Write answer in scientific notation

Total interest earned = 68

Total amount collected = 1268

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest.

Since nothiong mentioned the interest is considered simple

Total amount = 1200 (principal)

Time = 1 year 5 month = [tex]1\frac{5}{12} = \frac{17}{12}[/tex]

rate = 4 %

Total interest earned = [tex]\frac{1200 * 4 * \frac{17}{12} }{100}[/tex] = 68

Total amount generated = 1200 + 68 = 1268.

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Answer: d = √(5² + 9²) = √106, or approximately 10.3 units.

Answer:

D) 5x+15

Step-by-step explanation:

5×x+5×3

5x+15

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Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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The steps to solve two polynomial equations are given below.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Apply the Zero Factor Property to an Equation Solving.

ZERO. FACTOR, write the equation with one side equal to zero. the expression by a factor.

PROPERTY. Solve the equation by setting each factor to zero.

Check by adding substitutes to the initial equation.

Write a polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero once it has reached zero. The original equations' solutions are the solutions to the resulting equations. Factoring cannot always be used to solve polynomial equations.

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Answer:

-3.3

Step-by-step explanation:

-2.3 - (4.5-3.5)

-2.3 - (1.)

-3.3

Answer:

6

Step-by-step explanation:

I counted

The required point that satisfies each system of equation is (12, -1). Option B is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

To equations are given as,
y = -1/3x + 3 - - - - (1)
y = -3/4x + 8 -- - - - (2)

From equation 1 and 2
-1/3x + 3 = -3/4x + 8
3/4x - 1/3x = 8 - 3
9x - 4x / 12 = 5
5x = 60
x = 12

Now, to evaluate the y ordinate put the above x in equation 1
y = -1/3(12) + 3
y = -4 + 3
y = -1

Thus, the required point that satisfies each system of equation is (12, -1). Option B is correct.

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9514 1404 393

Answer:

  total purchase price: $27,722.01

Step-by-step explanation:

The price of the car plus tax is ...

  $25,625 × (1 +7.5%) = $27,546.88

Adding license and title charges brings the total to ...

  $27,546.88 +175.13 = $27,722.01 . . . total purchase price

_____

Additional comment

10% of that, or $2,772.20, will be the required down payment, leaving a balance due of $24,949.81. The payments on a 36-month loan at 9% will be $793.40, for a total loan cost of $28,562.30. Then the full cost of the car, including financing, is $31,334.50. The cost of the financing is $3,612.49.

Answer:

first graph is a function

Step-by-step explanation:

The cost of one ticket in Virginia is $8

A System of Linear Equations is when we have two or more linear equations working together.

Given that, 4 movie tickets in Virginia plus 5 movie tickets in Maryland cost $77, Also know that 8 movie tickets in Virginia plus 3 movie tickets in Maryland cost $91.

To find the cost of a ticket in Virginia we will establish a system of linear equations and then solve them,

Let V represents the cost in Virginia that of in Maryland be M

Therefore,

4v+5m = 77.......(i)

8v+3m = 91........(ii)

Multiplying the equation eq(i) by 2 and subtracting eq(ii) from eq(i) [Elimination]

(8v+10m = 154)  - (8v+3m = 91)

7m = 63

m = 9

Put m = 9 in eq(i)

4v+5(9) = 77

4v = 77-45

4v = 32

v = 8

Hence, Each ticket in Virginia and Maryland costs $8 and $9 respectively.

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Answer:

630

Step-by-step explanation:

you can search it up if you want.

Answer:

630

Step-by-step explanation:

Answer:

x = 3.25 m

Step-by-step explanation:

First, find the height of the triangle using sin31:

sin 31 = h/9 ---> h = 9sin31 = 4.64 m

Next, we can now solve for x using tan55:

tan 55 = h/x --> x = (4.64 m)/(tan 55) = 3.25 m

Answer:

y=3x-10

Step-by-step explanation:

first, we need to find the slope of line s, as that will determine the slope of line t

the formula for the slope calculated from 2 points is (y2-y1)/(x2-x1)

we can label the points for (3,4) and (2,1)

x1=3

y1=4

x2=2

y2=1

substitute into the formula:

m=(y2-y1)/(x2-x1)

m=(1-4)/(2-3)

m=-3/-1

m=3/1

m=3

the slope of line s is 3

as said above, parallel lines have the same slope, but different y intercepts.

that means that line t will have the same slope as line s (3).

typically, lines are written in the form y=mx+b, where m is the slope and b is the y intercept

here's what is line t so far:

y=3x+b

we need to find b

because the line passes through the point (4,2), we can use it to solve for b

plug 4 in as x and 2 as y

2=3(4)+b

2=12+b

-10=b

so that means that b is -10

therefore the equation for line t is y=3x-10

Hope this helps! Good luck on your assignment!

Answer: first u have to find the perimiter for each side

Step-by-step explanation:

the answer is 100 d z

Answer:

100π sq. ft

Step-by-step explanation:

Given,

Radius ( r ) = 10 ft

To find : Area ( circle ) = ?

Formula : -

Area ( circle ) = π r^2

Area ( circle )

= π x 10^2

= π x 100

= 100π sq. ft

Answer:

area of circle : πr^2

                      = π(10)^2

                      = 314.1592654

                      ≈ 314.16 cm2

Answer:

10 and 24units

Step-by-step explanation:

Pythagoras' Theorem applies to right angle triangles with the formula:

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

where c is the longest side, with a and b the shorter ones (interchangable)

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are 10 and 24 units.

Answer:

637 in^3

Step-by-step explanation:

V=(BxH)/2

V=((13x7) x 14)/2

V=(91x14)/2

V=1274/2

V=637 in^3

Answer:

(8,-2)

Step-by-step explanation:

Whatever the case a quadrilateral has always a sum of interior angles = 360°.

A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which cannot be collinear. A quadrilateral has four sides, four angles, and four vertices. The word "quadrilateral" is derived from the Latin words "quadra" (four) and "latus" (sides). A quadrilateral may or may not have equal lengths on each of its four sides.

A quadrilateral is a polygon with four sides, four angles, and four vertices. The arrangement of the vertices must be considered whenever a quadrilateral is named. For instance, the following quadrilateral should be referred to as ABCD, BCDA, ADCB, or DCBA. Since they alter the order of vertices in which a quadrilateral is formed, it cannot be called ACBD or DBAC.

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Answer: obtuse

Step-by-step explanation:

The population standard deviation of the data is 111.

1. Find the mean of the data:

Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5

2. Find the difference between each data point and the mean:

Feb: (314 - 171.5) = 142.5

Mar: (158 - 171.5) = -13.5

Apr: (482 - 171.5) = 310.5

May: (284 - 171.5) = 112.5

Jun: (310 - 171.5) = 138.5

Jul: (281 - 171.5) = 109.5

3. Square each of the differences:

Feb: (142.5)^2 = 20,312.5

Mar: (-13.5)^2 = 182.25

Apr: (310.5)^2 = 95,822.25

May: (112.5)^2 = 12,656.25

Jun: (138.5)^2 = 19,082.25

Jul: (109.5)^2 = 11,982.25

4. Sum all of the squared differences:

20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5

5. Divide the sum of the squared differences by the number of data points minus one:

149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5

Square root of 29,809.5 = 111 (rounded to the nearest integer)

Therefore, the population standard deviation of the data is 111.

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ok um 213=89Step-by-step explanation:ummmmmmmmmm

Answer:

Para el punto a. tenemos 312 elementos en el espacio muestral

Para el punto b. la probabilidad pedida es [tex]\frac{1}{26}[/tex]

Step-by-step explanation:

Comencemos explicando el principio de multiplicación. Supongamos que se tiene un experimento por etapas, es decir, una primera etapa que se puede llevar a cabo de '' [tex]x_{1}[/tex] '' maneras distintas, una segunda etapa que se puede llevar a cabo de '' [tex]x_{2}[/tex] '' maneras distintas y así sucesivamente hasta una etapa final que se puede llevar a cabo de '' [tex]x_{n}[/tex] '' maneras distintas. La cantidad total de formas de desarrollar todo el experimento se puede calcular como el producto de las distintas maneras en que se puede ejecutar cada etapa :

Formas de desarrollar todo el experimento = [tex]x_{1}x_{2}[/tex] ... [tex]x_{n}[/tex]

Para el punto a. del ejercicio vamos a utilizar este principio para calcular la cantidad de elementos del espacio muestral. La primera etapa del experimento sería el lanzamiento del dado y una segunda etapa el sacar una carta de una baraja de poker (52 cartas distintas). Entonces, para un dado tenemos 6 posibles opciones y cuando sacamos una carta podemos obtener 52 resultados distintos. Por lo tanto ⇒

[tex](6)(52)=312[/tex]

Tenemos un total de 312 elementos en el espacio muestral (todos distintos) y con la misma probabilidad de ocurrencia ya que suponemos que en el dado tenemos la misma probabilidad de obtener un uno, un dos, etc; así como en la baraja tenemos la misma probabilidad de sacar cada una de las cartas.

Para el punto b. utilizaremos el hecho de que estamos frente a un espacio muestral equiprobable y calcularemos la probabilidad del evento ''sale un número par en el dado y un AS en la baraja'' contando los casos favorables a este evento y dividiendo por la cantidad de elementos totales del espacio muestral. Podremos hacerlo de esta manera ya que el espacio muestral es equiprobable. Definimos para ello

[tex]A:[/tex] ''Sale un número par en el dado y un AS en la baraja''

[tex]P(A)=\frac{CasosFavorablesAlEventoA}{CasosTotales}[/tex]

Los casos totales son 312 (calculados en el inciso a.)

Los casos favorables al evento A se pueden escribir utilizando el principio de multiplicación como

[tex](3)(4)=12[/tex]

El 3 es por los tres números pares que podemos obtener del dado (estos números son el dos, cuatro y el seis).

El 4 se debe a la cantidad de ases en una baraja de Póker de 52 cartas (estos son el as de corazones, el as de picas, el as de trébol y el as de diamantes).

Reemplazando en la expresión de [tex]P(A)[/tex] obtenemos :

[tex]P(A)=\frac{12}{312}=\frac{1}{26}[/tex]

Otra forma de haber calculado esta probabilidad es utilizando el hecho de que tirar el dado y sacar una carta de la baraja son dos eventos independientes. Por ende, la probabilidad se puede calcular como el producto de la probabilidad parcial de cada evento. Esto es :

B : ''Sale un número par en el dado''

C : ''Saco un as en la baraja''

[tex]P(B)=\frac{3}{6}=\frac{1}{2}[/tex]

Tres casos favorables a que salga un número par de seis posibles.

[tex]P(C)=\frac{4}{52}[/tex]

Cuatro casos favorables a obtener un as de la baraja de 52 casos posibles.

Ahora escribimos

P ( B ∩ C ) = P(B).P(C)

Por ser B y C dos eventos independientes. Entonces

[tex]P(B)P(C)=(\frac{1}{2})(\frac{4}{52})=\frac{1}{26}[/tex]

Obteniéndose la misma probabilidad ya calculada.

Answer: Brady made 72 shots

Step-by-step explanation:

Number of shots taken on his pop- a- shot basketball hoop=80

Percentage of shots made into the basket=90%

Number of shots made into the basket= 90% x 80

= 90/100 x 80

= 72

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A:

f(x) = -x² + 4x - 10

f(2) = -(2)² + 4(2) - 10

f(2) = -4 + 8 - 10

f(2) = 4 - 10

f(2) = -6

Part B:

g(x) = 5x + 1

g(6) = 5(6) + 1

g(6) = 30 + 1

g(6) = 31

Part C:

f(x) = -x² + 4x - 10

f(-1) = -(-1)² + 4(-1) - 10

f(-1) = -1 - 4 - 10

f(-1) = -5 - 10

f(-1) = -15

Part D:

g(x) = 5x + 1

16 = 5x + 1

15 = 5x

3 = x

x = 3