Please help me with these three questions. Thank you!

Answer:

[tex]\frac{2}{3}[/tex]

Step by Step Explanation:

Convert any mixed numbers to fractions.

Reduce fractions where possible.

Then your initial equation becomes:

[tex]\frac{143}{120}[/tex] - [tex]\frac{21}{40}[/tex]

Applying the fractions formula for subtraction,

= (140 × 40) - (21 × 120)

          120 × 40

= [tex]\frac{5720 - 2520}{4800}[/tex]

= [tex]\frac{3200}{4800}[/tex]

Simplifying [tex]\frac{3200}{4800}[/tex], the answer is [tex]\frac{2}{3}[/tex].

Erin uses sugar at a faster rate than Lucia. This can be seen by comparing the equation for Lucia's cups of tea (y = 10x) to Erin's cups of tea (6, 8, 10, 4).

An equation is a statement that expresses the equality of two values. It consists of an expression containing variables, constants, and operators, and is used to solve mathematical problems. Equations are used to describe the relationships between different variables and can be used to solve for the unknown value of one of those variables. As the number of cups increases, the amount of sugar used by Erin increases at a faster rate than the amount of sugar used by Lucia.

For example, for 6 cups of tea, Erin uses 8 pounds of sugar, while Lucia uses 10 pounds of sugar. For 12 cups of tea, Erin uses 10 pounds of sugar, while Lucia uses 20 pounds of sugar.

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Using time value of money tables the following are -

(a) The future value of $450 six years from now at 7 percent is $675.33.

(b) The future value of $900 saved each year for 10 years at 8 percent is $13037.91.

(c) The amount a person would have to deposit today (present value) at an interest rate of 6 percent to have $1,000 five years from now is $747.26.

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent is $8691.93.

What in annuity?

An annuity is a contract that you have with an insurance provider that calls for regular payments to be made by the insurer to you, either now or in the future.

(a) The future value of $450 six years from now at 7 percent.

FV= PV × (1 + r)n

FV= $450 × (1 + 7%)6

FV= $450 × (1.07)6

FV= $450 × 1.50073

FV= $675.33

(b) The future value of $900 saved each year for 10 years at 8 percent.

This is annuity as $900 is saved each year

Formula :: FV = PMT * (((1 + r%)n - 1) / r%)

FV = $900 × (((1 + 8%)10 - 1) / 8%)

FV= $900 × 14.4865624

FV= $13037.91

(c) The amount a person would have to deposit today (present value) at a 6 percent interest rate to have $1,000 five years from now.

PV= FV / (1 + r)n

PV= $1000 / (1 + 6%)5

PV= $1000 / 1.3382255

PV=$747.26

(d) The amount a person would have to deposit today to be able to take out $600 a year for 10 years from an account earning 8 percent.

Annuity value = $600

FV= Annuity value × Annuity factor(10%,8 year)

= $600 × (((1 + 8%)10 - 1) / 8%)

= $600 × 14.4865624

= $8691.93

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Answer:

yes

Step-by-step explanation:

Use the vertical line test to determine whether or not a graph represents a function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. If the vertical line touches the graph at more than one point, then the graph is not a function.

So if you plug in the following values for x & y, you'll get a curve crossing the Y axis at 0,0

-1,-1

-2,-2

-3,-3

0,0

1,1

2,2

3,3

Prove of that if the lengths of two sides of a triangle are a and b, respectively, then the lengths of the corresponding altitudes to those sides are in the ratio b.

A triangle is a three by three-sided polygon having three angles and three sides. It is one of the most fundamental and basic shapes in geometry and is used in many other fields of physical science. Triangles are also utilized in architecture and other areas of design and come in a variety of shapes.

Let, a triangle Δ ABC be given, and let its sides be BC = a and AC = b

(figure is given below)

Let, AM and BN are altitudes of corresponding sides of traingle Δ ABC.

We know that the altitude of a triangle is the perpendicular drawn from the vertex of the triangle to the opposite side.

Notice two right-triangles triangles Δ AMC and Δ BNC

We can conclude that the pairs of congruent angles are:

Δ AMC ≅ Δ BNC ≅ 90°

∠ACM ≅ ∠BCN          (common angle)

So, Δ AMC ≈ Δ BNC by the Angle-Angle Similarity Theorem

The triangles are similar and therefore their corresponding angles are congruent:

AM/BN = AC /BC = a/b

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Answer:

56.57 km/h.

Step-by-step explanation:

Distance traveled:

First, we need to convert the time into hours to have the same unit. 1 hour 30 minutes is equivalent to 1.5 hours.

The total time the van traveled is 2 hours + 1.5 hours = 3.5 hours.

The distance traveled during the first 2 hours is 36 km/h * 2 hours = 72 km.

The distance traveled during the next 1.5 hours is 84 km/h * 1.5 hours = 126 km.

The total distance traveled is 72 km + 126 km = 198 km.

Average speed over the whole journey:

The average speed is the total distance traveled divided by the total time traveled.

Average speed = Total distance traveled / Total time traveled = 198 km / 3.5 hours = 56.57 km/h.

Answer:

56.6km/hr

Step-by-step explanation:

2 hours with a speed of 36km/hr is with a distance of (36×2) = 72km

1.5 hours with a speed of 84km/hr = 126km

Total distance = 72+126 = 198km

Average speed = 198/ total time taken = 198/3.5 = 56.6km/hr

The positive number we're looking for is 5/16.

What is the Equation?

An equation is a mathematical statement that asserts the equality of two expressions.

Let's call the positive number we're looking for x. Then, the problem can be expressed as two equations:

[tex]12x^2 = 4x + 5x^2 = (4/12)x + 5/12\\\x^2 = (1/3)x + 5/12\\\\x^2 - (1/3)x = 5/12\\(4/3)x = 5/12\\x = 5/12 * (3/4)\\x = 5/16[/tex]

Hence, the positive number we're looking for is 5/16.

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The positive number we're looking for is 5/16.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, the equation 6x + 5 = 20 consists of the two equations 6x + 5 and 20, which are separated by the 'equal' sign.

A mathematical statement that claims the equivalence of two expressions is known as an equation.

Let's call the positive number we're looking for x.

Then, the problem can be expressed as two equations:

12x² = 4x + 5x² = (4/12) x + (5/12)

x² = (1/3) x + (5/12)

x² - (1/3) x = (5/12)

(4/3) x = (5/12)

x = (5/12) × (3/4)

x = 5/16

Hence, the positive number we're looking for is 5/16.

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The expressions are solved and answered below.

Given are the expressions as shown in the image.

{ 1 } -

2[tex]$\frac{5}{6}[/tex] - 2[tex]$\frac{1}{5}[/tex]

17/6 - 11/5

17/6 - (11 x 1.2/5 x 1.2)

17/6 - 13.2/6

3.8/6

38/60

19/30

{ 2 } -

3[tex]$\frac{5}{8}[/tex] + 7/3

29/8 + 7/3

(29 x 3)/(8 x 3) + (7 x 8)/(3 x 8)

87/24 + 56/24

143/24

Similarly the remaining expressions can be evaluated.

Therefore, the expressions are solved and answered above.

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{Question in english -

Please help urgently with all the answers}

Answer: B

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The sum of y and 3 means addition, but twice means to multiply the sum of y and 3. So, the answer would be 2(y+3).

The volume of the trapezoidal prism shown is 168 in³

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The volume of the figure is the product of its base area and height. Hence:

Volume = area of base * height

The base is a trapezoid with parallel sides 3 in and 9 in, hence:

Area of base = 3 in * 9 in = 24 in²

Volume = area of base * height = 24 in² * 7 in = 168 in³

The volume of the figure is 168 in³

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Therefore , X is a continuous random variable, the probability of getting exactly X = 80 is zero. We can only find the probability of a range of values, such as P(79.5 < X < 80.5).

Calculating the likelihood that a statement is true or that a particular event will take place is the centre of probability theory, a branch of mathematics. Any number between  range 0 and 1, where 1 is usually used to express confidence as well as 0 is routinely used it to convey possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular occurrence will occur.

Here,

For P(78 < X < 127):

We first convert the values to standard scores:

Z1 = (78 - 72) / 22 = 0.27

Z2 = (127 - 72) / 22 = 2.50

Using a standard normal distribution table or a calculator, we find the area to the left of Z1 and the area to the left of Z2:

P(Z < 0.27) = 0.6064

P(Z < 2.50) = 0.9938

Then we subtract the smaller area from the larger area to find the area between Z1 and Z2:

P(0.27 < Z < 2.50) = 0.9938 - 0.6064 = 0.3874

So the probability that 78 < X < 127 is approximately 0.3874.

For P(60 < X < 90):

We first convert the values to standard scores:

Z1 = (60 - 72) / 22 = -0.55

Z2 = (90 - 72) / 22 = 0.82

Using a standard normal distribution table or a calculator, we find the area to the left of Z1 and the area to the left of Z2:

P(Z < -0.55) = 0.2912

P(Z < 0.82) = 0.7939

Then we subtract the smaller area from the larger area to find the area between Z1 and Z2:

P(-0.55 < Z < 0.82) = 0.7939 - 0.2912 = 0.5027

So the probability that 60 < X < 90 is approximately 0.5027.

For P(X = 80):

Since X is a continuous random variable, the probability of getting exactly X = 80 is zero. We can only find the probability of a range of values, such as P(79.5 < X < 80.5).

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The complete question is " X Is A Normally Distributed Random Variable With Mean 72 And Standard Deviation 22. Use Calculator To Find The Probability Indicated. P(78&Lt;X&Lt;127) P(60&Lt;X&Lt;90) P(X=80)

X is a normally distributed random variable with mean 72 and standard deviation 22. Use calculator to find the probability indicated.

P(78<X<127)

P(60<X<90)

P(X=80)"

The quadratic regression equation is y = 2x^2 + 16x - 0.75

From the question, we have the following parameters that can be used in our computation:

x 0 2 4 6 8

f(x) 2 31 54 71 82

Using a graphing calculator, we have the following summary:

The equation is represented as

y = ax^2 + bx + c

So,, we have

y = 2x^2 + 16x - 0.75

Hence, the equation is y = 2x^2 + 16x - 0.75

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The function f(x-3) is simplified to have x² - 6x + 13

Given the following quadratic function below

f(x) = x² + 4

We need to determine the value of the function f(x-3). Replace x with x -3 in f(x) to have:

f(x-3) = (x-3)² + 4

Expand the equivalent expression

f(x-3) = x² - 6x + 9 + 4

f(x-3) = x² - 6x + 13

Hence the simplified form of the expression is x² - 6x + 13

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Answer:

9800

Step-by-step explanation:

The median number is the middle term (or the average of the two middle terms, if there are an even number of terms) when sorted in an ascending order.

Sorting in ascending order:

8900, 9600, 9800, 12000, 15500

Hence, 9800 is the mean.

The required terminal point is Q(0,2).

By using the symbol |v|, the magnitude of a vector formula can be utilized to determine the length for a given vector (let's say v). In essence, this measurement represents the separation between the vector's starting and ending points.

For a vector v with endpoints at [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex], its magnitude is

[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We are given the following in the question:

Initial point of vector, P(1,0)

The terminal point Q has coordinates in the following format because it is on the y-axis:

Q(0,y)

The magnitude of the vector is [tex]\sqrt{5}[/tex].

Magnitude is given by,

[tex]v=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \sqrt{5} =\sqrt{(0-1)^2+(y-0)^2} \\5=1+y^2\\y^2=4\\y=_-^+2[/tex]

But because the terminal position is higher than the starting point,

y is greater than 0.

Therefore,

y=2

Thus, the terminal point is Q(0,2)

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Answer:

Step-by-step explanation:

The simple interest can be calculated as follows:

I = P * r * t

Where:

I = interest

P = principal amount (3000)

r = interest rate (0.10)

t = time in years (5)

So,

I = 3000 * 0.10 * 5

I = 1500

The final balance would be:

P + I = 3000 + 1500

P + I = 4500

The final balance, rounded to the nearest cent, is $4500.

Answer:

No solution.

Step-by-step explanation:

First, we can simplify both sides of the equation by squaring them. This gives:

(√x+12)² = (√x + 2)²

Expanding both sides, we get:

x + 24√x + 144 = x + 4√x + 4

Moving all the terms to one side, we get:

20√x + 140 = 0

Subtracting 140 from both sides, we get:

20√x = -140

Dividing both sides by 20, we get:

√x = -7

However, this is not a valid solution for x, since the square root of a number cannot be negative. Therefore, there is no solution for x that satisfies the given equation.

The area of the composite figure is equal to 26 square units.

Herein we find a composite figure formed by a parallelogram and a rectangle, whose area formula is described below:

Parallelogram / Rectangle

A = b · h

Where:

Now we determine the area of the composite figure:

Rectangle

b = √(3² + 1²)

b = √10

h = √(2² + 6²)

h = 2√10

A = √10 · 2√10

A = 20

Parallelogram

A = 6 · 1

A = 6

Composite figure

A = 20 + 6

A = 26

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Answer:

I think the coefficient is 1/3.

Because (x, y) to (1/3x, 1/3y)

Note that given the question which is related to Dimensional Analysis, Sam's Club package is more expensive. This means WalMarts prices are a better option.

Dimensional analysis is the examination of the connection between physical quantities using dimensions and measuring units.

To determine the better option, we simply derive the cost per sheet as follows:

For Sam's Club we have:

26.99/ (36 x 248)

= $0.0030230735/ Sheet

For Walmart, we have:

5.99/ (8 * 350)

= $0.0021392857/ Sheet

So based the above, it clear that the Sam's Club package is more expensive because:

$0.0021392857 < $0.0030230735

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Full Question:

A particular brand of toilet paper is offered at two stores in different kinds of packaging. To practice using rates, for each package determine both the number of sheets per dollar and the cost in dollars per sheet. Then determine which package is the better buy.

Sam's Club sells a 36-pack of toilet paper with 248 sheets per roll for $26.99

Walmart sells the toilet paper for $5.99 in an 8-pack with 350 sheets per roll. The Sam's Club package: ?

The exponential model that represents the number of cell phone subscribers y (in billions), t years after 2014 is; F = 233 ( 1.06)^t

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

The general formula for an exponential growth is:

F = P( 1 + i ) ^t

where F is the future amount in t years

P is the present amount

i is the fraction of increase per time

t is the time

For the increase cellphone subscriber

P = 233

i = 0.06

Therefore,

F = 233 ( 1 + 0.06)^t

F = 233 ( 1.06)^t

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The factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

The factorization of algebraic expressions is the process of identifying two or more expressions whose product is the given expression. A factor is a number that evenly divides the inputted number or expression.

Algebraic expressions can be factored by identifying two or more expressions whose product is the provided expression, which is known as finding the factors of the given expression.

Given that:

9x^5+x^2

Factor x^2 out of 9x^5.

= x^2 (9x^3 ) + x^2

= x^2 (9x^3 + 1)

Therefore, we can conclude that the factorization of  9x^5 + x^2 is  x^2 (9x^3 + 1).

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The value of a must be equal to (k + 2), and then the equation is only true if k = 6, then a = 8.

We want the equation:

(k + 2)x + 3k = ax + 18

To be true for all values of x, then we must have the same thing in both sides of our equation.

Now we wod want the dependence on x to dissapear, then:

(k + 2)x = ax

(k + 2) = a

That must be value of a, and then the equation becomes:

k*x + 2x + 3k = (k+ 2)x + 18

3k = 18

This is only true if k = 6, then:

k + 2 = a

6 + 2 = a

a = 8

That must the value of a.

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Answer:

A) The verb "waddled" most accurately and vividly describes the action in this situation, as "waddle" is a verb used to describe a slow and awkward gait often associated with a heavily pregnant woman. This verb conveys the idea of the woman's awkward and unsteady movement, making it the most accurate and vivid description of her actions.

The only restriction on the domain is that x can't be zero.

Here we have the following equation:

(7/5)*x - 8/5 = 3/x

And we want to see if there is a value of x that caueses a problem here.

We can see that on the right side, we have an x on the denominator. And remember that the division by zero is undefined, then we know that:

x ≠ 0

That is the only restriction, because x = 0 can't be on the domain.

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Answer:

Step-by-step explanation:

2:3 / 8/4

firt step you need factorize

2/3 /2

because 8/4 =2;

2/3:2/1

we have formula

2/3*1/2

answer is :2/6 => 2:2/6:2 => 1/3

The value of cot θ is [tex]\frac{15}{4\sqrt{9} }[/tex].

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given that, the circle is unit circle.

In polar form, x = r cos(θ)

Since it is unit circle, r = 1

x = Cos (θ)

Cos (θ) = 15/23

Sin (θ) = [tex]\sqrt{1 - (15/23)^2}[/tex]

           = [tex]\sqrt{\frac{304}{529} }[/tex]

           = [tex]\sqrt{\frac{19*16}{23^2} }[/tex]

           = [tex]\frac{4\sqrt{19} }{23}[/tex]

Cot (θ) = cos (θ) / sin (θ)

           = (15/23) /  ([tex]\frac{4\sqrt{19} }{23}[/tex])

           = [tex]\frac{15}{4\sqrt{9} }[/tex]

Hence the value of cot (θ) is [tex]\frac{15}{4\sqrt{9} }[/tex].

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Answer:First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7

Step-by-step explanation: First, use the positive value of the

±

to find the first solution.

x

=

7

Next, use the negative value of the

±

to find the second solution.

x

=

−

7

The complete solution is the result of both the positive and negative portions of the solution.

x

=

7

,

−

7