Question 9 of 10

Mark all the statements that are true.
A. This graph is not a function because the value x = 3 is assigned to
more than one y-value.
B. The equation of this line is x = 3.
C. This graph is a function whose range is the set (3).
D. This graph is a function because the value of x is the same for
every value of y.
E. This graph is a function whose domain is the set (3).

Answer: (-12,-1)

Step-by-step explanation: Point A=-1 and Point B=-12

:)

a) The decay formula for the mass of Strontium-90 is m(t) = 75 · [tex]e^{-t /40.395}[/tex].

b) The sample of Strontium-90 has a mass of approximately 13.258 miligrams after 70 days.

c) The sample of Strontium-90 takes a time of approximately 146.405 days.

The mass of Strontium-90 decays exponentially in time, whose model is described below:

m(t) = m' · [tex]e^{- t /\tau}[/tex]

Where:

And the time constant can be estimated by the following formula:

τ = t' / ㏑ 2

Where t' is the half-life of the isotope.

a) If we know that m' = 75 mg and t' = 28 d, then the expression for the mass of the sample is:

τ = 28 / ㏑ 2

τ ≈ 40.395 d

m(t) = 75 · [tex]e^{-t /40.395}[/tex]

b) And the mass of the isotope after 70 days is:

m(70) = 75 · [tex]e^{- 70 / 40.395}[/tex]

m(70) ≈ 13.258 mg

The current mass is approximately 13.258 miligrams.

c) If we know that m(t) = 75 · [tex]e^{-t /40.395}[/tex] and m(t) = 2 mg, then the time needed for the decay is:

75 · [tex]e^{-t /40.395}[/tex] = 2

[tex]e^{-t /40.395}[/tex] = 2 / 75

- t / 40.395 = ㏑ (2 / 75)

t = - 40.395 · ㏑ (2 / 75)

t ≈ 146.405 d

The needed time is approximately 146.405 days.

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Answer: It is positive and increasing

Step-by-step explanation:

From point e to f it is clearly going up, and is part of the positive side of the graph.

Answer:

67

Step-by-step explanation:

33,500/500 = 67

To check our work:

67 x 500 = 33,500

Answer:

67 percentStep-by-step explanation:

Answer:

12

Step-by-step explanation:

|-10+20| - |-4| + |6|

10 - 4 + 6

12

The probability of people not planning a new degree = [tex]\frac{35}{43}[/tex]  

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

And while solving these type of question we calculate the probability of a particular event.

The survey has 43 million people

Given is 8 million were planning to start a new degree program

Thus the probability of people planning a new degree program = 8 million divided by 43 million

Thus the probability of people not planning a new degree = 1 - [tex]\frac{8 million}{43 million}[/tex]

which is equal to [tex]\frac{35,000,000}{43,000,000}[/tex]

which on solving further will give us:

P ( people not planning a new degree ) = [tex]\frac{35}{43}[/tex]

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The interest rate on the loan is 5.25%.

It should be noted that the formula for calculating the simple interest is given as:

Interest = (Principal × Rate × Time) / 100

In this case,

Interest = 65625

Principal = 125000

Time = 10

Interest = (Principal × Rate × Time) / 100

65625 = (125000 × R × 10)/100

Cross multiply

6562500 = 1250000R

Divide

R = 6562500 / 1250000

R = 5.25

The rate is 5.25%

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The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

From the table:

At x=2,

f'(x) = 4

f(x) = 4x

= d/dx(5*4x - 4x)

= d/dx(20x - 4x)

= d/dx(16x)

= 16

Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.

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Answer: B

Step-by-step explanation: I believe this is correct. The arrows on both run all trough the x-axis, so it would be negative infinity to positive infinity. Then, you go from open circle ( ( ) -3 to closed circle ( } ) 4.

Answer:meh

Step-by-step explanation:good enough

Answer:

Let the girls be x

then, 5:4 = 5x and 4x

,

total stud.=36 so,

5x+4x=36

9x=36

x=36÷9

hence

x=4

now, boys = 5x=5×4=20

girls= 4x=4×4=16

so there are 16 girls

The value for the side of rectangle XZ is equal 14, using the trigonometric ratios of cosine and sine of angles.

The trigonometric ratios concerns the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the triangle WYZ, the cosine of angle Y;

cos(Y) = 21/YZ {adjacent/hypotenuse}

YZ = [21/cos(Y)] {cross multiply}

Considering the triangle XYZ, the cosine of angle Y;

cos(Y) = YZ/28

YZ = 28 × cos(Y)

Therefore,

28cos(Y) = [21/cos(Y)]

cos²(Y) = 21/28 {cross multiply}

cos(Y) = √(21/28) {take the square root of both sides}

cos(Y) = 0.8660

Y = cos^(-1)(0.8660) {cross multiply}

Y = 30°

To get the side XZ, considering the triangle XYZ the sine of 30°;

sin30° = XZ/28 {opposite/hypotenuse}

by cross multiplication

XZ = 28 × sin30°

XZ = 14

Therefore, by proper application of the trigonometric ratios of cosine and sine of the angle for the given triangle, the side XZ = 14.

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The amount of money that must be deposited today is $749   .

In the question ,

it is given that ,

the amount that is need to be made (A) = $2250

time (t) = 20 years

rate percent (r) = 5.5%  = 0.055

let the amount that must be deposited today be P .

The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .

A = P×[tex]e^{r\times t}[/tex]

Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]

2250 = P × [tex]e^{1.1}[/tex]

P = 2250/ [tex]e^{1.1}[/tex]

P = 748.9599

P ≈ 749

Therefore , The amount of money that must be deposited today is $749   .

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equation if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68 of his share hope this helped there a lot of extra information in the question

An equation is written as  expressions, connected by an equals signal ("=").[2] The expressions on the two facets of the equals signal are referred to as the "left-hand side" and "right-hand side" of the equation. Very regularly the right-hand side of an equation is assumed to be zero. Assuming this doesn't lessen the generality, as this can be realized through subtracting the right-hand side from each facets.

The most common sort of equation is a polynomial equation (commonly known as also an algebraic equation) wherein the 2 facets are polynomials. the edges of a polynomial equation incorporate one or greater terms

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Answer:

[tex] \binom{?}{?} [/tex]

Step-by-step explanation:

$40 Pam use type diagram

$45. bro

Answer: The answer is 5.

Step-by-step explanation:

4.5  ÷  0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10

Convert decimal 0.9 to fraction 9/10

Divide 450/90

Simply 450/90 = 5

Answer:

5

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

Had this question too ;)

The annual rainfall in 2016 is 336 mm.

Let the annual rainfall in 2016 be 100x mm.

Now it is given that rainfall in 2017 is 25% more than rainfall in 2016.

So. rainfall in 2017 is = 100x + 100x*(25/100) = 100x+25x = 125x mm

Also given that the amount of rainfall in 2017 = 420 mm.

According to question the suitable equation is,

125x = 420

x = 420/125

x = 3.36

Hence the rainfall in 2016 is = 100x = 100*3.36 = 336 mm.

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Answer:

Step-by-step explanation:

so this is a combined work problem,   both of the people are moving towards each other.  They are both doing some of the work to move towards each other.  

one is moving at 50 , the other at 60  , directly towards each other.  Now change the problem to one moving at 50+60 =110  at a destination 200 away

now you can solve this pretty easily , i'm guessing

200/110 = 1.818181

or approx.  1.82 hours

got it?

The change in the volume of water after 1 minute is 1 5/32 gallons.

Given that the volume of water in the rain barrel decreased by 4 5/8 gallons in 4 minutes.

The change after 1 minute will be:

= Total volume of water / Number of minutes

= 4 5/8 ÷ 4

= 37/8 ÷ 4

= 37/8 × 1/4

= 37 / 32

= 1 5/32

The change is 1 5/32 gallons.

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Answer:

x=10

y=5

Step-by-step explanation:

you have to find the length

The image of the end points X(-3 , 1) and Y(4 , -5) is

X'' = (-1 , 3) and Y'' = (5 , -4).

Given, a line segment with end points X(-3 , 1) and Y(4 , -5)

We have to find the image of the points after the given composition,

Reflection in the line y = x.

Rotation 180° about the origin.

After the reflection the image of the points X and Y be,

X' = (1 , -3) and Y' = (-5 , 4)

Now, after the rotation of the points of 180° about the origin be,

X'' = (-1 , 3) and Y'' = (5 , -4)

Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is

X'' = (-1 , 3) and Y'' = (5 , -4).

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Answer:

Step-by-step explanation:

f(0) = 4

f(x)=0   when x = 0.75

f(x) =5  when x =3

A{ x ∈ R ║ 3≤x}

Answer:

315

Step-by-step explanation:

2/180=3.5/x

2x=630

x=315

Step-by-step explanation:

x + y = 42

5x + 9y = 190

x = 42 - y

5(42 - y) + 9y = 190

210 - 5y + 9y = 190

210 + 4y = 190

4y = -20

y = -5

x = 42 - y = 42 - -5 = 42 + 5 = 47

63%

First, we have to take 20.00 - 7.40 which gets us 12.60.

Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.

We do 12.60 x 100 which makes 1260.

Lastly, we divide that by the 20.00 which gets us 63.

So, Julie has 63% of her money left.

I hope this helped!!!

The number of values of x to be excluded is 2.

To find out the values of x that must be excluded in the expression

(x+9)(x-5) as follows:

The value of x is 2.

We are given to find the number of value of x that must be excluded in the expression  below:

E = (x+9)(x-5)

We have to exclude those values of x for which the expression E becomes undefined.

Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.

That is,

(x+9)(x-5) = 0

= x+9 = 0         x-5 = 0

= x = -9            x = 5

Therefore, we need to exclude the values x = -9  and  x =5.

So, there are two values of x to be excluded from the given expression.

Hence the answer, the number of values of x to be excluded is 2.

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The expression 3x+11y cannot be factorized.

What is factorization?

To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.

Here the given expression 3x+11y didn't have any common factors.

The given expression has two variables 3x and 11y and they didn"t have any common terms.

Hence the expression 3x+11y cannot be factored.

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The equation of the line d that is parallel to line c is y = -5x + 4.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, c has an equation y = -5x + 3. Line d is parallel to line c. Therefore, they have the same slopes. Parallel lines have the same slope.

Hence, let's find the equation of line d passing through (2, -6)

Let's find the y-intercept

-6 = -5(2) + b

-6  = -10 + b

b = -6 + 10

b = 4

Therefore, the equation of the line d is y = -5x + 4

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Functions that are symmetric with respect to the x-axis are those with even degree of y, i.e y², y⁴ etc.

Correct choices are:

Answer:

[tex]x=\dfrac{1}{8}y^2[/tex]

[tex]x=-y^2+9[/tex]

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

Therefore, any function that includes the term y² will be symmetric with respect to the x-axis since (-y)² = y².

[tex]\begin{aligned}&\textsf{Given}: \quad& x&=\dfrac{1}{8}y^2\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=\dfrac{1}{8}(-y)^2\\&\textsf{Simplify}: \quad &x&=\dfrac{1}{8}y^2\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.

[tex]\begin{aligned}&\textsf{Given}: \quad& x&=-y^2+9\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=-(-y)^2+9\\&\textsf{Simplify}: \quad &x&=-y^2+9\\\end{aligned}[/tex]

Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.