Six car batteries weigh 46.2 pounds. Fourteen car batteries weigh 107.8 pounds. Does this represent a proportional relationship? If so, state the constant of proportionality.

The future value of $8904.56 compounded semi annually is $13,468.95 The interest earned is approximately $4,564.39

The future value of $8904.56 compounded continuously is $66,185.90.

The interest earned is approximately $57,281.34.

When an investment is compounded semi annually, it means that both the amount that was invested and the interest that has already been earned increases in value twice in a year.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = 8904.56 x 1.03^(7 x 2) = $13,468.95

Interest = future value - amount invested

$13,468.95 -  $8904.56 = $4,564.39

When an amount is compounded continusoly, it increases in value infinitely over the investment time horizon.

The formula for calculating future value when there is continuous compounding is : A x e^r x N

Where:

FV = 8904.56 x e^0.06 x 7 = $66,185.90

Interest = future value - amount invested

$66,185.90 - 8904.56 = $57,281.34

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The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.

An elevation simply means the height above sea level.

In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:

= 12.2 × 4

= 48.8 feet

He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:

= 3.6 × 10

= 36 feet.

Therefore, the change in elevation will be:

= Elevation up - Elevation down

= 36 - 48.8

= 12.8 feet.

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The unit rate which correctly corresponds to.the given rate; 6 eggs in 7 months is; 0.86 eggs per month.

A unit rate as the name implies is one in which case a given quantity is expressed in terms of one unit of the other quantity.

Such units are expressed as; a per b.

On this note, since the given rate is; 6 eggs in 7 months.

It follows that the rate can be expressed as;

6 eggs / 7 months

= 6/7 eggs per month.

= 0.85714 eggs per month.

And ultimately, when rounded to the nearest hundredth; we have; 0.86 eggs per month.

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The probability that your would get an odd number twice when the rolling is 1-8 is 12.5%

Probability is the chance of occurrence of an even (E) Over a period of time. That is, it is the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.

How to get the probability of the spinning?

From the analysis, the spinning is done twice from numbers 1-8

this means that in ever row, each number appears double.

The sample size is 8x8=64

1,1     1,2     1,3    1,4     1,5    1,6    1,7    1,8

2,1    2,2    2,3    2,4    2,5   2,6   2,7   2,8  

3,1     3,2    3,3   3,4     3,5   3,6   3,7   3,8

4,1    4,2    4,3   4,4    4,5   4,6    4,7   4,8

5,1      5,2   5,3   5,4     5,5    5,6    5,7  5,8

6,1      6,2    6,3  6,4     6,5    6,6   6,7   6,8

7,1      7,2     7,3   7,4    7,5    7,6   7,7  , 7,8

8,1     8,2     8,3  ,,8,4 ,,, 8,5 ,,8,6  8,7,,, 8,8

The required outcome is 8

These outcomes are

1,1  2,2   3,3   4,4   5,5   6,6  7,7  8,8=8 outcomes

Probability of and event is

P=[tex]\frac{number of required outcome}{number of possible outcome}[/tex]

P(E)=[tex]\frac{8}{64}[/tex]

P(E)=[tex]\frac{1}{8}[/tex]

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Answer: 25%

Step-by-step explanation:

You have 4/8 chances of getting an odd number on the spinner, which equals 1/2, or 50%. Now if you are going to get another odd number, you have an additional 1/2 (half your chances) or 50% of a chance of getting it after you get the first odd number. This means you must mutliply these chances. 1/2x1/2 which is 1/4 = 25%

The solution set. for the given inequality : x-5> -10. is (-5, ∞]

An inequality is a relationship that shows a non-equal comparison between two numbers or mathematical expressions.

We need to find the solution set for  x-5> -10.

x - 5 > - 10

x > -10 + 5

x > -5

The solution set = (-5, ∞]

Therefore, the  solution set. for the given inequality : x-5> -10. is (-5, ∞]

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The population of the country in 2003 is 302.5 million

From the question, we have the following parameters that can be used in our computation:

Exponential model, A = 302.5e^0.0211t

Where i is the number of years after 2003

In the year 2003, the value of t is 0

i.e. 0 years after 2003

So, we have

A = 302.5e^(0.0211 * 0)

Evaluate the products

A = 302.5 * 1

So, we have the following result

A = 302.5

Hence, the population is 302.5 million

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The value of n is given by either 4/5 or 16/25.

Given that the positive number is n which is n<1.

Reciprocal of the number is = 1/n

Addition of the number and the reciprocal is 2.05.

So the suitable equation for this,

n + 1/n = 2.05

[tex]n^2+1=\frac{41}{20}n\\20n^2-41n+20=0\\n=\frac{41\pm\sqrt{1681-1600}}{40}=\frac{41\pm9}{40}=\frac{50}{40},\frac{32}{50}=\frac{4}{5},\frac{16}{25}[/tex]

So the number can be either 4/5 or 16/25.

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Answer:

[tex]y=-43x-173[/tex]

Step-by-step explanation:

[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]

The length of the side JH in the triangle ΔHIJ is 97.9.

We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.

Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".

IJ ∝ FG

IJ = k*FG

k = IJ/FG

k = 47/12

The side JH is proportional to the side GE.

JH = k*GE

x = (47/12)*25

x = 97.9

Hence, the length of the side JH is 97.9 units.

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Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.

Here we want to see, based on a graph, how many solutions does the cubic equation:

x³ + 6x² + 12x +8 = 0

The graph of the function:

g(x) = x³ + 6x² + 12x +8

Can be seen below, the number of real solutions that the equation:

x³ + 6x² + 12x +8 = 0

has, will depend on how many times the graph intercepts the x-axis.

We can see that there is only one intercept, so there is one real solution.

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Answer:

slice it in the middle in the top and bottom or do it corner to corner.

Step-by-step explanation:

1. have 2 braincells

2. put them toghether and think.

The solution to the equation given as (x - 7)² = 36 are x = 1 and x = 13

From the question, the equation is given as

(x - 7)² = 36

To start with, we take the square roots of both sides

This gives

x - 7 = ±6

Add 7 to both sides of the equation

So, we have

x = 7 ± 6

Evaluate the like terms

x = 1 and x = 13

Hence, the values of x are x = 1 and x = 13

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Answer:-48

Step-by-step explanation:

a + 85 = 48

first we need to find what a

86-48=a

a=38

now we calculate

a-86?

38 - 86 = -48

Answer:

a - 86 = -124

Step-by-step explanation:

a + 86 = 48

a = 48 - 86

a = -38

Then:

a - 86 = -38 - 86

= -124

Answer:

x      y

1      0

2     10

5     40

10   90

Step-by-step explanation:

In a linear function, every time x is increased by 1, y is increased by a set amount. The only two complete rows in the table are when x = 1 and x = 5. x is increased four times in that interval while y has increased by 40(40 - 0). This means that every time x increases by 1, y increases by 10(40/4).

Therefore, when x is 2, y will be 10.

To get to ninety, 10 will needed to be added to 0(when x=1) 9 times. 1 + 9 is 10, so x = 10 when y = 90.

Answer:

Step-by-step explanation:

(1,0)   (5,40)

Using these coordinates we find the line equation y=mx+b:

[tex]\displaystyle\\m=\frac{y_2-y_1}{x_2-x_1} \\\\x_1=1\ \ \ \ \ x_2=5\ \ \ \ \ y_1=0\ \ \ \ y_2=40\\\\m=\frac{40-0}{5-1} \\\\m=\frac{40}{4} \\\\m=10\\\\Thus,\ y=10x+b \ \ \ \ (1)\\[/tex]

We substitute the value of coordinate (1,0) into equation (1):

[tex]0=10(1)+b\\\\0=10+b\\\\-10=b\\\\Thus, \ b=-10\\\\Hence,\\\\ y=10x-10\\\\x=2\\\\y=10(2)-10\\\\y=20-10\\\\y=10\\\\Thus,(2,10)\\\\y=90\\\\90=10x-10\\\\100=10x[/tex]

Divide both parts of the equation by 10:

[tex]10=x\\\\Thus, (10,90)[/tex]

   x   |    y

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

   1    |   0    

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

   2   |   10

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

   5   |   40

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

  10   |  90

8. The value of x is 9.

9. The value of x is 6.

Two triangles are congruent if all the corresponding sides and corresponding angle are equal.

8.

In the given triangle ∠A=(3x-4)°, ∠B=(13x+2)° and ∠C=(5x-7)°

The sum of all three angles of a triangle is 180°,

Implies that,

∠A+∠B+∠C=180°

3x-4+13x+2+5x-7=180

21x-9=180

21x=189

x=9

9.

In the given triangle, ∠A=(7x+1)°, ∠B=(19x-18)° and ∠C=(10x-9)°

The sum of all three angles of a triangle is 180°,

Implies that,

∠A+∠B+∠C=180°

7x+1+19x-18+10x-9=180

36x-26=180

36x=216

x=6

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Answer:

C. Trust me on this one, it is an easy one.

β=-α is the solution for alpha beta square +alpha square beta quadratic equation​

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

alpha beta square +alpha square beta quadratic equation​

αβ²+βα²

αβ(β+α)

αβ=0

and

β+α=0

β=-α

Hence β=-α is the solution for alpha beta square +alpha square beta quadratic equation​

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Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

What is Geometric Series?

The total of a geometric sequence's finite or infinite terms is known as a geometric series. The analogous geometric series is a + ar + ar2 +..., arn-1 + for the geometric sequence a, ar, ar2,..., arn-1,... The word "series" is known to mean "sum." The geometric series specifically refers to the total of phrases with a common ratio between every pair of neighboring terms. Geometric series can be of two different types: finite and infinite.

In the given question, we have:

The series: 3 + 12 + 48 +

So, here the first term (a) = 3;

The second term = +12;

and, we know that the common ratio in the geometric series is the ratio of the second term and the first term.

So,

Common ratio, r = [tex]\frac{12}{3}[/tex]

r = 4;

so, The common ratio will be the same everywhere. So, It will be 4 in all the cases.

And, The first term, a is 3;

Hence,

Option a is correct.

The first term, a is 3;

Common ratio, r = +4;

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely to }x^2}{y=\cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} y=5\\ x=3 \end{cases} \\\\\\ 5=\cfrac{k}{(3)^2}\implies 5=\cfrac{k}{9}\implies 45=k\hspace{5em}\boxed{y=\cfrac{45}{x^2}} \\\\\\ when~y=1\frac{4}{5}\textit{ what is "x"?}\implies 1\frac{4}{5}=\cfrac{45}{x^2}\implies \cfrac{9}{5}=\cfrac{45}{x^2} \implies 9x^2=(5)(45) \\\\\\ x^2=\cfrac{(5)(45)}{9}\implies x^2=25\implies x=\sqrt{25}\implies {\Large \begin{array}{llll} x=5 \end{array}}[/tex]

The probability that the total duration of the 500 calls is greater than 18 hours, using the normal distribution, is of:

0.618 = 61.8%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Hence, for the total duration of the 500 calls, in seconds, the mean and the standard deviation are given as follows:

[tex]\mu = 500 \times 130 = 65000, \sigma = 30\sqrt{500} = 670.82[/tex]

Each hour has 3600 seconds, hence the number of seconds in 18 hours is given as follows:

3600 x 18 = 64800.

The probability that the total time is greater than 18 hours is one subtracted by the p-value of Z when X = 64800, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (64800 - 65000)/670.82

Z = -0.3.

Z = -0.3 has a p-value of 0.382.

1 - 0.382 = 0.618 = 61.8% probability.

The problem says that:

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The measure of angles are

The sum of angles around a point is equal to 360 degrees

The consider the angle a

The equation will be

∠a + 312 = 360 degrees

∠a = 360 - 312

∠a = 48  degree

The angle a is less than 90 degrees then it is an acute angles

Consider the angle b

∠b + 220 = 360

∠b = 360 -220

∠b = 140 degrees

Angle b is greater than 90 degrees and less than 180 degrees then it is an obtuse angle

Consider the angle c

∠c + 36 = 360

∠c = 360 - 36

∠c = 324 degrees

Angle c is grater than 180 degrees and less than 360 degrees then it  is a reflex angle

Hence, the measure of angles are

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The measure of the exterior angle to triangle X is D. 97.55°.

It is important to note that the sum of the angles in a triangle is 180°.

In this case, triangle XYZ, m∠Y = 43.85° and m∠Z = 38.6.

The exterior angle to X will be:

= Total angle - (43.85 + 38.6)

= 180 - 82.45

= 97.55°

In conclusion, the correct option is D.

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Answer:

I got the answer d when I took the test

Step-by-step explanation:

I hope this helps...

Answer:

40% decrease

Step-by-step explanation:

[tex]\frac{1090-654}{1090}[/tex] = .4  x 100 to make a percent equals 40%

Answer:There is no decrease from 2,820 kilograms to 2,820 kilograms.

The percent of decrease in the size of the sugar order is 0%.

Step-by-step explanation:

Answer:

we can't give an answer if there's not explanation of which "t" is

a) The linear function is:

y = 2 + 0.25x.

b) The amount of snow on the ground after 4 hours will be of 3 inches.

c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.

The slope-intercept representation of a linear function is presented by the rule as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

In this problem, the values of these coefficients are given as follows:

Hence the equation is:

y = 2 + 0.25x.

After four hours, the amount of snow on the ground will be of:

y = 2 + 0.25(4) = 2 + 1 = 3 inches.

The time until the amount reaches 6 inches is of:

2 + 0.25x = 6

0.25x = 4

x/4 = 4

x = 16 hours.

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Answer:

Step-by-step explanation:

7*5

Answer:

he got 8 apples left and made a profit of 16

Step-by-step explanation:

The fraction of strawberry and chocolate flavored candies that Aurora has in her box is 5/4

From the information illustrated, 30 of the candies are strawberry flavored and 24 are chocolate flavored.

Therefore, to get the fraction, we have to divide them. This will be illustrated as:

= Number of strawberry candies / Number of chocolate candies

= 30 / 24

= 5/4

The fraction is 5/4.

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Complete question

In Aurora’s candy box, 30 of the candies are strawberry flavored and 24 are chocolate flavored. What is the fraction of strawberry and chocolate flavored candies that Aurora has in her box?

Answer:

27/8 or 3.375 or 3 3/8

Step-by-step explanation:

The intervals for the concavity of the odd function are given as follows:

The definition of even and odd functions depends on the relation between f(x) and f(-x), as explained as follows:

In this problem, we have that the function is odd, hence the following statement is true:

f(-x) = -f(x) for all values of x.

This means that the concavity intervals are exchanged, hence:

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