm and the size of angle EDC in degrees is 56.5°

From the question, we are to determine the length of BC

From the given information,

m ∠ABC = 30°

AC = 9 cm

By using SOH CAH TOA, we can write that

tan (m ∠ABC) = AC / BC

tan (30°) = 9 / BC

BC = 9 / tan (30°)

BC = 15.588

BC ≈ 15.6 cm

To determine the measure of angle EDC,

First we will determine the length of CD

From the diagram,

BD = BC + CD

20 = 15.588 + CD

CD = 20 - 15.588

CD = 4.412

Now, using SOH CAH TOA

cos (m ∠EDC) = CD / DE

cos (m ∠EDC) = 4.412 / 8

cos (m ∠EDC) = 0.5515

m ∠EDC = cos⁻¹(0.5515)

m ∠EDC = 56.5300°

m ∠EDC ≈ 56.5°

Hence, the length of BC is 15.6 cm and the measure of EDC is 56.5°

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For the given amplitude , period and displacement , equation of the modelling the displacement d as a function for the given time t for the initial movement in negative direction is equal to

d(t) = -13sin(8πt + (-8πt₀)) .  

As given in the question,

It is given that object moves in simple harmonic motion ,

Amplitude = 13cm

Period 'T' = 0.25 seconds

f = 1/T

 = 1/ 0.25

 = 100/25

 = 4 / sec

displacement d from rest position is 0.

t  = t₀

Equation of modelling the displacement d as function of time given time t

is given by :

d(t) = A sin(2πft + -2πft₀)

⇒d(t) = -13sin[2π(4t) + -2π(4t₀)]

⇒d(t) = -13sin[8πt -8πt₀]

As initial movement in negative direction.

Therefore, for the given amplitude , period and displacement , equation of the modelling the displacement d as a function for the given time t for the initial movement in negative direction is equal to

d(t) = -13sin(8πt + (-8πt₀)) .  

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The function, g(x), has a constant rate of change and will increase at a faster rate than the function f(x) for all the values of x.  

Given:

g(x) = 5/2 x -3 ..... (1)

f(x) = - 3.5 at x = 0

So, putting the value of x=0 in equation (1) for comparison. We get,

g(x) at x = 0

=> g(x) = 5/2 x (0) - 3

=> g(x) = -3

In this value of x function g(x) is faster than function f(x) having a value equal to -3.5.

Similarly, put x = 1 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (1) - 3

=> g(x) = (5-6)/2

=> g(x) = -1/2

In this value of x function g(x) is faster than function f(x) having a value equal to -1.

Similarly, put x = 2 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (2) - 3

=> g(x) = (5-3)

=> g(x) = 2

In this value of x function g(x) is faster than function f(x) having a value equal to 1.5.

Similarly, put x = 3 in equation (1) for comparison. We get,

=> g(x) = 5/2 x (3) - 3

=> g(x) = (15/2 - 3)

=> g(x) = 7.5 - 3

=> g(x) = 4.5

In this value of x function g(x) is faster than function f(x) having a value equal to 4.

Therefore, for all values of x function g(x) is faster than function f(x).

function f(x).

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The population of Shanghai is 5 times larger than population of Monterrey.

What is population?

Typically, the term "population" refers to the total number of people living in a particular area, be it a city or town, region, country, continent, or the entire world.

Main body:

The population of Monterrey, Mexico is  people = [tex]4*10^6[/tex]

The population of Shanghai, China is  people  = [tex]2*10^7[/tex]

To find how many times the population of Shanghai is lager than Monterrey.

In order to find how many times the population of Shanghai is lager than Monterrey we will find the ratio of populations of Shanghai and  Monterrey.

Thus we divide the population of Shanghai by the population of Monterrey to find how many time the population of Shanghai is larger.

Thus, we have:

[tex]\frac{2*10^7}{4*10^6}[/tex]

Simplifying by using properties of exponents.

⇒  [tex]\frac{2*10^7}{4*10^6}[/tex] , USING [tex]a^{x} -a^{y} =a^{(x-y)}[/tex]

⇒ [tex]\frac{2*10}{4}[/tex]

⇒ 20/4

⇒ 5

Therefore, we can say that the population of Shanghai is 5 times larger than population of Monterrey.

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Using the inequality concept, the expression which models the maximum

number of days in which she can rent the car is 56. 37x + 45 ≤ 440.

Maximum amount allowed to spend

= $440

Rental car company fixed charge per day to rent a car = $56.37

Hawa drives a car to 500 miles.

Rate per mile drive = $0.09

let x days be maximum number of days hawa afford rent with budget.

the inequality equation exists here is

(days × charge of rent per day) + (rate per mile x number of miles) ≤ 440

=> 56.37x + 0.09 × 500 ≤ 440

=> 56.37x + 45 ≤ 440

Therefore, the required inequality is 56.37x + 45 ≤ 440

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The value of x is when the value of the function f(x) = 7 is x= -24 and x = 16

Function:

A correspondence from one value x of the first set A to another value y of the second set B. It relates inputs to output is known as the function of the relation.

Given,

Here we have the function f(x) = 0.5|x - 4| - 3.

Now, we have to find the value of x when the value of f(x) = 7.

In order to find the value of x as have to equate the give function with the value of f(x), that is 7,

So, when we apply these on the function then we get,

=> 7 = 0.5|x - 4|-3

Now, we have to move all the numbers instead of x, then we get,

=> 7 + 3 = 0.5|x - 4|

=> 10 = 0.5 |x - 4|

=> 10/0.5 = |x - 4|

=> 20 = |x - 4|

So in this place we can get the following forms,

=> x - 4 = 20 and

=> x - 4 = - 20

Because we get two values being an absolute value function.

Now, we have to add 4 on both sides

Then we get

=> x - 4 + 4 = 20 + 4 and

=> x - 4 + 4 = - 20 + 4

So, the value of x is

=> x = 24 and x = - 16

Therefore, for the given function the values of x are 24 and - 16.

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

let the denominator of the fraction be x , then the fraction is

[tex]\frac{x-5}{x}[/tex]

increasing the numerator and denominator by 4

[tex]\frac{x-5+4}{x+4}[/tex] = [tex]\frac{x-1}{x+4}[/tex]

this fraction is then equal to 3 times ( triple ) the value of the fraction, so

[tex]\frac{x-1}{x+4}[/tex] = [tex]\frac{3(x-5)}{x}[/tex] ( cross- multiplying )

3(x - 5)(x + 4) = x(x - 1) ← expand factors on left using FOIL

3(x² - x - 20) = x(x - 1) ← distribute parenthesis on both sides

3x² - 3x - 60 = x² - x ( subtract x² - x from both sides )

2x² - 2x - 60 = 0 ( divide through by 2 )

x² - x - 30 = 0 ← in standard form

(x - 6)(x + 5) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 5 = 0 ⇒ x = - 5

however, x > 0 , then x = 6

original fraction

= [tex]\frac{x-5}{x}[/tex] = [tex]\frac{6-5}{6}[/tex] = [tex]\frac{1}{6}[/tex]

Answer: We conclude that the mean commute time in the U.S. is less than half an hour. We are given a random sample of 500 people from the 2000 U.S. Census is selected who reported a non-zero commute time. In this sample, the mean commute time is 27.6 minutes with a standard deviation of 19.6 minutes.

So, Null Hypothesis,  :  30 minutes      {means that the mean commute time in the U.S. is more than or equal to half an hour}

Alternate Hypothesis,  :  < 30 minutes     {means that the mean commute time in the U.S. is less than half an hour}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                          T.S. =    ~

where,  = sample mean commute time = 27.6 minutes

           s = sample standard deviation = 19.6 minutes

           n = sample of people from the 2000 U.S. Census = 500

So, the test statistics  =    ~

                                      =  -2.738

The value of t test statistic is -2.738.

Also, P-value of test statistics is given by the following formula;

          P-value = P(  < -1.645)

Since, we know that at large sample size, the t distribution follows like normal distribution, that means;

             P(  < -1.645)  =  P(Z < -1.645) = 1 - P(Z  1.645)

                                        =  1 - 0.95002 = 0.04998

Now, at 5% significance level the t table gives critical values of -1.645 at 499 degree of freedom for left-tailed test.

Since our test statistic is less than the critical value of t as -2.378 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

Answer:

Step-by-step explanation:

1 is correct

2 is correct

3 is wrong

4 is correct

5 is correct

6 is wrong

7 is wrong

For 7:

360 - 90 - 61 - 65

= 144

For 6:

180 - 144

= 36

For 3:

180 - 115 - 36

= 29

The area of the trapezoid formed is equal to 12 square meters.

The area of the trapezium is calculated by using the formula.

A =(a + b) × h / 2

In the given trapezium the length of the parallel sides are:

2 m and 4 meters.

The distance between the parallel sides is 4 m

Area of the trapezium = (2+4) × 4÷2 = 12 square meters

A trapezoid is a quadrilateral that has at least one pair of parallel sides.

A trapezoid is a convex quadrilateral by definition in Euclidean geometry. The parallel sides serve as the trapezoid's bases. The remaining two sides are referred to as the lateral sides or the legs if they are parallel; otherwise, the trapezoid appears to be a parallelogram, with two pairs of bases.

Therefore the area of the trapezium is 12 square meters .

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Answer:

$24.27

Step-by-step explanation:

Original price: $

34.99

Discount percentage:

25

%

Results

Discount:

$8.75

Final Price:

$26.24

Details

Discount = Original Price x Discount %/100

Discount = 34.99 × 25/100

Discount = 34.99 x 0.25

You save = $8.75

Final Price = Original Price - Discount

Final Price = 34.99 - 8.7475

Final Price = $26.24

- 7.5% = $24.27

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

A sweater priced at 34.99 is on sale for 25% off. Then the cost after the discount is calculated as,

⇒ (1 - 0.25) x 34.99

⇒ 26.24

If the sales tax is 7.5%. Then the cost after the sales tax is given as,

⇒ (1 + 0.075) x 26.2425

⇒ 28.21

The cost of the sweater after a 25% of discount and 7.5% of sales tax will be 28.21.

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