budget planning


Ryan is trying to save money to buy a home. He wants to write out a budget for himself so he can put some money into savings each month

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Answer:

Inverse Variation

Step-by-step explanation:

Answer:

(x+3)² + (y+4)²=25

Step-by-step explanation:

The question is on equation of a circle

The distance formula is given by;

√(x-h)²+ (y-k)²=r

The standard equation of  circle is given as ;

(x-h)²+ (y-k)²=r²

The equation of this circle with center (-3, -4) and radius 5 will be;

(x--3)² + (y--4)²=5²

(x+3)² + (y+4)²=25

ANSWER

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

EXPLANATION

The equation of a circle with center (h,k) and radius r units is given by:

[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

From the given information the center of the circle is (-3,-4) and the radius is r=5 units.

We substitute the known values to obtain:

[tex]{(x - - 3)}^{2} + {(y - - 4)}^{2} = {5}^{2} [/tex]

We simplify to get:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

Therefore the equation of the circle in standard form is:

[tex]{(x + 3)}^{2} + {(y + 4)}^{2} = 25[/tex]

Answer:

A. 10cm

B. 8 times

Step-by-step explanation:

The question is on volume of a conical container

Volume of a cone= [tex]\pi r^{2} h/3[/tex]

where r is the radius of base and h is the height of the cone

Given diameter= 12 cm, thus radius r=12/2 =6 cm

[tex]v=\pi r^2h/3 \\120\pi =\pi *6*6*h/3\\120\pi =12\pi h\\10=h[/tex]

h=10 cm

B.

If height and diameter were doubled

New height = 2×10 =20 cm

New diameter = 2×12 = 24, r=12 cm

volume = [tex]v=\pi r^2h/3\\v=\pi *12*12*20/3\\v=960\pi[/tex]

To find the number of times we divide new volume with the old volume

[tex]N= 960\pi /120\pi \\\\N= 8[/tex]

Answer: The height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.

Step-by-step explanation:

The volume of a cone can be calculated with this formula:

[tex]V=\frac{\pi r^2h}{3}[/tex]

Where "r" is the radius and "h" is the height.

We know that the radius is half the diameter. Then:

[tex]r=\frac{12cm}{2}=6cm[/tex]

We know the volume and the radius of the conical container, then we can find "h":

[tex]120\pi cm^3=\frac{\pi (6cm)^2h}{3}\\\\(3)(120\pi cm^3)=\pi (6cm)^2h\\\\h=\frac{3(120\pi cm^3)}{\pi (6cm)^2}\\\\h=10cm[/tex]

The diameter and height doubled are:

[tex]d=12cm*2=24cm\\h=10cm*2=20cm[/tex]

Now the radius is:

[tex]r=\frac{24cm}{2}=12cm[/tex]

And the container capacity is

[tex]V=\frac{\pi (12cm)^2(20cm)}{3}=960\pi cm^3[/tex]

Then, to compare the capacities, we can divide this new capacity by the original:

 [tex]\frac{960\pi cm^3}{120\pi cm^3}=8[/tex]

Therefore,  the container's capacity would be 8 times its original capacity.

Answer: D. F(x)= (x-1)^2+3

Step-by-step explanation:

Answer:

2 and 45/60 which simplifies to 2 and 3/4

Answer:

x = 3

Step-by-step explanation:

There are two ways to do this. The simplest way is to realize that the exterior angle (45x) = the sum of the two remote interior angles.

25x and 57 + x

45x = 25x + 57 + x                      Subtract 26x from both sides.

45x - 26x = 25x - 25x + 57   Combine

19x = 57                                Divide by 20

19x/19 = 57/19                     Do the division

x = 3

===================================

Second method.

The supplement of the 45x angle is 180 - 45x

Now add the three angles together.

180 - 45x + x + 57 + 25x = 180     Combine like terms.

180 + 57 - 45x + x + 25x = 180

237 - 19x = 180                              Subtract 237 from both sides.

- 19 x = 180 - 237                           Combine the right side

- 19x = -57

x = 3

Good thing you made me redo it. Sorry!! I made an error. I lost 1 of the xs.

option A

f(x) = (x – 1)2 + 3

Given in the question a function,

f(x) = 4 + x² – 2x

Step 1

f(x) = 4 + x² – 2x

here a = 1

        b = -2

        c = 4

Step 2

x = -b/2a

h = -(-2)/2(1)

h = 2/2

h = 1

Step 3

Find k

k = 4 + 1² – 2(1)

k = 3

Step 4

To convert a quadratic from y = ax² + bx + c form to vertex form,

y = a(x - h)²+ k

y = 1(x - 1)² + 3

y = (x - 1)² + 3

Answer: 8, 40, 80, 120

1 gallon is equal to 8 pints

The number of pints Jordan needs to fill the fish tank of [tex]15[/tex] gallons is as follow:

gallons :[tex]1 \ \ \ \ \ \ \ \ \ 5\ \ \ \ \ \ \ \ \ \ 10\ \ \ \ \ \ \ \ \ \ \ 15[/tex]

pint       :[tex]8 \ \ \ \ \ \ \ \ \ 40\ \ \ \ \ \ \ \ \ \ 80\ \ \ \ \ \ \ \ \ \ \ 120[/tex]

" Number is defined as the count of a given quantity."

According to the question,

Capacity of fish tank [tex]= 15\ gallons[/tex]

Capacity of a container used to fill the fish tank [tex]= 1 \ pint[/tex]

Standard relation gallons to number of pints

[tex]1 \ gallon = 8\ pints[/tex]

Number of pints required :

[tex]1 \ gallon = 8\ pints[/tex]

[tex]5\ gallon = (8\times 5)\ pints[/tex]

             [tex]= 40 \ pints[/tex]

[tex]10\ gallons = (10 \times 8) \ pints[/tex]

                [tex]= 80\ pints[/tex]

[tex]15\ gallon = (15 \times 8) \ pints[/tex]

               [tex]= 120 \ pints[/tex]

Hence, the number of pints Jordan needs to fill the fish tank of [tex]15[/tex] gallons is as follow:

gallons :[tex]1 \ \ \ \ \ \ \ \ \ 5\ \ \ \ \ \ \ \ \ \ 10\ \ \ \ \ \ \ \ \ \ \ 15[/tex]

pint       :[tex]8 \ \ \ \ \ \ \ \ \ 40\ \ \ \ \ \ \ \ \ \ 80\ \ \ \ \ \ \ \ \ \ \ 120[/tex]

Learn more about number here

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The 95% confidence interval for the difference of the two sample means, given a mean difference of 22 and a standard deviation of 10, ranges from 2.4 to 41.6.

The problem provided involves the concept of confidence intervals in statistics. When working with two sample means and you want to find the 95% confidence interval of the difference, the standard deviation of the difference is essential. The difference of two sample means is 22 and the standard deviation of this difference is estimated to be 10.

The 95% confidence interval for a mean can be calculated using the formula:
Confidence Interval = mean difference ± (Z-score * standard deviation).

With a 95% confidence interval, our Z-score (also known as the critical value) is approximately 1.96 (from Z tables or any statistical calculator). Thus, substituting the provided figures into the formula, we have:
Confidence Interval = 22 ± (1.96 * 10).

This gives us a confidence interval range of: 22 - 19.6 to 22 + 19.6, thus the 95% confidence

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The difference of the means of two populations at a 95% confidence interval is between 2.4 and 41.6.

To find the difference of the means of the two populations at a 95% confidence interval, we can use the formula:

CI = (difference of sample means) ± (critical value) × (standard deviation of the difference of sample means)

In this case, the difference of the sample means is 22 and the standard deviation of the difference of the sample means is 10. The critical value for a 95% confidence interval is approximately 1.96.

Using these values, we can calculate the confidence interval as follows:

CI = 22 ± (1.96) × 10

Simplifying the expression, the confidence interval is (2.4, 41.6).

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Answer:

2/10

Step-by-step explanation:

First you - 20 from 40 (aka 2/10 - 4/10) and you will get 20 (aka 2/10).

To find out what fraction more of the pack Dan used on Saturday compared to Sunday, subtract 2/10 from 4/10.

To find out what fraction more of the pack Dan used on Saturday compared to Sunday, we need to subtract the amount used on Sunday from the amount used on Saturday and express it as a fraction of the original pack.

On Saturday, Dan used 4/10 of the pack. On Sunday, he used 2/10 of the pack. To find the fraction more, we subtract 2/10 from 4/10:

4/10 - 2/10 = 2/10

Therefore, Dan used 2/10 more of the pack on Saturday compared to Sunday.

An odd function like f(x) = -2x^5 + x^3 − 7x satisfies the property that y(x) = -y(-x), which indicates that the function is symmetric around the origin. The multiplication of odd and even functions results in an odd function, and the integral of an odd function over all space equals zero due to the cancelation of negative and positive areas.

The rule satisfied by the function f(x) = -2x^5 + x^3 − 7x, which is an odd function, is that y(x) = −y(-x). Essentially, what that means is that when you plug -x into the function, the sign of the result will be the opposite of the result of plugging x into the function. This rule manifests itself graphically as a kind of symmetry: odd functions are symmetric around the origin. They are produced by reflecting the graph of y(x) across the y-axis and then the x-axis. In contrast to even functions, which have symmetry around the y-axis, odd functions display this kind of 'rotational' symmetry.

Also worth noting, multiplying an odd function by an even function always yields an odd function. For instance, x*e^-x² is an odd function because x is an odd function and e^-x² is an even function. Additionally, the property of odd functions to integrate over space to zero is particularly useful, as they effectively 'cancel out' negative and positive areas along the x-axis.

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The perimeter of the shaded region is 39 ft.

The perimeter is the total length of all the sides of the shaded region. To find the perimeter, we need to add up the lengths of all the sides.

The perimeter of the shaded region is the sum of the lengths of all its sides.

Perimeter of a polygon = Sum of the lengths of all its sides

Perimeter of the shaded region = 14 ft + 6 ft + 15 ft + 4 ft

Perimeter of the shaded region = 39 ft

Therefore, the perimeter of the shaded region is 39 ft.

Let x represent those who both football and basketball

The given information can be illustrated in a Venn diagram as shown in the attachment.

We solve the equation below to find the value of x.

[tex](53-x)+x+(24-x)+31=101[/tex]

[tex]\implies -x+x-x=101-53-31-24[/tex]

[tex]\implies -x=-7[/tex]

[tex]\implies x=7[/tex]

From the second diagram;

25. [tex]P(Basketball)=\frac{17}{101}[/tex]

26. [tex]P(Football)=\frac{46}{101}[/tex]

27. [tex]P(Football\: \cap\:Basketball)=\frac{7}{101}[/tex]. This is because 7 play both Football and Basketball.

28. [tex]P(Football\: \cup\:Basketball)=\frac{46}{101}+\frac{17}{101}-\frac{7}{101}=\frac{56}{101}[/tex]. This is because there is intersection.

29. [tex]P(Neither\: \cup\:Both)=\frac{31}{101}+\frac{7}{101}=\frac{38}{101}[/tex]. The two events are mutually exclusive.

Answer:

Area of the biggest square: 25 m²

Area of the second biggest square: 16 m²

Area of smallest square: 9 m²

Area of triangle: 6 m²

Answer:

The answer is A.

Step-by-step explanation:

Rational numbers are any real numbers (including negatives) and -5 + -4 = -9 which is a real number, so it is rational.

Answer:  The answers are given below.

Step-by-step explanation:  Given that the graph shows the relationship between the number of months different students practiced boxing and the number of matches they won:.

Part A : We are to find the approximate y-intercept of the line of best fit and state what does it represent.

From the graph, we note that

at x = 0, the value of y is approximately 3.

So, the approximate y -intercept of the line of best fit is 3.

It represents that before starting the matches, the students can win 3 matches without any practice.

Part B : We are to write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice.

From the graph, we note that the line of best fit passes through the points (2, 7) and (9, 18).

So, the slope of the line of best fit will be

[tex]m=\dfrac{18-7}{9-2}=\dfrac{11}{7}.[/tex]

Therefore, the slope-intercept form of the equation of the line of best fit is given by

[tex]y=mx+c\\\\\Rightarrow y=\dfrac{11}{7}x+3.[/tex]

Thus, the number of matches that could be won after 13 months of practice is

[tex]y=\dfrac{11}{7}\times13+3=23.42.[/tex]

That is, students can win 23 matches with 13 months of practice.

The approximate y-intercept is 35.25 and it represents the starting point on the graph. The equation for the line of best fit is y = 0.09x + 35.25. After 13 months of practice, the prediction is that the student could win approximately 36 matches.

Part A: The approximate y-intercept of the line of best fit is 35.25. The y-intercept represents the number of matches a student would have won without any months of practice. In other words, it is the initial starting point on the graph when the number of months practiced is zero.

Part B: The equation for the line of best fit in slope-intercept form is y = 0.09x + 35.25. To predict the number of matches after 13 months of practice, we substitute the value of x (number of months) into the equation. Therefore, y = 0.09(13) + 35.25 = 36.42.

Therefore, the prediction is that the student could win approximately 36 matches after 13 months of practice.

Answer:

160 children, 112 boys and 48 girls.

Step-by-step explanation:

You can translate this into two equations:

g = 3/7 * b

g+64 = b

Then fill in one in the other and simplify:

3/7 b + 64 = b =>

4/7 b = 64

b = 64 * 7/4 = 112

g = 112 * 3/7 = 48

Final answer:

By setting up equations with the given proportions and difference in numbers, we can calculate that there are 112 boys and 48 girls in the field, totaling 160 children.

Explanation:

To solve the problem of how many children are in the field, we need to set up an equation based on the information given. It states that there are 3/7 girls there are boys, and that there are 64 more boys than girls. Let's define the number of boys as B and the number of girls as G. According to the problem, B = G + 64 and G = (3/7) * B.

To find the solution, we need to substitute G from the second equation into the first to get B = (3/7) * B + 64. Simplifying this equation, we multiply both sides by 7 to get rid of the fraction 7B = 3B + 448. Then we subtract 3B from both sides yielding 4B = 448. Dividing both sides by 4 gives us B = 112. Now that we have the number of boys, we can find the number of girls using the second equation: G = (3/7) * 112 = 48. Finally, we add the number of girls and boys to find the total number of children in the field 112 + 48 = 160.

Answer:

MAD = 1.5.

Step-by-step explanation:

MAD is the Mean Absolute Deviation.

The MAD is a measure of the spread of the data.

The mean of these numbers is (1 + 4 + 5 + 6) / 4

= 16/4 = 4.

Now you subtract this from the individual values and take the absolute values:

1 - 4 = -3 (absolute value = 3).

4-4 = 0

5-4 = 1

6-4 = 2.

Adding 0+1+2+3 = 6.

The MAD = 6 / 4 = 1.5.

Answer:

Step-by-step explanation:  The mad is 1.5

For this case we have that by definition, the associative property states that:

The order in which the factors (or addends) are associated does not alter the product (or the sum).

On the other hand, the commutative property states that:

The order of the factors (or addends) does not alter the product (or the sum).

Answer:

t = 2 s= 96

t = 3 s = 64

t = 4 s= 32

t= 5 s = 0

t= 6 s = -32

t = 7 s = -64

t = 8 s = -96

t= 9 s = -128

Step-by-step explanation:

We have the equation of the position of the rocket as a function of time t.

[tex]f(t) = -16t^2 + 160t[/tex]

The instantaneous velocity of the rocket as a function of time is given by the derivation of the position with respect to time.

So

[tex]S(t)=\frac{df(t)}{dt} = -2*16t + 160\\\\S(t) = -32t+160[/tex]

[tex]s(1) = -32(1)+160=128\ ft/s\\\\s(2) = -32(2)+160=96\ ft/s\\\\s(3) = -32(3)+160=64\ m/s\\\\s(4) = -32(4)+160=32\ m/s\\\\s(5) = -32(5)+160=0\ m/s\\\\s(6) = -32(6)+160=-32\ m/s\\\\s(7) = -32(7)+160=-64\ m/s\\\\s(8) = -32(8)+160=-96\ m/s\\\\s(9) = -32(9)+160=-128\ m/s[/tex]

So

t = 2 s= 96

t = 3 s = 64

t = 4 s= 32

t= 5 s = 0

t= 6 s = -32

t = 7 s = -64

t = 8 s = -96

t= 9 s = -128

Final answer:

To match time values with the rocket's velocity after launch, we take the derivative of the position function f(t) to obtain the velocity function v(t) = -32t + 160. The corresponding velocity for each time value can be calculated by plugging the time into the velocity function.

Explanation:

The height of a rocket as a function of time after launch is given by f(t) = -16t2 + 160t, and we are asked to match each value of time elapsed with the rocket's corresponding instantaneous velocity. To find the instantaneous velocity, we need to take the derivative of the position function with respect to t, which represents time in seconds. The derivative of f(t) with respect to t is f'(t) = -32t + 160. This is the velocity function v(t), which gives the instantaneous velocity at any given time t.

At t = 2, the velocity v(2) = -32(2) + 160 = 96 feet/second.

At t = 3, the velocity v(3) = -32(3) + 160 = 64 feet/second.

At t = 4, the velocity v(4) = -32(4) + 160 = 32 feet/second.

At t = 5, the velocity v(5) = -32(5) + 160 = 0 feet/second. (This is the point at which the rocket reaches its peak and starts descending.)

At t = 6, the velocity v(6) = -32(6) + 160 = -32 feet/second (indicating the rocket is now falling back to the ground).

The values for t = 7, t = 8, and t = 9 can be calculated in a similar manner using the velocity function v(t).

Answer:

Option 4 is correct

Step-by-step explanation:

If the rate is compounded continuously, the formula used to find the future value is:

A= Pe^rt

Where A = Future Value

P= Principal amount

r = interest rate in decimal

t = time

For the given data:

A=?

P = $5000

r = 7% or 0.07

t = 6

Putting values in the above formula

A= 5000e^(0.07 *6)

A = 7609.81

So, Option 4 is correct.

[tex]d. \: y = 6 + 3x \\ \\ 1. \: 3x + 6 = y \\ 2. \: 3x = y - 6 \\ 3. \: \frac{3x}{3} = \frac{y - 6}{3} \\ x = \frac{1}{3} y - 2[/tex]

Factors:

15 = 1, 3, 5, 15

21 = 1, 3, 7, 21

The GCF is 3

That means that you can take three out of 15 and 21

15/3 = 5

21/3 = 7

so...

3 (5 + 7)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The function f(x) is a geometric sequence

Step-by-step explanation:

If we let the first value of this function be denoted by y, then the second value will grow by;

12% of y

= (12/100)*y = 0.12y

The second value will thus be;

y + 0.12y = 1.12y

The third value will grow by;

12% of 1.12y

= (12/100)*1.12y = 0.12(1.12y)

The third value will thus be;

1.12y + 0.12(1.12y)

= 1.12y(1 + 0.12)

= 1.12y * 1.12 = [tex]1.12^{2}y[/tex]

The function f(x) will thus have the sequence;

y, 1.12y, [tex]1.12^{2}y[/tex], ans so on. This is clearly a geometric sequence since we have a common ratio of 1.12.

Answer: B

Ive done the test before, this was correct. glad i could help

For this case we have the following expression:

[tex]\sqrt {64}[/tex]

We have to:

[tex]64 = 8 * 8 = 8 ^ 2[/tex]

By definition of properties of powers and roots we have to meet:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

Then, rewriting the expression we have:

[tex]\sqrt {8 ^ 2} = 8 ^ {\frac {2} {2}} = 8 ^ 1 = 8[/tex]

Thus, we have that the result is a whole number "8".

Answer:

whole number

Answer:

Step-by-step explanation:

y = f(x) + n - moves the graph n units up

y = f(x) - n - moves the graph n units down

y = f(x + n) - moves the graph n units to the left

y = f(x - n) - moves the graph n units to the right

===================================================

5.5 units to the right

y = f(x - 5.5) = |x - 5.5|

Answer:

120

16

Step-by-step explanation:

Givens

Solution

4xyz = 4(3)(2)(5)

4xyz = 30 * 4

4xyz = 120

======================

z^2 - x^2

5^2 - 3^2

25 - 9

16

Answer:

361. 362,363

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 1086.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 1086. Therefore, you can write the equation as follows:

X + X + 1 + X + 2 = 1086

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 1086

3X + 3 = 1086

3X + 3 - 3 = 1086 - 3

3X = 1083

3X/3 = 1083/3

X = 361

Which means that the first number is 361, the second number is 361+1 and third number is 361+2. Therefore, three consecutive integers that add up to 1086 are:

361

362

363

Follow below steps;

The question asks to find three consecutive natural numbers that add up to 1086. Let's denote the smallest of these three numbers as n. Then, the next two numbers can be represented as n + 1 and n + 2. The sum of these three numbers is:

n + (n + 1) + (n + 2) = 1086

Combining like terms, we get:

3n + 3 = 1086

Subtracting 3 from both sides, we get:

3n = 1083

Dividing both sides by 3, we find:

n = 361

So the three consecutive numbers are 361, 362, and 363, and they indeed sum up to 1086:

361 + 362 + 363 = 1086

Answer:

The Area of the first figure is 18[tex]in^{2}[/tex]

Step-by-step explanation:

Since the question states that both of the figures are similar we can use the information from figure 2 in order to find the area of figure 1. We do this by using the simple rule of three.

8[tex]in[/tex] ----> x

12[tex]in[/tex] ---> 27[tex]in^{2}[/tex]

Since the ratios (figures) are stated to be similar we just solve the rule of three as shown above.

[tex]\frac{(8in)(27in^{2} )}{12in} = x[/tex]

[tex]\frac{216in^{3} }{12in } = x[/tex]

[tex]18in^{2} = x[/tex]

Therefore the Area of figure 1 is 18[tex]in^{2}[/tex]

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer: 12

Step-by-step explanation: I know this website, this is the answer there

Using kinematic equations, we determine that the accelerating police car will catch up to the speeding car moving at a constant velocity in 20 seconds.

To solve the problem of when a police car accelerating at 4 m/s² will catch up to a speeding car moving at a constant velocity of 40 m/s, we can use kinematic equations for motion. The speeding car's position over time is given by the equation x = vavgt, where vavg = 40 m/s is the average velocity. Since the police car starts from rest (vo = 0) and has an acceleration of 4 m/s², its position over time is given by the equation x = 0.5at².

We set the displacement of both cars equal to each other to find the time (t) when they are at the same position:
40t = 0.5(4)t².

This simplifies to: 40t = 2t², and by further simplification, we find that t = 20 seconds. Thus, it will take the police car 20 seconds to catch up to the speeding car.

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