or
Find the distance between the points (
–
4,2) and (
–
9,
–
10)

The exponential formula that shows population is y = y₀ (1.031)ˣ.

An exponential function is a function which can be defined as y = y₀ aˣ, Where 'x' is a variable and 'a' is a constant.

Given that,

The growth of population is exponential.

Also,

The initial population y₀ = 3190.

And after 4 year the population y = 3605.

Use exponential formula

y = y₀ aˣ     (1)

Where x = time

Substitute the values in the formula,

3605 = 3190 a⁴

3605/3190 = a⁴

1.13009  = a⁴

a = 1.031

Substitute the value of a in equation (1),

y = y₀ (1.031)ˣ

The required formula is y = y₀ (1.031)ˣ.

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Answer:

4

Step-by-step explanation:

let n be the integer , then n tripled is 3n, so

[tex]\frac{3}{4}[/tex] n + 9 = 3n ( multiply through by 4 to clear the fraction )

3n + 36 = 12n ( subtract 3n from both sides )

36 = 9n ( divide both sides by 9 )

4 = n

the required integer is 4

The growth of the mass of the sample of a bacteria is represented by the exponential model m(x) = 5 · 1.02ˣ.

In this problem we find the case of mass of a sample of a bacteria (m(x)), in miligrams growing in time (x), in days. This growth is done exponentially, the exponential model is shown below:

m(x) = m' · (1 + r / 100)ˣ

Where:

We have that the mass of the sample was initially 5 miligrams and grows at a rate of 2 % during 10 days. If we know that m' = 5 mg and r = 2, then the exponential model for the sample is:

m(x) = 5 · 1.02ˣ

The exponential model for the sample of a bacteria is equal to m(x) = 5 · 1.02ˣ.

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Answer:

The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.

Answer:

Hi!

If you're trying to solve for z, the answer would be -34.

I hope this helps you :)

The average speed of the winning car is  79.38 miles per hour.

Given : Distance covered by rally car race course = 515.97 miles

Time taken to complete the course by winning car = 6.5 hours

The average speed of the winning car = ( Distance covered by rally car race course) ÷  (Time taken to complete the course by winning car)

= (515.97)÷ (6.5) miles per hour

= 79.38 miles per hour

Hence, the average speed of the winning car =  79.38 miles per hour.

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there you go i think

Answer:

Below

Step-by-step explanation:

.94 % is .0094 in decimal

   this exponential growth is like a bank account compounded yearly

         factor =  ( 1+.0094)^30  = 1.3240  

                   which would represent 32.40% growth

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]

(The square of the square root of a value is the value itself

[tex](\sqrt{x} )^2 \;is\;x[/tex])

The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]

Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

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Answer:

(7,-1)

Step-by-step explanation:

x + 7y = 0

x = -7y  Substitute -7y for x

2x -8y = 22

2(-7y) - 8y = 22

-14y - 8y = 22

-22y = 22  Divide both sides by -1

y = -1

Solve for x:

x - -7y

x = -7(-1)

x = 7

(7,-1)

Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

Answer:

  (d)  The other solution to function f is -3 + 5i

Step-by-step explanation:

Given a solution to quadratic function f is -3-5i, you want to know the other solution.

The complex solutions to quadratic equations come in conjugate pairs. That is, if one solution is -3-5i, the other solution will be the same thing with the sign of the imaginary part reversed:

  The other solution is -3+5i.

__

Additional comment

This is true only if the quadratic has real coefficients. (We typically don't study any other kind.)

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

The equation in the form Ax+ By=C is 4x-3y=27 if the line passes through the point (-6, 1) and slope is 4/3.

A mathematical formula that connects two expressions with the equals sign (=) expresses the equality of the two expressions. The word equation and its translations in several languages might have slightly different meanings. For instance, in French, an equation is defined as including one or more variables, whereas in English, an equation is defined as any properly expressed formula that consists of two expressions joined by the equals sign.

The values of the variables that must fulfill the equality to make up the solution are referred to as the unknowns, together with the variables for which the equation must be solved.

Given point is (-6, 1)

Slope m=4/3

The equation of the line is:

y-y₁=m(x-x₁)

y-1=(4/3)(x+6)

3y-3=4x+24

4x-3y=27

Therefore, the equation in the form Ax+ By=C is 4x-3y=27

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After using trigonometric function the value of to the nearest tenth digit is 11.11

What is Trigonometric function ?

Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA

Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.

Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11

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Answer:

  B.  False

Step-by-step explanation:

You want to know if it is true that a tessellation can be created from circles.

A tessellation is the covering of a plane, using one or more geometric shapes with no overlaps and no gaps.

As the attachment shows, it is not possible to cover a plane with circles, leaving no gaps.

A tessellation cannot be created using circles. The proposition is False.

True , a 95% confidence interval for the risk difference for obesity among members of the poor population compared to the affluent population is (-0.03, 0.23).

The critical value for alpha is 0.05 and z is 1.96 .

The corresponding confidence interval is ( 6.235 , 7.165).

Therefore the above statement is true.

Confidence Interval, to put it simply, is a range within which we are confident that the genuine value exists. The probability that a confidence interval will contain the real parameter value depends on the confidence level that is chosen for the interval.

The phrase "Confidence Interval" refers to the range of values that is typically used to handle population-based data, extracting precise, important information with a given level of confidence.

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The slope and y intercept of the equation are -6 and 75 respectively.

The slope of a line is a number that describes both the direction and the steepness of the line.

Given that, the equation of a line is y = 75 - 6x

Comparing to the standard equation of the line, y = mx+c

m = slope and c is the y intercept.

In the equation, we can see,

The slope (m) = -6

The y intercept (put x = 0) = y = 75 - 6x0

y = 75

Hence, the slope is -6 and y intercept is 75.

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Answer:

  (a)  2

Step-by-step explanation:

You want the greatest common factor of 18, 24, 40.

The prime factorization of these numbers is ...

The only common factor is 2.

2 is the greatest common factor of 18, 24, and 40.

If Liana is indifferent between the bundles (2,6) and (6,2), then it means that she values these two bundles equally. This means that Liana does not have a preference for one bundle over the other.

If Liana's indifference curves are bowed inward, it means that she is willing to give up more units of one good in order to get more units of the other good, as she moves along the indifference curve. This implies that Liana has a diminishing marginal rate of substitution (MRS) between the two goods.

Therefore, if Liana is indifferent between (2,6) and (6,2), it does not necessarily follow that she prefers (4,4) to (6,2). It is possible that Liana may also be indifferent between (4,4) and (6,2), or she may prefer (6,2) to (4,4). This would depend on the specific shape and location of Liana's indifference curves.

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Answer:

The original price of the tie was 20 dollars

Step-by-step explanation:

The price of the t-shirt was originally 24, but because he bought it on sale, he would have payed 12 because 24x.5=12.  This means we can subtract the value payed for the shirt from the total money payed. 22(total)-12(shirt)=.  10 (tie). However, 10 is the price he payed for the tie, not its original value. We can find this by multiplying 10x2, which gives us our answer.

Answer:

20 dollars is the original price

The claim of the producer can be accepted at 5% significant level since the 30 hours is within 21.8118 < X < 30.932

The claim of the producer cannot be accepted at 20% significant level since the 30 hours is not within 23.648 < X < 29.102

The claim is done using t score as the sample is less than 30. the formula for t scores is as follows

= x-bar ± t(s/√n)

from the given data the mean is calculated

sample mean, x-bar = (15 + 28 + 33 + 24 + 28 + 25 + 31 + 27) / 8

= 211/8

= 26.375

sample standard deviation, s

variance = (15 - 26.375)² + (28 - 26.375)² + (33 - 26.375)² + (24 - 26.375)² + (28 - 26.375)² + (25 - 26.375)² + (31 - 26.375)² + (27 - 26.375)²) / (8 - 1)

= 207.875 / 7

= 29.696

standard deviation = √variance

= √29.6964

= 5.45

Definition of variables

mean, x-bar = 26.375

standard deviation, s = 5.45

sample size, n = 8

significance level = 5%

confidence level = 1 - significance level = 1 -  0.05 = 0.95 = 95%

z score, z

For sample size less than 30, n < 30. t scores are used

degree of freedom, df = n - 1 = 8 - 1 =7

t score for 95% confidence level and df of 7  = 2.365

substituting into the formula

= x-bar ± t(s/√n)

= 26.375 ± 2.365 (5.45 / √8)

= 26.375 ± 4.557

= 21.8118 < X < 30.932

t score for 20% significant level and df of 7 = 1.415

substituting into the formula

= x-bar ± t(s/√n)

= 26.375 ± 1.415 (5.45 / √8)

= 26.375 ± 2.727

= 23.648 < X < 29.102

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The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

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The statement "Return on equity will not change if the firm increases its use of debt" is false.

Return on equity (ROE) is a financial ratio that shows how well a company is managing the capital that shareholders have invested in it. To calculate ROE, one would divide net income by shareholder equity.

Given is a statement, "Return on equity will not change if the firm increases its use of debt".

As we know that, The equity equals the assets minus total debt, a company decreases its equity by increasing the debt, or we can say, when debt increases, the equity decreases and since equity is ROE's denominator, ROE in turns gets a boost.

Hence, the statement "Return on equity will not change if the firm increases its use of debt" is false.

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a) The probability that Cathy passes the CPA on the first try is of: 0.56 = 56%.

b) The probability that Cathy passes the CPA exam on the second or third try is of: 0.3548 = 35.48%.

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

56% of students who graduated pass the CPA exam, hence the probability of passing on each test, including the first, is of:

0.56 = 56%.

Then the probabilities for the second or the third test are given as follows:

Then the probability that Cathy passes the CPA exam on the second or third try is calculated as follows:

p = 0.44 x 0.56 + 0.44² x 0.56 = 0.3548 = 35.48%.

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The ice cream that the machine produces during the 2nd minute will be 0.8 cups of ice cream.

Rate demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Typically, a rate is defined as the ratio of two quantities expressed in different units. The first quantity is typically written as the numerator of a fraction, and the second quantity is written as the denominator. By condensing them into the simplest form possible, we can calculate the rate.

A rate is a ratio that contrasts two distinct quantities represented by various units. A comparison of two numbers with various quantities or units is called a rate. A ratio or a rate out of 100 is what is known as a percentage.

Here, landon's ice cream machine produced 1.2 cups of ice cream in 3 minutes. If it produced the same amount each minute, the ice cream that the machine produces during the 2nd minute will be:

= (1.2 / 3) × 2

= 0.4 × 2

= 0.8 cups.

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