Find the amount A in an account (to the nearest cent) after 10 years if

dA
dt = rA, A(0) = 15,000 and A(8) = $22,377.37

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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Answer:

The standard error for the new sample size is of 23.4.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Interpretation:

From this, we can gather that the standard error is inversely proportional to the square root of the sample size, that is, for example, if the sample size is multiplied by 4, the standard error is divided by the square root of 4, which is 2.

Standard error of 52.4, sample size multiplied by 5. What is the standard error for the new sample size?

The standard error of 52.4 divided by the square root of 5. So

\(s = \frac{52.4}{\sqrt{5}} = 23.4\)

The standard error for the new sample size is of 23.4.

The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

With the given information, we have proved that EC ≅ AD as corresponding sided of congruent triangles are congruent too.

Both triangles are said to be congruent if the three angles and three sides of one triangle equal the corresponding angles and sides of the other triangle. We can see in the examples PQR and XYZ that PQ = XY, PR = XZ, and QR = YZ, and that P = X, Q = Y, and R = Z. Then, we can state that XYZ and PQR are related.

We have given that that ∠ADB = ∠ECB

And ∠ABC = ∠EBC as they are vertically opposite angles

And given that AB = EB

Thus, Triangle ABC ≅ Triangle EBC

And as  ABC ≅  EBC

EC ≅ AD as corresponding sided of congruent triangles are congruent too.

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Answer:

A. 1.4 pounds

Step-by-step explanation:
She divided 5.6/4 so in each jar there would be 1.4 pounds.
You can check your work by multiplying 1.4 to 4 and you'll get 5.6.

Answer:

780

Step-by-step explanation:

We want to use partial quotients in the division problem 858 ÷ 26.

In partial quotients method, what we do is to repeatedly subtract from the dividend easy multiples of the divisor.

In this case, the dividend is 858 and the divisor is 26.

Thus, the first easy multiple of the divisor we can use will be 30 because 30 × 26 = 780 yields the closest value to 858.

Therefore, the best choice for first number to subtract is 780

Answer: 780

Step-by-step explanation:

The best choice for the division problem will be 780.

Answer:

the experimental probability that the next vase produced at the factory will be chipped is 1/5.

Step-by-step explanation:

Since 5 out of the 13 boats that docked were from North Carolina, the experimental probability of the next boat being from North Carolina is the number of favorable outcomes (i.e., the number of boats from North Carolina) divided by the total number of outcomes (i.e., the total number of boats that docked).

Therefore, the experimental probability that the next boat to dock will be from North Carolina is:

P(North Carolina) = 5/13

For the second question:

Since 2 out of the last 10 vases produced were chipped, the experimental probability that the next vase will be chipped is:

P(chipped) = 2/10 = 1/5

Therefore, the experimental probability that the next vase produced at the factory will be chipped is 1/5.

Answer:

35

Step-by-step explanation:

Using the elimination method,  the value of A and B must 3 and 4 respectively to eliminate x in the equation. The value of A and B must be 3 and 7 respectively to eliminate y.

System of equation can be solved using elimination method, substitution method of graphical method.

But we are asked to use elimination method.

Therefore, the system of equation are as follows:

Equation 1: A [-4x + 7y = 4]

Equation 2: B [3x - 3y = 6]

Therefore,

If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 4.

If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 7.

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Answer:

-42

Step-by-step explanation:

Answer:negative square of 16

Step-by-step explanation:

Thx for the points god bless you

Answer:

The question is not complete

Answer: C

Step-by-step explanation:

Answer:

9/16

Step-by-step explanation:

The two sides with 3 cubes are 3/4, and the side with 4 cubes is 1

3/4 x 3/4 x 1 = 9/16

Answer:

1) congruent

2) corresponding angles

3) 3x+21 = 6x-60

4) x =9

Step-by-step explanation:

1) congruent becuase supplementary means that these 2 angles add up to make 180 degrees.

2) the file below

3) we know they are equal because the congruent correspoding angles.

4) 3x+21 = 6x-60

=> 21 = 9x-60

=> 81 = 9x

=> 9 = x

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Answer:

54

Step-by-step explanation:

angle A+angle B+Angle C =180 degree [ angle sum property of a triangle]

36 +90 + angle B =180 degree

126 +angle B =180 degree

angle B= 180-126

54 degree

Ans

The correct option regarding the mean of X + Y is given as follows:

a. MX+MY.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

Hence, when two variables are added, we can add their means, as we add all the observations and divide by the number of observations, considering the two variables.

This means that the correct option is given by option A.

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Answer:

1/2

Step-by-step explanation:

pues el ejercicio te da la respuesta

te dice que el aula usa la MITAD = 1/2 para trabajos artisticos.

respuesta 1/2

Answer:

Sub in the numbers given to x, y, z and use calculator to solve

The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The surface area of the right triangular prism is 270 sq ft

The total surface area of the prism is the  sum of all the area of its faces

For the two triangles

A = 2(0.5bh)

A = bh

A = 7 * 12 = 84 sq.ft

For the two rectangles

A = 2lw

A = 2(6*12)

A = 2 * 72 = 144 sq.ft

For the third triangle;
Area  6ft * 7ft

Area = 42 sq.feet

Taking the sum of the areas

TSA = 84 + 144 + 42

TSA  = 270 sq ft

Hence the surface area of the right triangular prism is 270 sq ft

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Alright, Nancy, let's do this.

If dimes are d, then quarters is d + 3.

10d + 25(d + 3) = 1090

I'm dealing with cents to get rid of the pesky decimal.

10d + 25d + 75 = 1090

                    35d = 1015

                        d = 29

Since quarters = d + 3, there are 32 quarters and 29 dimes.

Hope this helps!

i friend i am sorry but i can not answer your question there is no picture of wha tu need help with i am truley sorry but give the other person brainliest they need it :) have a great week!

Answer:

2 years

Step-by-step explanation:

If you have $9000 in the saving account, and you take $500, you are left with:

$9000 - $500 = $8500

in one year you will have 3% more of the 8500 which is:

8500/100*3 = $255

so in one year the number on your savings account is:

8500 + 255 = $8755

and by the next year you will have 3% more of the 8755 which is:

8755/100*3 = $262.65

so in two years the number on your savings account is:

8755 + 262.65 = $9017.65

which is a little bit more than the $9000.

so it will take 2 years until the calance again reaches $9000

Please mark braniliest if this reaches 2 answers because I want to get to Expert ;w;

Answer:

no

Step-by-step explanation:

Answer:

Step-by-step explanation:

one fifth