Use the compound interest formula A =​P(1 + ​r) t and the given information to solve for r.
A =​$2300​, P =​$1600​, t =6 r =?

Answer:

1) yes

2) Option B

3) 9200

Step-by-step explanation:

1) yes

The exponential function is: y=-(x)^3

Putting the values of x in the given function we get the values of y.

x =1 , y= -(1)^3, y=-1

x= 2, y= -(2)^3, y = -8

x= 3, y= -(3)^3,y = -27

x= 4, y= -(4)^3,y = -64

2) f(x) = 160.2^x

if value of x = 2

then f(2) = 160.2^(2)

f(2) = 160.4

f(2) = 640

So, Option B is correct.

3) f(x) = 2300.2^x

if value of x = 2 decades then

f(2) = 2300.2^2

f(2) = 2300.4

f(2) = 9200

Since all options are not visible, so correct answer is 9200

Answer:

[tex]\large\boxed{\left(-\dfrac{6}{5},\ -\dfrac{8}{5}\right)}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x+y=-4&(1)\\y=3x+2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\2x+(3x+2)=-4\\2x+3x+2=-4\qquad\text{subtract 2 from both sides}\\5x=-6\qquad\text{divide both sides by 5}\\\boxed{x=-\dfrac{6}{5}}\qquad\text{put it to (2)}\\\\y=3\left(-\dfrac{6}{5}\right)+2\\\\y=-\dfrac{18}{5}+\dfrac{10}{5}\\\\\boxed{y=-\dfrac{8}{5}}[/tex]

Answer:

Step-by-step explanation:

The solution of the system of equations are the coordinates of the point of intersection.

We have two parallel lines. The intersection point does not exist.

Therefore, this system of equations has no solution.

Answer:

[tex]\large\boxed{C.\ g(x)=3x^2}[/tex]

Step-by-step explanation:

[tex]f(x)=x^2\to f(1)=1^2=1\\\\g(1)=3\to\text{given point (1,\ 3)}\\\\3=3\cdot1=3\cdot1^2=3f(1)\to g(x)=3f(x)=3x^2[/tex]

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 48

b = x

c = 50

^^^Plug these numbers into the theorem

[tex]48^{2} +x^{2} =50^{2}[/tex]

simplify

2304 + [tex]x^{2}[/tex] = 2500

Isolate x^2 by subtracting 2304 to both sides

[tex]x^{2}[/tex] = 196

To remove the square from x take the square root of both sides to get you...

14 = x  

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

6!

or

6*5*4*3*2*1

or

720

Step-by-step explanation:

The word 'PLANTS' contains no letter more than once.

It is say 6 letter word.

_  _  _ _ _ _

There are 6 ways to choose the first blank (after than there are 5 letters left to choose from)

After the first blank, there are 5 letter left to choose from so there are 5 ways to choose the second blank.

Then 4 ways for the third blank.

3 ways for the fourth blank.

2 ways for the fifth blank.

1 way for the sixth blank.

Now to figure out the number of permutations you must multiply the number of different ways we have above for each blank.

That is we are doing 6*5*4*3*2*1 or 6!

There are 720 different permutations of the letters in the word 'PLANTS' when used without repetition. This is calculated as the factorial of the number of letters, which is 6. Therefore, 6 factorial (6!) equals 720.

The subject of the question falls under the topic of permutations in Mathematics. The question is asking for the number of different ways that the letters in the word 'PLANTS' can be arranged if all letters are used without repetitions. This is a concept in combinatorics, a subject of discrete mathematics that deals with counting and arranging objects.

To solve this, we need to calculate the factorial of the number of letters in the word 'PLANTS'. There are 6 letters in the word. The factorial of a number (denoted as n!) is the product of all positive integers less than or equal to that number. Therefore, the number of permutations is 6!, which equates to 6 x 5 x 4 x 3 x 2 x 1 = 720.

So, there are 720 different permutations of the letters in the word 'PLANTS' if all the letters are used without repetition.

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Answer:

r = ∛(3V/4π)

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³.

We want to solve this first for r³ and then for r.

Multiplying both sides of V = (4/3)πr³ by 3 yields an equation without fractions:  3V = 4πr³.

Dividing both sides of this equation by 4π isolates r³:

       3V

r³ = -------

       4π

To find r, take the cube root of both sides of

       3V

r³ = -------

       4π

obtaining r = ∛(3V/4π)

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} V=113 \end{cases}\implies 113=\cfrac{4\pi r^3}{3}\implies 339=4\pi r^3 \\\\\\ \cfrac{339}{4\pi }=r^3\implies 26.98\approx r^3\implies \sqrt[3]{26.98}=r\implies 2.999 \approx r\implies \stackrel{\textit{rounded up}}{3=r}[/tex]

1) Find the unit rate

$18/6 attendees = 3

2) Apply the unit rate to find the answer

$48/$3= 16 attendees

Therefore, there can be 16 attendees if the budget is $48.

Hope this helps!

      10 pounds of each type of coffee should be mixed to make a 20 pound blend that sells for $9.50 per pound.

 Charges for Kenyan French Roast coffee = $10 per pound

 Charges for Sumatran coffee = $9 per pound

Let the amount of Kenyan French Roast used = K pound

And the amount of Sumatran coffee used = S pound

If the total amount of the mixture = 20 pounds

Equation for the total amount will be,

K + S = 20 ------- (1)

If the cost of this mixture = $9.50

Equation for the cost of the mixture will be,

10K + 9S = 20×9.50

10k + 9S = 190 ------- (2)

Multiply equation (1) by 9 and subtract this equation from equation (2),

(10k + 9S) - (9K + 9S) = 190 - 180

K = 10 pounds

Substitute the value of K in equation (1),

10 + S = 20

S = 10 pounds

     Therefore, 10 pounds of each blend of coffee should be mixed.

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To make a 20 pound blend of coffee that costs $9.50 per pound using Kenyan French Roast coffee ($10 per pound) and Sumatran coffee ($9 per pound), you should use 10 pounds of each type.

To solve this problem, we can set up a system of equations to represent the given information. Let x represent the amount of Kenyan French Roast coffee and y represent the amount of Sumatran coffee. We have the following equations:

x + y = 20 (equation 1 - representing the total weight of the blend)

10x + 9y = 9.50 * 20 (equation 2 - representing the total cost of the blend)

To solve this system, we can first multiply equation 1 by 10 to get:

10x + 10y = 200 (equation 3)

We can then subtract equation 3 from equation 2 to eliminate the variable x:

10x + 9y - (10x + 10y) = 9.50 * 20 - 200

9y - 10y = 190 - 200

-y = -10

y = 10

Substituting this value back into equation 1 gives us:

x + 10 = 20

x = 10

Therefore, we should use 10 pounds of Kenyan French Roast coffee and 10 pounds of Sumatran coffee to make the 20 pound blend.

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Answer:

y=800 km

Step-by-step explanation:

Let the distance traveled by train be y and by bus be x.

Bus -x

Train -y

y=x+150 (since they traveled by train for a distance of 150 km more than by bus.)

The sum of the two is equal to 1450

x+y=1450

The two equations form simultaneous  equations which when solved simultaneously give the values of x and y.

y+x=1450

y-x=150

Adding the two we get:

2y=1600

Divide both sides by two:

y=800 km

Y is the distance traveled by train= 800 km

Step-by-step explanation:

the correct answer is c

The answer is:

They spent $176 together.

We are given an expression which represents the money spent for each girl, it's a function of time and it will show how much they can spend in terms of hours.

Assuming that you have committed a mistake writing the equation, otherwise, the given options would not fit, the expression is:

[tex]p(t)=5x^{4}-3x^{3}+2x^{2}+24[/tex]

Now, from the statement we know that the function represents how much money each girl spent, so, if we need to calculate how much money they will spend together, we need to multiply the expression by 2, so we have:

[tex]p(t)=2(5x^{4}-3x^{3}+2x^{2}+24)[/tex]

Then, calculating the spent money for 2 hours, we need to substitute the variable "x" with 2.

Calculating we have:

[tex]p(2)=2(5*(2)^{4}-3*(2)^{3}+2*(2)^{2}+24)=2(5*16-3*8+2*4+24)[/tex]

[tex]p(2)=2(5*16-3*8+2*4+24)=2(80-24+8+24)=2*88=176[/tex]

Hence, we have that they spent $176 together.

Have a nice day!

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

None of them do to me. The last one does not. And certainly the second last one cannot.

In B, you are subtracting 4 from zero which doesn't work.

A adds 0 to 4 which gives 4

Unless I misreading D and O is a variable (sneaky), there is no answer.

Answer:

y - 9 = 1/2(x + 3)

Step-by-step explanation:

For the equation y = -2x + 8, your slope, m, is -2. To find the slope for a line perpendicular to the original line, we do the opposite reciprocal of this number. The slope of the perpendicular line is 1/2.

Point-slope form is: y - y1 = m(x - x1) where x1 and y1 are the x- and y-coordinates of an ordered pair.

With this new slope for the perpendicular line, and the point we are given, we just plug in the info.

Your equation is: y - 9 = 1/2(x + 3)

2a. 14,9; 2b. 15,4; 2c. 30,8; 3. 32

For 2a., you have to set it up like this: csc 48° = 20⁄x [OR sin 48° = ˣ⁄20]. Then you would have to isolate the variable by getting rid of the denominator. The cosecant function has an extra step because you will get xcsc 48° = 20. As stated, isolate the variable; this time, divide by csc 48°. This is what 20 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2b., you have to set it up like this: sec 39° = ˣ⁄12 [OR cos 39° = 12⁄x. Then you would have to isolate the variable by getting rid of the denominator. The cosine function has an extra step because you will get xcos 39° = 12. As stated, isolate the variable; this time, divide by cos 39°. This is what 12 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

For 2c., you have to set it up like this: cot 64° = 15⁄x [OR tan 64° = ˣ⁄15]. Then you would have to isolate the variable by getting rid of the denominator. The cotangent function has an extra step because you will get xcot 64° = 15. As stated, isolate the variable; this time, divide by cot 64°. This is what 15 will be divided by to get your x, whereas the other side cancels out. Then you have to round to the nearest tenth degree.

Now, for 3., it is unique, but similar concept. In this exercise, we are solving for an angle measure, so we have to use inverse trigonometric ratios. So, we set it up like this: cot⁻¹ 1⅗ = m<x [OR tan⁻¹ ⅝ = m<x]. We simply input this into our calculator and we get 32,00538321°. When rounded to the nearest degree, we get 32°.

WARNING: If you use a graphing calculator, you have to input it uniquely because most graphing calculators do not have the inverse trigonometric ratios programmed in their systems. This is how you would write this: tan⁻¹ 1⅗⁻¹. You set 1⅗ to the negative first power, ALONG WITH the inverse tangent function, because without it, your answer will be thrown off. Since Cotangent and Tangent are multiplicative inverses of each other, that is the reason why the negative first power is applied ALONG WITH the inverse tangent function.

**NOTE: 1⅗ = 8⁄5

Take into consideration:

sin θ = O\H

cos θ = A\H

tan θ = O\A

sec θ = H\A

csc θ = H\O

cot θ = A\O

I hope this helps you out alot, but if you are still in need of assistance, do not hesitate to let me know and subscribe to my channel [username: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Answer:

im sorry this never got answered but you would put the third one i believe

Step-by-step explanation:

Answer:

the correct answer is D. Funtion 1 and 3 have the same rate of change but funtion 1 has greater y intercept

Step-by-step explanation:

If we organize the funtion 1, we have y= 2x+8

Funtion 2 the need to calculate the slope m = (y2-y1)/(x2-x1) the point on the y represent (y2,x2) and is (4,0) the point onn the x axis is (x1,y1) and is (-2,0)

So, m=(4-0)/(0-(-2) => m=(4/2) => m=2

Then, y=m(X-Xo) + Yo  . From the plot, I choose (x2,y2) as (Xo,Yo) So, (0,4)

y=2(X-0) +4 then y= 2x+4

From 3 equation the choose the value x=o and g(x)= 5 and x=1 and g(x)=7 and following the same m=(7-5)/(1-0) the slope is m=2. Following the same procedure before I choose x=0 and y=5

Then the equation is: y=2(x-0) + 5

So, opcion D is true

Using sampling concepts, it is found that the sentence is:

C. If a population is all actors, a sample of the population could be movie actors.

A sample is a group taken from the population. It has to come from a more restrict group of the population, that is, an subset of the population.

In option A, baseball players is a subset of all athletes, so all athletes would be the population and baseball players would be the sample. The same can be applied in options B and D.

In option C, movie starts is a subset of all actors, thus the roles of sample and population are correct.

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Answer:

-8.95 ,, -8.36 ,, 7/28 ,, 8 22/40

Step-by-step explanation:

Answer:

-8.95, -8.36, 7/28, 8 22/40

Step-by-step explanation:

Answer:

d no is correct

I hope it will help you

The equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

According to the theorem;

[tex]x^2 + y^2 = r^2[/tex]

Given the following

x = [tex]r cos \theta[/tex]

y = [tex]r sin \theta[/tex]

Substitute into the formula

[tex](rcos \theta)^2 + (r sin \theta)^2 = r^2\\cos^2 \theta + sin^2 \theta =1[/tex]

Multiplying through by minus, the equivalent Pythagorean identity is [tex]-cos^2 \theta - 1 = -sin^2 \theta[/tex]

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Answer:

He is incorrect. The path will have an area of (4)(40) = 160 ft². The yard has an area of 600 ft². The area of the lawn will be the difference of the yard and path, so it is 440 ft².

Step-by-step explanation:

1. Original area of yard

A = lw = 40 × 15 = 600 ft²

2. Area of path

The path is a parallelogram.

A = bh = 4 × 40 =160 ft²

3. Remaining area

Remaining area = original area - area of path = 600 - 160 = 440 ft².

Answer:

A is correct

Step-by-step explanation:

I got 100 on edg

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the point (3, -3) and the slope m = -2. Substitute:

[tex]y-(-3)=-2(x-3)[/tex]

[tex]y+3=-2(x-3)[/tex] - point-slope form

Convert to the slope-intercept form (y = mx + b):

[tex]y+3=-2(x-3)[/tex]        use the distributtive property

[tex]y+3=-2x+(-2)(-3)[/tex]

[tex]y+3=-2x+6[/tex]      subtract 3 from both sides

[tex]y=-2x+3[/tex] - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=-2x+3[/tex]        add 2x to both sides

[tex]2x+y=3[/tex] - standard form

Convert to the general form (Ax + By + C = 0):

[tex]2x+y=3[/tex]      subtract 3 from both sides

[tex]2x+y-3=0[/tex] - general form

Answer:

108 feet cubed

Step-by-step explanation:

i think its 24 because you do l*w*h so 4 times 6 equals 24, times 4.5 and its 108.

Answer : The volume of the swimming pool is, [tex]142ft^3[/tex]

Step-by-step explanation :

In the given figure, there are two figures are included which are cuboid and 2 hemisphere.

As we know that 2 hemisphere combine to form a sphere.

Volume of swimming pool = Volume of cuboid + Volume 2 hemisphere

Volume of swimming pool = Volume of cuboid + Volume sphere

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

where,

l = length of cuboid = 6 ft

b = breadth of cuboid = 4 ft

h = height of cuboid = 4.5 ft

r = radius of sphere = [tex]\frac{Diameter}{2}=\frac{4ft}{2}=2ft[/tex]

Now put all the given values in the above formula, we get:

Volume of swimming pool = [tex](l\times b\times h)+(\frac{4}{3}\pi r^3)[/tex]

Volume of swimming pool = [tex](6ft\times 4ft\times 4.5ft)+(\frac{4}{3}\times 3.14\times (2ft)^3)[/tex]

Volume of swimming pool = [tex]108ft^3+33.49ft^3[/tex]

Volume of swimming pool = [tex]141.49ft^3[/tex]

Volume of swimming pool ≈ [tex]142ft^3[/tex]

Therefore, the volume of the swimming pool is, [tex]142ft^3[/tex]

Answer:

-1

Step-by-step explanation:

2x-10

-------------- = 3x

4

Multiply each side by 4

     2x-10

4*-------------- = 3x*4

      4

2x-10 = 12x

Subtract 2x from each side

2x-10 -2x = 12x-2x

-10 = 10x

Divide each side by 10

-10/10 =10x/10

-1 =x

Answer:-1

Step-by-step explanation:GOT it right on my quiz (FLVS)

[tex]w=\dfrac{1+i+i}{i(1+i)+2}\\\\w=\dfrac{1+2i}{i-1+2}\\\\w=\dfrac{1+2i}{1+i}\\\\w=\dfrac{(1+2i)(1-i)}{1+1}\\\\w=\dfrac{1-i+2i+2}{2}\\\\w=\dfrac{3+i}{2}\\\\w=\dfrac{3}{2}+\dfrac{1}{2}i[/tex]

To find the value of w, substitute the given value of z into the equation for w. Simplify the expression to obtain the value of w in the form x + iy, where x and y are real numbers.

To find the value of w, we first substitute the given value of z into the equation for w.

Given z = 1 + i, we have:

w = (1 + i + i) / (i(1 + i) + 2)

Simplifying the numerator:

w = (1 + 2i) / (i + i^2 + 2)

Since i^2 = -1, we can rewrite the equation as:

w = (1 + 2i) / (-1 + i + 2)

Simplifying further:

w = (1 + 2i) / (1 + i)

To divide complex numbers, we multiply the numerator and denominator by the conjugate of the denominator.

w = ((1 + 2i)(1 - i)) / ((1 + i)(1 - i))

w = (1 - i + 2i - 2i^2) / (1 - i^2)

Using i^2 = -1 again:

w = (1 + i + 2i + 2) / (1 - (-1))

Simplifying the numerator:

w = (3 + 3i) / 2

Dividing both terms by 2:

w = 3/2 + 3/2i

Therefore, w = 3/2 + 3/2i in the form x + iy, where x = 3/2 and y = 3/2 are real numbers.

Answer:

3/2

Step-by-step explanation:

3^-4 x 2^3 x 3^2/2^4 x 3^-3

base 3 will be numerator and base 2 will be denominator:

3^-4 * 3^2 * 3^3 / 2^4*2^-3

Now add the exponents of the base:

3^-4+2+3/ 2^4-3

3^-4+5/ 2^1

3/2

The correct option is 3/2 ....

Answer:

[tex]g(x)=\frac{x-12}{4}[/tex]

Step-by-step explanation:

To find the inverse of y=4x+12, all you need to is swap x an y and then remake y the subject.

y=4x+12

Swap x and y:

x=4y+12

Solve for y:

Subtracting 12 on both sides:

x-12=4y

Dividing 4 on both sides:

[tex]\frac{x-12}{4}=y[/tex]

So [tex]g(x)=\frac{x-12}{4}[/tex]

Answer:

[-12 + x]\4 = g(x)

Step-by-step explanation:

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I guess one more does not hurt.

Notice that choice D is equivalent to the given equation y = -4x - 12.

The only equation that does not cross the given equation is y = -4x.

They have THE SAME SLOPE. This means they are parallel and thus lead to NO SOLUTION.

ANSWER: y = -4x

Answer:

[tex]y=-4x[/tex]

Step-by-step explanation:

A Linear System with no solution, therefore inconsistent, is graphically represented by a pair of parallel lines.

According to Analytic Geometry, a parallel line shares the same slope.

Given the options, the only parallel line to [tex]y=-4x-12[/tex] is [tex]y=-4x[/tex] Since [tex]y=-4(x+3)[/tex] despite having the same slope, is actually the same line [tex]y=-4x+12[/tex]

So [tex]y=-4x[/tex] will form a system that has no solution.

To find the probability that Jenny will be called on twice, we multiply the probabilities of picking her on the first and second calls, which is 1/992.

To find the probability that Jenny will be called on twice, we need to consider the total number of possible outcomes and the number of favorable outcomes.

There are 32 students in Jenny's class, so the total number of possible outcomes is 32.

For the first call, the probability of picking Jenny is 1/32. After the first call, there are now 31 students left, with 1 of them being Jenny. So, the probability of picking Jenny again on the second call is 1/31.

To find the probability of both events happening, we multiply the probabilities together: (1/32) x (1/31) = 1/992.

The probability that Jenny will be called on twice is 1/992.

The probability that Jenny will be called twice in a class of 32 students is 0.00098. This rounds to 0.00 when rounded to the nearest hundredth.

To determine the probability that Jenny is called on twice when there are 32 students in the class, we start by finding the probability for one instance and then consider the repeated scenario.

To find the combined probability of both events happening (Jenny being called twice), we multiply the probabilities of each individual event:

(1/32) * (1/32) = 1/1024

Thus, the probability that Jenny will be called on twice is approximately 0.00098 when rounded to the nearest hundredth.