A mother wants to invest $15,000.00 for her son's future education. She invests a portion of the money in a bank certificate of deposit (CD account) which earns 4% and the remainder in a savings bond that earns 7%. If the total interest earned after one year is $900.00, how much money was invested in the CD account?
The total interest earned after one year is $900.00.
How much money was invested in the CD account? $
(Round to the nearest cent, if necessary.)

Answer:  b

Step-by-step explanation:

I think

297 mm is  nearest millimetre complete this statement .

The definition of convert units?

1 cm = 10mm

the length of a sheet of paper = 29.7 cm

the nearest millimetre = 29.7 * 10 = 297 mm

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I just think this way if it is wrong sry but at least I try

Answer:

C= [tex]\frac{AD}{B}[/tex]

Step-by-step explanation:

the answer is c because I said it c and the way you get the answer is by dividing the equality of the fraction

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))

Given the function

f(x)= 5-3x/2 and

g(x)= 5-2x/3

f(g(x)) = f(5-2x/3)

Substitute

f(g(x)) = 5-3(5-2x)/3)/2

f(g(x)) = (5-5+2x)/2

f(g(x)) = 2x/2

f(g(x)) = x

Similarly

g(f(x)) = 5-2(5-3x/2)/3

g(f(x)) = 5-5+3x/3

g(f(x)) = 3x/3

g(f(x)) =x

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

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domain = { 3,1,4,6} and range = { 2, 2 , 3 ,-2} are each relation is a function.

Describe domain.

Describe Range?

Range is the difference between the largest and lowest values in a dataset in statistics and mathematics. One indicator of data dispersion is the range.

function = ((3, 2), (1,2), (4,3), (6, -2)}

domain = { 3,1,4,6}

range = { 2, 2 , 3 ,-2}

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The ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.

In mathematics, Ratio is a term that is used to compare two or more numbers.

Given that their are 20 sports drinks in a cooler out of which 8 are orange flavored. Therefore, we can write that -

Number of orange flavored bottles = n[O] = 8

Total number of bottles = n[T] = 20

We can calculate the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler as follows -

Total number of non - orange flavored bottles will be -

n[C] = n[T] - n[O]

Now, the ration of non - orange bottles to the total number of bottle's can be written as -

n[C] / n[T]

(n[T] - n[O]) / n[T]

(20 - 8) / 20

12 / 20

3 / 5

Assume that the ratio is denoted by R. Therefore -

R = 3 : 5

Hence, the ratio of sports drinks that are not orange-flavored to all the sports drinks in the cooler is 3 : 5.

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Answer: 29°

Step-by-step explanation:

(2x-2)° + (x+5)° + 90° = 180°

(2x-2)° + (x+5)° = 90°

(2x + x)° = 87°

(3x)° = 87°

x° = 29°

Answer:

60.2 is the average

Step-by-step explanation:

add all numbers together to get: 301

divide 301 by 5 because there are 5 numbers total to get: 60.2

The x- and y-intercepts of the function both are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The relationship between the quantity of Fun Pass tickets sold and the amount of the overall sales are represented on the given graph.

Positive and negative functions are performed here, and the meanings are interpreted in the context of the situation.

Therefore, the x- and y-intercepts of the function are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

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The area of the rectangular-shaped building is 2448 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-

Area of rectangle = Length x width

Area of rectangle = 34 x 72

Area of rectangle = 2448 square feet

Therefore, the area of the rectangular-shaped building is 2448 square feet.

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For the functions in this problem, we have that:

a) The function is exponential, and the table is completed as follows.

b) The function is linear, and the table is completed as follows.

c) The function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

A function with initial value 1 and where the y-value is computed by multiplied the previous y-value by 5, as in item a, is an exponential function with parameters a = 1 and b = 5, hence the rule is:

[tex]y = 5^x[/tex]

Then:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

A proportional relationship is also classified as linear with a intercept of 0. For item b, since each y-value is the x-value multiplied by 5, the rule is:

y = 5x.

Hence the table is:

For item c, when x changes by 1, y is always multiplied by 1/2, and due to the multiplication, the function is exponential and given by:

[tex]y = -16\left(\frac{1}{2}\right)^x[/tex]

The -16 is because when x = 0, y = -16.

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The total interest earned at the end of first year is $250 and the percentage of interest for his total investment is 6.25%.

Given, Chau invested his money by purchasing the following:

a certificate of deposit for $1000 at the rate of 2% per year, and

corporate bonds for $3000 at the rate of 7% per year.

we know that simple interest is calculated by multiplying the amount invested P by the interest rate r times the number of years invested t.

therefore, I = P × r × t

a. The first investment has a principal of P = $1,000, r = 2% = 0.02, t = 1 yr

I₁ = 2000 × 0.04 × 1

I₁ = 40

The second investment has a principal P = $3,000, interest rate r = 7% = 0.07 and time t = 1yr

I₂ = 3000 × 0.07 × 1

I₂ = 210

Therefore, total interest  = I₁ ₊ I₂

= 40 ₊ 210

= $250

b. The overall rate of interest can be found by dividing:

Total interest/Total amount invested × 100

= 250/(1000 ₊ 3000) × 100

= 250/4000 × 100

= 25/4

= 6.25%

Hence we get the total interest earned at the end of first year as $250 and its overall rate of interest as 6.25%

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Your question was incomplete. Please find the missing content here.

Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for $1000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 7% interest per year.

(a) What was the total investment earned at the end of 1 year?

(b) What was the percentage interest for her total investment?

The answer is option C, No; the graph fails the vertical line test.

The graph given doesn't show a function.

The method that is used to determine whether a given graph is a function or not is called the vertical line test. In this test, a vertical line is drawn at an arbitrary point x. If this line touches the given graph at more than 2-points, then the given graph is not a function.

In the given graph, if we draw a vertical line for any x > -1, then this vertical line touches the graph at more than two points.

In other words, for any value x > -1, the corresponding value of y is not unique.

So, the answer is option C, No; the graph fails the vertical line test.

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When the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

Therefore, when the relationship between the unit of measurement of a scale (strength) and an outcome (pounds lifted) can be described by a linear equation y = a bx, the scale is said to have a property of equal intervals.

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These forecasts illustrate bias.

Therefore, these forecasts illustrate bias.

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Answer:

Graph in the picture

Answer:

18000

Step-by-step explanation:

We can multiply the number of students by the number of flowers per student.

[tex](1.2 \times 10^2)(1.5 \times 10^3) \\ \\ =(1.2)(1.5)(10^5) \\ \\ =1.8 \times 10^5 \\ \\ =18000[/tex]

Answer:

16

Step-by-step explanation:

Answer:

[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]

[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]

[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]

[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]

[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]

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

Question 2

[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]

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

Question 3

[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]

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

Question 4

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]

Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.

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

Question 5

[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Answer:

∠T and ∠STP

Step-by-step explanation:

You can name an angle by their middle vertex letter which, in this case, is T.

And you can name an angle using the three letters provided. P, T, and S are the three letters provided. However, the vertex letter always has to be in the middle. So, it could be ∠STP or even ∠PTS.

Let me know if you don't understand or need more explanation.

Answer:

Step-by-step explanation:

Answer: closed circle on -2 with the arrow to the left

               open circle on 1 with the arrow to the right

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

From the question, we are to order the equations from least to greatest by the value of the slope

The given equations are

y = (-3/4)x + 2

3x - 4y = 7

y = 12(x - 19) + 5

y - 3 = 1/2(x - 4)

To determine the slopes of the line, we will compare the equations to the general form of the equation of a line

The general form of the equation of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = -3/4

∴ Slope = -3/4

First, rearrange

3x - 7 = 4y

4y = 3x - 7

y = (3/4)x - 7/4

By comparison,

m = 3/4

∴ Slope = 3/4

First, simplify

y = 12x - 228 + 5

y = 12x - 223

By comparison,

m = 12

∴ Slope = 12

y - 3 = 1/2(x - 4)

First, simplify

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

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

y = (1/2)x + 1

By comparison,

m = 1/2

∴ Slope = 1/2

Now,

The slopes ordered from the least to greatest is

-3/4 < 1/2 < 3/4 < 12

Thus,

The equations ordered from the least to greatest is

y = (-3/4)x + 2

y - 3 = 1/2(x - 4)

3x - 4y = 7

y = 12(x - 19) + 5

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Answer: It is 3.5

Step-by-step explanation:

I think this because 2/2x=3/2=1.5 but you have 2 left to add which=3.5

Answer:5

Step-by-step explanation:

Answer:

Simplify the expression, Your answer would be :

Step-by-step explanation:

And to find the Value of the following expression, Your answer would be :

hopefully this helps you ! ~

Raíz cuadrada de 864

Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:

The general equation of ellipse is given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , where, a is length of semi-major axis and b is length of semi-minor axis.

centro: (0,0)

focus : (0, -√28) , (0, √28)

eje conjugado = 2√3

por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:

de los focos podemos obtener que: √28

y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:

b = √3

podemos utilizar la siguiente fórmula para obtener a:

si despejamos a en la ecuación obtenemos lo siguiente:

ahora podemos sustituir los valores:

a=5

así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:

si graficamos la hipérbola, queda como en el documento adjunto.

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Miranda made error by combining unlike terms, She added 5x and 9y then subtracted 4 from the answer. Answer is already in simplified form, it cannot be simplified further.

Like terms are ones whose exponent power and variables are the same. These variables' coefficients could differ. Terms that are comparable to one another are known as algebraic terms. As an illustration, consider the algebraic statement 8y + 2y, where y is the same variable as in the expression but has different coefficients.

Terms that have variables and exponents that differ from one another are said to be unlike terms. In contrast to terms, an expression is known to obtain when the coefficient, variables (in this case, two variables), and exponent powers (if any) are all distinct. Contrary to algebraic terms, the algebraic formula 3x + 9y is known as, where x and y are two separate variables with different coefficients.

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Answer: ≈578 cm²

Step-by-step explanation:

[tex]V_{cyl}=1056\ cm^3\ \ \ \ H=21\ cm\\V_{cyl}=\pi R^2H\\1056=\pi *R^2*21\\1056=21\pi *R^2\\[/tex]

Divide both parts of the equation by 21π:

16=R²

4²=R²

4=R

[tex]S{tot\ sur}=\pi R^2+2\pi RH\\S{tot\ sur}=\pi R*(R+2H)\\S{tot\ sur}=\pi *4*(4+2*21)\\S{tot\ sur}=4\pi *(4+42)\\S{tot\ sur}=4\pi *46\\S{tot\ sur}=184\pi \\S{tot\ sur}\approx578\ cm^2[/tex]

The area of parallelogram ABCD is found to be 2√3 square units.

A quadrilateral is known as a parallelogram in geometry. The opposite sides of a parallelogram are parallel & equal in length. Rhombus, rectangle, & square are a few examples of parallelograms.

We know that diagonal of such a parallelogram divides it into two equal triangles.

So, parallelogram area,

ABCD = 2× area of ΔABC (equation 1)

The area pf the triangle is found through the vertices are (x₁,y₁), (x₂,y₂), (x₃,y₃) is;

Area = (1/2)×[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

The vertices of the triangles are given as;

A(2,4), B(2+ √3 ,5) and C(2,6)

Area = (1/2)×[2(5−6) + (2+√3)(6−4) + 2(4−5)]

Area = (1/2)×[−2+2(2+ √3)−2]

Area = √3

When we plug this value into equation (1),

Parallelogram area,

ABCD = 2×the area of ABC

ABCD = 2×√3

ABCD = 2√3

Thus, the area of the parallelogram ABCD id estimated as 2√3 square units.

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The correct question is -

Find the area of a parallelogram ABCD if three of its vertices are A(2,4), B(2+ √3 ,5) and C(2,6)