Write an equation of an exponential function of the form y=ab^x passing through the points (0,8) and (6,0.125)

Answer:

Final answer is p=2.

Step-by-step explanation:

Given equation is [tex]\frac{4-p}{p-1}=\frac{2}{p-1}[/tex]

Cross multiply

[tex]\left(4-p\right)\left(p-1\right)=2\left(p-1\right)[/tex]

[tex]4p-4-p^2+p=2p-2[/tex]

[tex]4p-4-p^2+p=2p-2[/tex]

[tex]0=p^2-4p+4-p+2p-2[/tex]

[tex]0=p^2-3p+2[/tex]

[tex]0=p^2-1p-2p+2[/tex]

[tex]0=(p-1)(p-2)[/tex]

[tex]0=(p-1)[/tex] or [tex]0=(p-2)[/tex]

[tex]1=p[/tex] or [tex]2=p[/tex]

But p=1 will make denominator 0 and make the problem not defined.

Hence final answer is p=2

Answer:

I just took the test the answer is: None

Step-by-step explanation:

A class consists of ten individuals. The instructor selects three kids to accompany her to the library. It makes no difference in whatever sequence they are picked. There are 120 options for selecting pupils.

A permutation is a process of putting items or pieces in a certain order. Combinations are a method of picking things or pieces from a set of objects or collections when the order of the objects is irrelevant.

No of student=10

Students to be choosen=3

The ways are there to choose the students are found with the help of combination as;

If n is the number of the ways:

n= 10C₃

[tex]\rm nCr = \frac{n!}{r!(n-r)!}\\\\[/tex]

Where n is the total of students and r is the teacher to be chosen:

[tex]\rm 10 C_3= \frac{10 !}{3!7!}\\\\ 10 C_3= \frac{3628800}{30240} \\\\ n=120[/tex]

Hence, there is 120 no of ways are there to choose a student.

To learn more about permutations and combinations, refer to:

https://brainly.com/question/11958814

#SPJ2

Answer: A class consists of ten individuals. The instructor selects three kids to accompany her to the library. It makes no difference in whatever sequence they are picked. There are 120 options for selecting pupils.

Step-by-step explanation:

Answer:

63.36 years

Step-by-step explanation:

This is a compound interest problem and the following information has been provided;

Principal, P = 1200

Interest rate, r = 4%

Accumulated amount, A = 14400

We are required to determine the number of years for the principal to accumulate to the given amount. We use the compound interest formula;

[tex]A=P(1+r)^{n}[/tex]

We substitute the given values into the formula and solve for n;

[tex]14400=1200(1+\frac{4}{100})^{n}\\12=(1.04)^{n}\\[/tex]

The next step is to introduce natural logarithms;

[tex]ln12=nln(1.04)\\n=\frac{ln12}{ln1.04}\\n=63.36[/tex]

Thomas has invested $1,200 at a 4% interest rate. Using the formula for compound interest and solving for time, it will take approximately 29.1 years for his account balance to reach $14,400.

Thomas has invested an amount of $1,200 into an account with a 4% interest rate. This type of problem involves the use of the formula for compound interest. The general formula for compound interest is: A = P(1 + r/n)^(nt), where:

In this case, we assume the interest is compounded annually, so n = 1. We rearrange the formula to solve for t, giving us the formula t = log(A/P) / log(1 + r).

Substituting the given values into the formula, we get t = log(14400/1200) / log(1 + 0.04), which gives a result of approximately 29.1 years. So, it will take around 29.1 years for the account balance to reach $14,400.

https://brainly.com/question/14295570

#SPJ3

Answer:

[tex]0.069\ kg[/tex]

Step-by-step explanation:

we know that

1 kg=1,000 g

so

using proportion

Find out how many kilograms are 69 grams

Let

x -----> the weight in kg

[tex]\frac{1}{1,000}\frac{kg}{g} =\frac{x}{69}\frac{kg}{g}\\\\x=\frac{69}{1,000}\\\\x=0.069\ kg[/tex]

69 grams is equal to 0.069 kilograms.

To find how many kilograms 15 crackers weighing 69 grams is, convert 69 grams to kilograms by recognizing that there are 1000 grams in 1 kilogram.

15 crackers weigh 69 grams. To find how many kilograms this is, we need to convert grams to kilograms. There are 1000 grams in 1 kilogram. Therefore, 69 grams is equal to 0.069 kilograms.

i think b i’m not sure

Answer:

B

Step-by-step explanation:

Y=-2/5x -1 is the answer I believe, if anything check Photomath, that should be the right slope double check the y-intercept by plugging it in with your points provided to u

Answer:y = -2x + 7

Step-by-step explanation:

The equation of a straight line when two points are given is y - y1 = m(x - x1) but m is gradient which is y2 - y1 / x2 - x1

Substitute the points (3 ,1 ) and (7 , -7)

To the gradient equation and solve for the gradient which is m = -2 .Now with the gradient and the first point (3 , 1) solve for the equation

:• y - 1 = -2(x -3 )

y - 1 = -2x +6

. y = -2x + 7

0.3125 is the correct answer

ANSWER

[tex] \frac{5}{16} [/tex]

bushels

EXPLANATION

It was given that,

Irma picked

[tex] \frac{5}{8} [/tex]

of a bushel.

If Mathew picked half as many bushels, then Mathew has:

[tex] \frac{1}{2} \times \frac{5}{8} = \frac{5}{16} [/tex]

Hence, Mathew has

[tex] \frac{5}{16} [/tex]

bushels.

The answer is A because the input is x and the out put is y so that would make it 9.

Answer:

Step-by-step explanation:

D

Answer:

Option D

Step-by-step explanation:

Larry scored x points

Ervin scores half as many points in a game as Larry

We need to make an expression using the given statement

For larry points we use the variable x.

Half as many points means 1/2 as larry

Ervin = half as larry

Ervin scored [tex]\frac{1}{2}[/tex] of larry

Ervin scored [tex]\frac{1}{2}[/tex] x

The product of c and 7 is less than or equal to -28  is  7c≤-28.

A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.

solving this we will get the valve of Y if x is given.

Learn more about the equation here:- https://brainly.com/question/2972832

#SPJ2

Answer:

3

Step-by-step explanation:

The assumed frequency of defects is 2/16.

When we apply this rate to 24, (2/16)*24, we get 3.

Therefore, we can assume around 3 defective boxes tomorrow.

Answer:

Work:

first you want to change 1/2 so the denominator is a 4

1/2 is equivalent to 2/4

now you have -1 1/4 + 2/4

then you want to get rid of the whole number and make -1 1/4 into a fraction

-1 is -4/4 so add that to the 1/4

now you have -5/4 + 2/4

you can add that now easily and get -3/4

Answer:

-3/4 aka C                                                  hope this helped

[tex]P(x)[/tex] has degree 3, so it takes the general form

[tex]P(x)=ax^3+bx^2+cx+d[/tex]

It has a root [tex]x=1[/tex] of multiplicity 2, which means [tex](x-1)^2[/tex] divides [tex]P(x)[/tex] exactly, and it has a root of [tex]x=-3[/tex] of multiplicity 1 so that [tex]x+3[/tex] also is a factor. So

[tex]P(x)=a(x-1)^2(x+3)[/tex]

Expanding this gives

[tex]P(x)=a(x^3+x^2-5x+3)=ax^3+ax^2-5ax+3a[/tex]

[tex]\implies\begin{cases}a=b\\-5a=c\\3a=d\end{cases}[/tex]

The [tex]y[/tex]-intercept occurs for [tex]x=0[/tex], for which we have

[tex]P(0)=d=2.1[/tex]

Then

[tex]3a=d\implies a=0.7[/tex]

[tex]a=b\implies b=0.7[/tex]

[tex]-5a=c\implies c=-0.14[/tex]

So we have

[tex]\boxed{P(x)=0.7x^3+0.7x^2-0.14x+2.1}[/tex]

Answer:

4

Step-by-step explanation:

on edge.

Answer: 2 pizzas with 2.50 left

Step-by-step explanation: First you subtract the 3.50 from the 20, that'll leave you with 16.50 and then from there you subtract 7 from it until you can't anymore

Division is a method of distributing a group of things into equal parts.

According to the given question, we have the following data:

So, first of all, we have to pay the delivery charge whether we are ordering a single or bulk. That's why we have to deduct that from the total Sebastian has.

$20 - $3.50 = $16.50

So, now Sebastian has $16.50.

Now, each pizza is for $7.

So, it's clear now that, Sebastian has to divide his total amount by the price of each pizza to get how many pizzas he can order.

Number of pizzas Sebastian can order = (Total amount Sebastian has / price of each pizza)

= ($16.50 / $7)

= 2.36

But wait how can he order a fraction of pizzas so we have to take 2 as our answer.

Therefore, Sebastian could order a total of 2 pizzas.

To know more about division refer here - brainly.com/question/194007

#SPJ2

Answer:

1.28 is the amount you get off

Step-by-step explanation:

Answer: C: $1.28

Step-by-step explanation: took test

Answer:

D 70/3

Step-by-step explanation:

5 /3 * 2/3 * 21

10/9 * 21/1

210/9

We can divide by 3 on the top and bottom

70/3

the final product is 70/3, making the correct answer D).

The question asks to find the product of the numbers (5/3), (2/3), and 21. To solve this, we will multiply these numbers step by step.

So, the final product is 70/3, making the correct answer D).

The cat weighs 14.375 pounds (or 230 ounces even).

Hope this helps!

Answer:

[tex]x=t[/tex]

[tex]y=\pm\sqrt{3t-t^2}[/tex]

Step-by-step explanation:

The given polar equation is;

[tex]r=3\sin \theta[/tex]

We multiply  both sides by r

[tex]r^2=3r\sin \theta[/tex]

The corresponding rectangular equation is

[tex]y^2+x^2=3x[/tex]

[tex]y^2=3x-x^2[/tex]

[tex]y=\sqrt{3x-x^2}[/tex]

Let x=t,

Then;

[tex]y=\pm \sqrt{3t-t^2}[/tex]

Answer:

108.505 is greater.

Step-by-step explanation:

It is 5 thousandths bigger.

Answer:

B. (-3, 0) and (-6,0)

Step-by-step explanation:

x intercept when y = 0

so x^2 + 9x + 18 = 0

Factor

(x + 6)(x + 3) = 0

x+6 = 0; x = -6

x+3 = 0; x = -3

Answer

B. (-3, 0) and (-6,0)

Answer: Option B.

Step-by-step explanation:

The graph of the quadratic equation is a parabola.

The parabola intercepts the x-axis when [tex]y=0[/tex].

Then, you need to substitute [tex]y=0[/tex] into the equation:

[tex]y=x^2+9x+18\\0=x^2+9x+18[/tex]

Factor the quadratic equation: find two number that when you add them you get 9 and when you multiply them you get 18. In this case these numbers are 6 and 3. Then:

 [tex]0=(x+6)(x+3)\\\\x_1=-6\\x_2=-3[/tex]

Therefore, the x-intercepts are:

(-3,0) and (-6,0)

the answer is a concave decagon

Answer:

I believe this is a "Concave Decagon."

Step-by-step explanation:

A Decagon consists of 10 sides. This abstract shape has 10 sides, so this shape is a Decagon.

Hope this helps! :)

Answer:

n < 6

Step-by-step explanation:

n/-3 + 8 > 6

Subtract 8 from each side

n/-3 + 8 -8> 6-8

n/-3 > -2

Multiply each side by -3 to isolate n.  Remember to flip the inequality since we are multiplying by a negative

n/-3 * -3 < -2 *-3

n < 6

Answer:

the diameter, d, must be 6

Step-by-step explanation:

Formula for circumference of a circle with diameter d is C = πd.  

If C = 6π = πd, then the diameter, d, must be 6.

Step-by-step explanation:

Given equation of circle is,

[tex] {x}^{2} + {y}^{2} - 6y - 12 = 0 \\ by \: compairing \: it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\2 g = 0 \: or \: g = 0 \\ 2f= - 6 \\ or \: f= - 3 \\ c = - 12[/tex]

again the another form of circle is,

[tex] {x}^{2} + {(y - k)}^{2} = 21 \\ or \: {x}^{2} + {y}^{2} - 2ky + {k}^{2} - 21 = 0 \\ by \: compairing \:it \: with \: \\ {x}^{2} + {y}^{2} + 2gx + 2fy = 0 \: we \: get \\ g = 0 \\f = - k \\ c = {k}^{2} - 21[/tex]

now equating the values of f in both equations,

-k=-3

i.e. k=3

therefore k=3

Equilateral triangle: all sides are equal lengths, all angles are equal too

Scalene triangle: has three different sides, all angles are different

Isosceles triangle: 2 sides are equal, one isn’t, 2 angles are the same, one is different

Acute triangle: angles are less than 90 degrees

Obtuse triangle: angles are larger than 90 degrees

Right triangle: angle forms a 90 degree angle

Those are the triangles :)

Final answer:

There are different types of triangles in geometry, including equilateral, isosceles, and scalene triangles. The sum of angles in a triangle is always 180 degrees.

Explanation:

In geometry, there are several types of triangles, including:

As for the sum of angles in a triangle, it is always 180 degrees. This is known as the Triangle Angle Sum Theorem

45, it is the highest number in the range

i don't need it but brainliest it is appreciated

[tex]\boxed{h=\frac{6}{b}}[/tex]

Solving for [tex]h[/tex] is the same as isolating it. In this problem, we have the following equation:

[tex]6=bh[/tex]

So we need to do the following steps:

Step 1: Interchange the order of the equation:

[tex]bh=6[/tex]

Step 2: Divide the whole equation by [tex]b[/tex]:

[tex]\frac{1}{b}bh=\frac{1}{b}6[/tex]

Step 3: Simplify

[tex]h=\frac{6}{b}[/tex]

Finally, this h is in term of b and is:

[tex]\boxed{h=\frac{6}{b}}[/tex]

it will be 31,995 but we have to estimate yo the nearest cent so 10 cents

Answer:

197,500

Step-by-step explanation:

200500*25-184000/6.25-2560.43=4980499.57 Which rounds to 197,500.

Allison owes approximately $1,380.50 in prorated taxes and interest for the property she's closing on September 17.

To calculate the prorated taxes and interest that Allison owes, we need to break down the calculation into two parts: prorated property taxes and prorated interest.

1. **Prorated Property Taxes:**

  - Allison is closing on September 17, which means she will own the property for 106 days of the year (September 17 to December 31).

  - The seller has already paid $2,560.43 in property taxes for the entire year.

  - To calculate Allison's portion of the property taxes, we need to divide the seller's payment by the number of days in the year and then multiply by the number of days Allison will own the property.

Prorated Property Taxes = Seller's Property Tax Payment/

Days in Year × Days Allison Owns the Property

 [tex]\[ \text{Prorated Property Taxes} = \frac{2,560.43}{365} \times 106 \][/tex]

 [tex]\[ \text{Prorated Property Taxes} = \frac{2,560.43}{365} \times 106 = 741.12 \][/tex]

2. **Prorated Interest:**

  - Allison is taking out a 25-year fixed-rate mortgage for $185,000 at 6.25% interest.

  - To calculate the prorated interest, we need to find out how much interest Allison will owe for the remaining days of September.

 Daily Interest Rate [tex]$=\frac{\text { Annual Interest Rate }}{\text { Days in Year }}=\frac{6.25 \%}{365}$[/tex]

  Prorated Interest for September = [tex]Loan Amount $\times$ Daily Interest Rate $\times$ Number of Days in September[/tex]

  [tex]\[ \text{Prorated Interest for September} = 185,000 \times \frac{6.25\%}{365} \times 14 \][/tex]

 [tex]\[ \text{Prorated Interest for September} \approx 639.38 \][/tex]

Now, let's add up the prorated property taxes and prorated interest:

[tex]\[\text{Total Prorated Taxes and Interest} = \text{Prorated Property Taxes} + \text{Prorated Interest for September}\][/tex]

[tex]\[\text{Total Prorated Taxes and Interest} = 741.12 + 639.38\][/tex]

[tex]\[\text{Total Prorated Taxes and Interest} = 1380.50\][/tex]

So, Allison will owe approximately $1,380.50 in prorated taxes and interest.