Jackson invested $320 in an account paying an interest rate of 3. 2% compounded

continuously. Assuming no deposits or withdrawals are made, how long would it

take, to the nearest tenth of a year, for the value of the account to reach $410?

Answer:

x = 67.5 degrees

Step-by-step explanation:

this is an octagon which has 8 sides

the sum of all interior angles can be found by taking the number of sides, reducing it by 2, and then multiplying by 180

(8-2)*180 = 6(180) = 1080

the 1080° must be split equally among all 8 angles because it is a 'regular' polygon

1080/8 = 135

however, 'x' represents half of each regular angle so it is 67.5 degrees

the term for the given Table is given below:

Mathematics is all about theorems. A rigorous proof is a specific form of logical argument that has been used to demonstrate the truth of a claim, which is what a theorem is.

A. Definition refers to a statement that exactly defines the object, thing, or everything.

B. Postulate or axiom is a statement that is accepted as true in order to initiate an argument.

C. Common notion is the statement that helps to understand the common sense of the subject.

D. Theorem is a statement that shows proof on the basis of previously made statements.

E. Corollary is a statement that acts as a small proof that has already been proven.

Therefore, the correct matching for the given terms will be:

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Complete question:

Explain the main parts and uses of two kinds of proofs. March the word with the right definition.

A. Definition

B. Postulate(axiom)

C. Common notion

D. Theorem

E. Corollary

1. A statement that is assumed to be true without proof

2. A statement that has already been proven to be true

3. A statement that tells exactly what something is or means

4. A statement that makes sense based on another statement that has already been proven

5. A statement that is not officially defined but that is understood to be common sense.

Help pls :3

Answer:

The function y = 5 + 2x represents a linear function.

Answer:

Step-by-step explanation:

-2/11

Answer:

-1/5 × 10/11 = -2/11

Step-by-step explanation:

If you multiply -1/5 by 10/11, it becomes the fraction -2/11 or 0.1818...

Answer:

15 percent

Step-by-step explanation:

There are total 40 students in class because 6 plus 12 plus 14 plus 20 is 40. Fraction would be 6/40

Answer:

below

Step-by-step explanation:

Interest = prt       p = principle = 500   r = rate in decimal = .12   t = years

            = 500 ( .12)(4) = 240 dollars

Answer:

7^3

Step-by-step explanation:

since seven is being multiplied by itself 3 times, it is being cubed. So it needs to be raised to the third power.

hope this helps!!! :3

Answer: (-7)(-7)(-7) is equal to -7^3 (just imagine that the three is on the top right outer corner of the 7)

Step-by-step explanation:

A power is when you multiply a number by itself a certain number of times, in this case, we are multiplying the number 7 by itself 3 times. Every time it is multiplied by its self, the power of that number goes up (if you are using a power of one for any number, it will stay the same). Here is an example:

-7 to the first power is just -7.

-7 to the second power, or squared is just (-7)(-7) or (-7) x (-7).

-7 to the third power, or cubed, is just (-7)(-7)(-7) or (-7) x (-7) x (-7).

Hope this helps!!!

Answer:

Mixed Number: 11 1/4

Decimal: 11.25

Step-by-step explanation:

Answer:

[tex] \red {\boxed{\tt{ 11\frac{14}{56} }}}[/tex]

Step-by-step explanation:

[tex] \tt4 \frac{3}{8} \times 2 \frac{4}{7} \\ \\ \tt \frac{8 \times 4 + 2}{8} \times \frac{7 \times 2 + 4}{7} \\ \\ \tt \frac{35}{8} \times \frac{18}{7} \\ \\ \tt{ \frac{35 \times 18}{8 \times 7} } \\ \\ \tt {\frac{630}{56}} \\ \\ \tt{ 11\frac{14}{56} }[/tex]

The growth factor in the function is 5.

An exponential function with the form A(t) = [tex]C a^t[/tex], where a > 0

When t = 0, the function's initial value is represented by the number C, and the growth (or decay) factor is represented by the number a.

If a > 1, the function represents growth; If 0 < a < 1, the function represents decay.

Given:

y = 4 x [tex]5^7\\[/tex]

we know the general form of Exponential function

g(x) = [tex]ab^x[/tex]

where a is the initial amount

b is the growth or decay factor

and, x is the time

Now, comparing to the given function

Initial amount= 4

Growth factor = 5

time = 7

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People who dislike cantaloupe are marginally more likely to be (0.455) likely to be.

The joint relative frequencies in a row or column of a data table are added in this case.

Therefore, we will create a representation of the table using the findings from the survey of 200 randomly selected individuals as follows:

Watermelon The total is not a watermelon

Cantaloupes: 93, 16, and 109

Not a cantaloupe 66 25 91

Total 159 41 200

The marginal relative frequency for those who dislike cantaloupe is therefore 0.455.

The complete complete question is,

How common are those who dislike cantaloupe, on a relative basis? startfraction 91 over 200 endfraction startfraction 25 over 91 endfraction startfraction 66 over 200 endfraction startfraction 91 over 200 endfraction.

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Answer:

The seismic coefficient represents the maximum horizontal equivalent acceleration expected in a failure wedge in slip potential and is obtained by averaging the horizontal forces in the deformable sliding mass, according to the equation: kmax=¯ah.

It is calculated by dividing the maximum acceleration response of a building by the peak ground acceleration of the underlying seismic hazard.

To calculate the seismic response coefficient, the following steps should be followed:

1. Identify the seismic hazard in the area. This can be done by consulting geological surveys and geological maps.

2. Calculate the peak ground acceleration of the seismic hazard. This can be done using the various seismic hazard assessment techniques such as the probabilistic seismic hazard analysis (PSHA) method.

3. Determine the maximum acceleration response of the building. This can be done by performing a dynamic analysis of the building using a computer simulation program or a hand calculation.

4. Divide the maximum acceleration response of the building by the peak ground acceleration of the seismic hazard to obtain the seismic response coefficient.

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The correct 2-variable equation that models how many feet Nick can run is: 25x = m,

Hence, option (d) is correct choice.

As per the data given,

We have,

Nick can run at a speed of 25 feet per second.

We need to convert the above statement in 2-variable equation models

We can write it as:

Distance covered by Nick will be:

25x = m

where x is the time in seconds that Nick runs and

m is the distance in feet that Nick runs.

The equation represents the relationship between time and distance using the constant speed of 25 feet per second.

The distance travelled is equal to the speed multiplied by the time.

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The period for which the force acts on the body is  0.6 seconds.

Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force acting on the particle equals the time rate of change of momentum.

Given the force applied is 4600 N

F = 4600 N

and change in momentum = Δm = 2760 kg m/s

force is given by a change in momentum to the change in time

F = Δm/Δt

Δt = Δm/F

Δt = 2760/4600

Δt = 0.6 seconds

Hence the change in time is 0.6 seconds.

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Answer:

Find the slope (1,3), (5,5): m = 0.5

Find the slope (0,-1), (2,3): m = 2

Find the slope (2,-3), (5,-4): m = -1/3

Step-by-step explanation:

m = y2-y1/x2-x1

Answer: 2, 1, -1/3

Step-by-step explanation:

y2-y1/x2-x1

5-3 = 2

5-4=1

2

The mean of this sampling distribution is 70.9, which is less than the value of the population median of  73, therefore, the sample median is a biased estimator of the population median.

The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

A statistic used to estimate a parameter is an unbiased estimator if the mean of its sampling distribution is equal to the value of the parameter being estimated.

We obtained the following data from part (a) of this problem,

Sample 1: 64, 65, 73, and median is 65.

Sample 2: 64, 65, 74, and median is 65.

Sample 3: 64, 65, 76, and median is 65.

Sample 4: 64, 73, 74, and median is 73.

Sample 5: 64, 73, 76, and median is 73.

Sample 6: 64, 74, 76, and median is 74.

Sample 7: 65, 73, 74, and median is 73.

Sample 8: 65, 73, 76, and median is 73.

Sample 9: 65, 74, 76, and median is 74.

Sample 10: 73, 74, 76, and median is 74.

Let us calculate the mean of this sampling distribution,

μ(median) = ( 65+65+65+73+73+73+73+74+74+74)/10

μ(median) = 709/10

μ(median) = 70.9

The mean of the sampling distribution is found to be equal to 70.9.

(b) 70.9, which is less than the value of the population median of

73, therefore, the sample median is a biased estimator of the population median.

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Given that point T is the center of dilation, we know that the length of line segments TX' and TY' are proportional to the length of line segments TX and TY, respectively.

We can express this as:

TX' = k * TX

TY' = k * TY

where k is the scale factor.

We are given the lengths of TX' and TY':

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

Next, we are given the length of XX':

XX' = 2

And using the dilation formula, we can find XX:

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

Finally, we can find TX by using the Pythagorean theorem:

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

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TX' = k * TX

TY' = k * TY

TX' = 6

TY' = 9

So, we can solve for k:

9 / k = 6

k = 9 / 6 = 3 / 2

Now that we know the value of k, we can find TY:

TY = TY' / k = 9 / (3 / 2) = 6 * (3 / 2) = 9

XX' = 2

XX = XX' / k = 2 / (3 / 2) = 2 * (2 / 3)

TX^2 = TY^2 + XX^2

TX^2 = 9^2 + (2 * (2 / 3))^2

TX^2 = 81 + (4 / 3)^2

TX^2 = 81 + 16 / 9

TX^2 = 81 + 16 / 9

TX = √(81 + 16 / 9) = √(81 + 16 * 9 / 9) = √(81 + 16) = √97

So, TY = 9 and TX = √97. Therefore, YT = TY - TY' = 9 - 9 = 0.

Answer:

y = 10x + 60

Step-by-step explanation:

Hope this will help on your test.

The variable "Gallons of water in a swimming pool" is a quantitative variable.

Quantitative variables are variables that are numerical and can be measured on a scale, such as height, weight, or time. In this case, the number of gallons of water in a swimming pool can be measured and can take any value within a range, such as 0 to 100,000 gallons. Therefore, "Gallons of water in a swimming pool" is a quantitative variable.

In contrast, qualitative variables are variables that describe an attribute or characteristic of a person, place, or thing, and they do not have a numerical value. Examples of qualitative variables include hair color, religious affiliation, or nationality.

"

Complete question

Determine whether the variable is qualitative or quantitative. explain your reasoning.

Variable: Gallons of water in a swimming pool

"

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The probability of getting omeone is  25.3%

Find the probability of getting omeone in the 18-21 age bracket or omeone who repond?

Define the two events

A = someone is in the 18-21 age bracket

B = the person does not respond

Based on the table, we have

n(A) = number of people in set A = 76

n(B) = 31

n(A and B) = 11

So,

n(A or B) = n(A) + n(B) - n(A and B)

n(A or B) = 76+31-11

n(A or B) = 96

We have 96 people in the age 18-21 bracket, they didn't respond, or both.

Divide this over the 379 people surveyed

96/379 = 0.253 = 25.3%

Answer: 25.3%

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The equation of the each of the lines in slope-intercept form are:

5. y = -1/3x + 3.

6. y = 2x - 2

7. y = -8/3x + 4.

8. y = -2x + 1.

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

5. Slope (m) = rise/run = -1/3

y-intercept (b) = 3

The equation is: y = -1/3x + 3.

6. Slope (m) = rise/run = 2/1 = 2

y-intercept (b) = -2

The equation is: y = 2x - 2

7. Slope (m) = rise/run = -8/3

y-intercept (b) = 4

The equation is: y = -8/3x + 4.

8. Slope (m) = rise/run = -2/1 = -2

y-intercept (b) = 1

The equation is: y = -2x + 1.

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Answer:

The answer is x = 2. To solve for x, divide both sides of the equation by 8 to get x = 16/8 = 2.

Step-by-step explanation:

Answer:

[tex]8x = 16 \\ x = 16 - 8 \\ x = 8[/tex]

Answer:

Vipul answered correctly.

The nature of the roots of a quadratic equation depends on the value of the discriminant, which is given by b^2 - 4ac, where a, b, and c are coefficients in the equation ax^2 + bx + c = 0. If the discriminant is positive, the roots of the equation will be real and distinct, and their sign will depend on the sign of the coefficients a, b, and c. If p, q, and r are positive, the value of the discriminant (q^2 - 4pr) will be positive, and the roots of the equation px^2 + qx + r = 0 will be real and distinct, but their sign cannot be determined just based on the values of p, q, and r alone.

The limit of f(s) as s approaches 6 does not exist because the function has two different values for s approaching 6 from the left and from the right.

A limit is a concept in mathematics that deals with finding the value that a function approaches as the independent variable approaches a certain value.

We need to consider two different cases, as the function f(s) has different definitions for s less than or equal to 6 and s greater than 6.

For s less than or equal to 6, the function f(s) is defined as

=> 3s - 4.

As s approaches 6, the value of f(s) will approach

=> 3 * 6 - 4 = 14.

For s greater than 6, the function f(s) is defined as

=> 7 - 1/2 * s.

As s approaches 6, the value of f(s) will approach

=> 7 - 1/2 * 6 = 4.

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Answer:

1494

Step-by-step explanation:

15%($2,870+$3,150+$3,940) =1494

Therefore , the solution of the given problem of compound statements comes out to be choice D is right.

Like in any language, connectives are used to combine simpler statements to create complex statements in mathematics. And, or, if... then, and if and only if are the connectives that are frequently employed in mathematics. The truth value of the a compound statement is determined by variable the truth values of its simpler parts.

Here,

Given :function

To discover the true values

Which compound statement,

if p →q  is true, will have the same truth value?

The formulation of the logic biconditional link

p ↔ q, which is "p → q and q → p," provides the direct connection to the solution.

As a result, choice D is right.

Therefore , the solution of the given problem of  compound  statements comes out to be choice D is right.

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Answer:

E. - 11

Step-by-step explanation:

This is by the simple quantum physics moving by the gravitational carbon dioxide in the air that causes the numbers to evolve into the number 11 while mixed together

Answer:

I don't know. I hope this helps!

Step-by-step explanation:

Answer:

Tuna sandwich to likely

chicken sandwich to unlikely

Egg sandwich to impossible

Step-by-step explanation:

there is a lot more tuna than chicken sandwiches so it's likely

there is no egg sandwiches so it's impossible

Answer:

tan K = 4/3

Step-by-step explanation:

Tangent is a ratio. The side marked 32 is opposite from angle K. And the side marked 24 is adjacent to (next to) angle K.

Tangent K is the ratio:

opposite/adjacent

tan K = opp/adj

fill in the given side lengths

tan K = 32/24

simplify, both numbers are divisible by 8

tan K = 4/3

The possible values of two consecutive even integers, of which the sum of their squares is 1684, are 28 and 30 for positive integers, while for negative integers, they are  -28 and -30.

The difference between two consecutive even integers is 2.

Let the integers be a and (a+2). Then,

a² + (a + 2)² = 1684

a² + a² + 4a + 4 = 1684

2a² + 4a - 1680 = 0

a² + 2a -840 = 0

Hence, we get a quadratic equation.

There are three methods of solving a quadratic equations: by factoring, completing the square, and by using the abc formula.

Use the factoring method:

a² + 2a -840 = (a - 28) (a + 30)

a = 28  and a = -30

Hence, if the integers are positive, they are: 28 and 30.

If the integers are negative, they are -28 and -30.

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Answer:

Slope-intercept form is

y = mx + b

We want to get the y by itself on one side of the equation.

0 = 18x + 6y – 2

First let's subtract 6y from both sides.

-6y = 18x – 2

Next let's divide both sides by -6.

y = (18 / -6)x - (2 / -6)

y = -3x + 1/3

Step-by-step explanation: