Sarah deposits $500 into a bank account earning 2% interest per year. The amount
(A) of money in the account at any time (t), in years, is represented by the equation
A (t) = 500(1.02)
Which best describes the equation in words?

A. The amount of money present in the account at any time is a product of 500 and a
power of 1.02.
B. The amount of money present in the account at any time is a power of 500 and a
product of 1.02.
C. The amount of money present in the account at any time is a sum of 500 and
apower of 1.02
D. The amount of money present in the account at any time is a power of 500 and a
sum of 1.02

Answer:

{-1, 10}

Step-by-step explanation:

Next time please share the entire set of instrutions.

x^2 - 9x - 15 = -5 should be rewritten in standard quadratic form:

x^2 - 9x - 10 = 0 = (x - 10)(x + 1) = 0.

Setting each factor equal to zero and then solving for x yields {-1, 10}

Answer:

{-1,10}

Step-by-step explanation:

\(x^2-9x-15=-5\)   given

\(x^2-9x-10=0\)   addition property of equality

\(x^2+(x-10x)-10=x^2+x-10x-10=0\)   x-10x = -9x

\(x(x+1)-10(x+1)=0\)   distributive property ( x( y + z ) = xy + xz

\((x-10)(x+1)=0\)   distributive property (backwards)

\(x-10=0;x=10;x+1=0;x=-1\)   at least one factor of 0 has to be 0

{-1,10}

Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

9514 1404 393

Answer:

  (x -4)^2 +(y -7)^2 = 36

Step-by-step explanation:

The equation of a circle with radius r and center at (h, k) is ...

  (x -h)^2 +(y -k)^2 = r^2

When the diameter is 12, the radius is 6 (half the diameter). Then for your center point, the equation is ...

  (x -4)^2 +(y -7)^2 = 36

To determine the intervals of continuity for the function f(x) = (x - 3) / (x^2 + 3x - 18), we first need to identify any discontinuities. Discontinuities occur when the denominator is equal to zero. We can factor the denominator as follows:

x^2 + 3x - 18 = (x - 3)(x + 6)

The denominator is equal to zero when x = 3 or x = -6. Therefore, the function has discontinuities at x = 3 and x = -6.

Now, we can describe the intervals of continuity using interval notation:

(-∞, -6) ∪ (-6, 3) ∪ (3, ∞)

For the identified discontinuities, the conditions of continuity that are not satisfied are:

A. There is a discontinuity at x = c where f(c) is not defined.
C. There is a discontinuity at x = c where lim x→c f(x) does not exist.

In summary, the function f(x) is continuous on the intervals (-∞, -6) ∪ (-6, 3) ∪ (3, ∞) and has discontinuities at x = 3 and x = -6, with conditions A and C not being satisfied.

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The answer is:

The interval on which the function is continuous is (-∞, -6) U (-6, 3) U (3, +∞).

The discontinuities are x = -6 and x = 3.

The conditions of continuity that are not satisfied are B and C.

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

To determine the intervals on which the function is continuous, we need to check for any potential discontinuities. The function is continuous for all values of x except where the denominator is equal to zero, since division by zero is undefined.

To find the discontinuities, we set the denominator equal to zero and solve for x:

x² + 3x - 18 = 0

Factoring the quadratic equation, we have:

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

Setting each factor equal to zero, we find two possible values for x:

x + 6 = 0 --> x = -6

x - 3 = 0 --> x = 3

Therefore, the function has two potential discontinuities at x = -6 and x = 3.

Now, we can analyze the conditions of continuity for these potential discontinuities:

A. There is a discontinuity at x = c where f(c) is not defined.

Since f(c) is defined for all values of x, this condition is not met.

B. There is a discontinuity at x = c where lim x→c f(x) ≠ f(c).

To determine this condition, we need to evaluate the limit of the function as x approaches the potential discontinuity points:

lim x→-6 (x - 3) / (x² + 3x - 18) = (-6 - 3) / ((-6)² + 3(-6) - 18) = -9 / 0

Similarly,

lim x→3 (x - 3) / (x^2 + 3x - 18) = (3 - 3) / (3^2 + 3(3) - 18) = 0 / 0

From the calculations, we can see that the limit at x = -6 is undefined (not equal to -9) and the limit at x = 3 is also undefined (not equal to 0).

C. There is a discontinuity at x = c where lim x→c f(x) does not exist.

Since the limits at x = -6 and x = 3 do not exist, this condition is met.

D. There are no discontinuities; f(x) is continuous.

Since we found that there are two potential discontinuities, this choice is not applicable.

Therefore, the answer is:

The interval on which the function is continuous is (-∞, -6) U (-6, 3) U (3, +∞).

The discontinuities are x = -6 and x = 3.

The conditions of continuity that are not satisfied are B and C.

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The absolute maximum value of f on the interval [0, 5] is 15.

The absolute minimum value of f on the interval [0, 5] is 5.

To find the absolute maximum and absolute minimum values of f on the given interval:

We need to evaluate f(x) at the endpoints of the interval and at any critical points within the interval.
First, we find the derivative of f(x):
f'(x) = 15 - 2x
Then, we set f'(x) = 0 and solve for x:
15 - 2x = 0
x = 7.5
However, 7.5 is not within the interval [0, 5], so we do not have any critical points within the interval.
Next, we evaluate f(x) at the endpoints of the interval:
f(0) = 15
f(5) = 5
Therefore, The absolute maximum value of f on the interval [0, 5] is 15 and the absolute minimum value of f on the interval [0, 5] is 5.

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Answer:

0.976 or 97.6%

Step-by-step explanation:

To calculate the frequency of the recessive allele, we need to use the information provided about the frequency of the dominant trait.

Let's assume that the particular dominant trait is determined by a single gene with two alleles: the dominant allele (A) and the recessive allele (a).

Given that 45 out of 1,000 babies are born with the dominant trait, we can infer that the remaining babies (1,000 - 45 = 955) do not have the dominant trait and can be considered as the recessive trait carriers.

The frequency of the recessive allele (q) can be calculated using the Hardy-Weinberg equation:

q = sqrt((Recessive individuals) / (Total individuals))

In this case, the total number of individuals is 1,000, and the number of recessive individuals is 955.

q = sqrt(955 / 1,000)

Using a calculator, we can find the value:

q ≈ 0.976

Therefore, the frequency of the recessive allele is approximately 0.976 or 97.6%.

Answer:

180 degrees is half of a full turn 360 degrees in a full turn

Step-by-step explanation:

Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

Answer:

one trillion

Step-by-step explanation:

Answer: 5/12

Step-by-step explanation: basically divide each number (10 &24) by 2

Answer:

8 munutes

Step-by-step explanation:

let :

x is the final level for both tanks (in ft) and

t is the time (in minutes)

the equation :

x = 6 - 0.5 t (eq.1)

x = 10 - 1t (eq.2)

eq. 1 = eq. 2

=>

6-0.5t = 10-1t

1t - 0.5t = 10-6

0.5t = 4

t = 4/0.5 = 8

t = 8 minutes

Answer:               8 minutes

Step-by-step explanation:

Write an equation for the level of oil in each tank.

Let t = the number of minutes.

Tank A: y = 6 − 0.5t

Tank B: y = 10 − 1t

Solve the system by using a table of values

When t = 8 minutes, the level in both tanks will be at 2 feet.

The following equation is m=d-10+k×i represent the total amount in account(m) in dollar.

Although the question does not specify the options, but I have specified my answer as follows:

Given:

The equation representing the total amount in the account, m, when starting with d dollars and being charged a 10$ fee.

Account Opening Charges: $10

Starting amount: $d

The total amount in the account: $m

Let us say the depositor deposits an amount $k for 'i' number of months

Banks deduct their charges from the account balance itself, hence account opening charges are deducted from the bank balance.

I have assumed an amount $k invested every month. You can remove that term as per the requirement of the question.

The total amount at a point in time = starting amount - Account Opening Charges + monthly deposit till that time

⇒m=d-10+k×i

This equation shows that the total amount in the account will be equal to the initial deposit minus the fee charged by the bank.

Therefore, the following equation is m=d-10+k×i.

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Answer:

(5,-1)

Step-by-step explanation:

To take the reflection of a point across the y-axis, simply take the negative of the y-value. Therefore, to reflect Point P, (5,1), you just turn the 1 into a -1 so your result is (5,-1).

The reflection of point P(5, 1) is C(5, - 1) accross the x-axis.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, point A is (- 4, - 1), point B is (- 4, 1), point C is (5, - 1), and point D is (5, 2) and Point P is at (5, 1).

We know the reflection of a point(x, y) across the x-axis is (x, - y).

Therefore, Reflection of point P(5, 1) across the x-axis is P'(5, - 1).

Now, P' is equal to C.
So, C(5, - 1)  is a reflection of Point P across the x-axis.

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The prediction we can make is that there were about 169 principals in attendance at the conference. The answer is D.

A type of ratio known as proportions describes the size of one segment of a group in relation to the size of the group as a whole, or population.

If 80 people represent a certain percentage of the total attendance, then we can use that same percentage to estimate the number of principals in attendance. Specifically:

percentage of principals in exhibit room = 15/80 = 0.1875

percentage of total attendance in exhibit room = 80/900 = 0.0889

If we assume that the percentage of principals in the exhibit room is similar to the percentage of principals in the entire conference, then we can set up the following proportion:

0.1875 / x = 0.0889 / 900

where x represents the total number of principals in attendance.

here, Solve for x, then:

x = 169

Therefore, the prediction we can make is that there were about 169 principals in attendance at the conference. The answer is D.

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Answer:

after the 30 years they would make 2325359.66 so 2025659 dollars and 66 cents.

Step-by-step explanation:

The length L and width W (with W≤L ) of the enclosure that is most economical to construct. L=10 W=20 the enclosure with dimensions L = 10 and W = 10 is the most economical to construct, as it has the minimum cost among the feasible options.

To find the enclosure that is most economical to construct given that L = 10 and W = 20, we need to minimize the cost function associated with constructing the enclosure.

Let's assume the cost function is given by C(L, W) = 2L + 5W, which represents the cost of constructing the enclosure based on its length and width.

To find the most economical enclosure, we can minimize the cost function C(L, W) subject to the constraint W ≤ L.

Since we are given L = 10, we need to find the width W that minimizes the cost function C(10, W) = 2(10) + 5W = 20 + 5W.

To minimize this function, we can take the derivative of C with respect to W and set it to zero:

dC/dW = 5

Setting this derivative equal to zero, we find that there is no critical point since the derivative is a constant.

However, since we have the constraint W ≤ L, we need to consider the endpoint W = L = 10 as a possible solution.

Calculating the cost at this endpoint:

C(10, 10) = 2(10) + 5(10) = 20 + 50 = 70

Therefore, the enclosure with L = 10 and W = 10 has a cost of 70.

In conclusion, the enclosure with dimensions L = 10 and W = 10 is the most economical to construct, as it has the minimum cost among the feasible options.

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The valid size for matrix C such that the multiplication DC can be performed is (C) 4×3

To determine a valid size for matrix C such that the multiplication DC can be performed, we need to consider the dimensions of matrices D and C.

The number of columns in matrix D must be equal to the number of rows in matrix C for the multiplication DC to be defined.

Let's check the given options:

(A) 3×6: In this case, the number of columns in D is 3, and the number of rows in C is 6. Since these numbers do not match, the multiplication DC cannot be performed.

Therefore, (A) is not a valid size.

(B) 4×6: In this case, the number of columns in D is 3, and the number of rows in C is 4.

Since these numbers do not match, the multiplication DC cannot be performed.

Therefore, (B) is not a valid size.

(C) 4×3: In this case, the number of columns in D is 3, and the number of rows in C is 4.

Since these numbers match, the multiplication DC can be performed.

Therefore, (C) is a valid size.

(D) 5×6: In this case, the number of columns in D is 3, and the number of rows in C is 5.

Since these numbers do not match, the multiplication DC cannot be performed.

Therefore, (D) is not a valid size.

(E) 3×4: In this case, the number of columns in D is 3, and the number of rows in C is 3. Since these numbers do not match, the multiplication DC cannot be performed.

Therefore, (E) is not a valid size.

(F) Does not exist: This option implies that no valid size exists for matrix C. However, we have already found a valid size in option (C), so this option is incorrect.

(G) None of the above: This option is incorrect since we have found a valid size in option (C).

Therefore, the valid size for matrix C such that the multiplication DC can be performed is (C) 4×3.

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Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

The translation to the center (-7,6) to the center (12,12) is given by the rule

On the other hand, the dilation from circle 1 to circle 2 has a scale factor given by the ratio of the given radii, that is,

Then the scale factor is 1/2.

Answer:

A

Step-by-step explanation:

the first number in slope intercept is the slope and the second number is the y-intercept

Answer:

The answer is Choice a

Step-by-step explanation:

Answer:

11 11/12 lb

Step-by-step explanation:

"3 2/3 times more than the small bag" comes out to:

(3 2/3)*(3 1/4) lb.

Convert both mixed numbers to improper fractions:

11     13       143

--- * ---- = ----------- = 11.917

3      4         12

The large bag weighs 11.917 lb, which may be converted to the mixed number 11 11/12 lb

Step-by-step explanation:

Using slope intercept for y = mx + b, substitute m = - 1/4, and (-8, 5) in for (x, y) to find the y-intercept

The options that shows expressions which are functions in the ranges they are defined are;

Option A: f(x) = 2x + 5

Option B:  f(x) = x² + 1

Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.

Now, integers are defined as whole numbers that can be positive, negative or zero.

a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.

b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.

c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.

d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.

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Answer:

d. 0.2 ( x + 4 )

Step-by-step explanation:

0.2x + 0.8

Both 0.2x and 0.8 have a common factor of 0.2, hence pull 0.2 out.

0.2x + 0.8

0.2 ( x + 4 )

Answer:

  -7/10

Step-by-step explanation:

You want the value of |a +3|÷(a -3) when a = -17.

Put the value where the variable is and do the arithmetic.

  |-17 +3| ÷ (-17 -3)

  = |-14| ÷ (-20) . . . . . . . . . . simplify

  = 14/(-20) = -14/20 . . . . . absolute value

  = -7/10 . . . . . . . . . . . . reduce the fraction

The value of the expression is -7/10.

__

Additional comment

A calculator or spreadsheet can help.

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\( \sqrt{ {a}^{2} - {b}^{2} } \)

Answer:

....

Step-by-step explanation:

3.6 units

Answer:

x=1, y=-6. (1, -6).

Step-by-step explanation:

y=-6x

-2x-7y=40

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

-2x-7(-6x)=40

-2x+42x=40

40x=40

x=40/40

x=1

y=-6(1)=-6