The rare tweety-birds are decreasing at a rate proportional to the
amount present. On January 1st there are 10,000 tweety-birds.
Fifteen days later, there are only 9,000.
(Problem la, 3 points)
Write a formula for the total amount of birds.

Answer:

31

Step-by-step explanation:

Let x and (x + 1) be the page numbers Josiah can see

Hint 1: x(x + 1) = 930

⇒ x² + x = 930

⇒ x² + x - 930 = 0

Using quadratic formula,

\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)

a = 1, b = 1 and c = -930

\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)

\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)

Sice x is a page number, it cannot be negative

⇒ x = 30 and

x + 1 = 31

The two pages Josiah can see are pg.30 and pg.31

Hint 2: The page he is reading is an odd number

Out of the pages 30 and 31, 31 is an odd number

Thereofre, Josiah is reading page 31

The pairs of events that are disjoint and cannot occur at the same time are:

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time.

For example, the results of a single coin flip, which can result in either heads or tails but not both is a disjoint event since both head and tail cannot appear.

Considering the events given:

Event A: Spin an odd number

Event B: Spin a number greater than 5

Event C: Spin a 4

Event D: Spin a multiple of 2

Event A and Event C are disjoint because one cannot spin an odd number and a 4 since it is an even number.

Event A and Event D are disjoint because one cannot spin an odd number and a multople of 2 since it will an even number.

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Answer:

Step-by-step explanation:

7. y=0.25x

8. No, the graph is a positive slope. Saying y=-x implies that there is a negative slope when it is not the case.

9a. y=12x

9b. The equation or graph is proportional relationship if there isn't a change in the graph or equation at all, and it roots back to a consistent ratio. for this one it's 1:12

The person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

To determine how high up the person was shot, we can use the principles of projectile motion and the dimensions of the blood drop. Since we have the horizontal distance and the dimensions of the blood drop, we can assume that the drop followed a parabolic trajectory.

First, let's convert the distance from feet to meters for consistency. 5.1 feet is approximately 1.554 meters. Now, we need to calculate the time of flight. Since there is no information about the drop's initial velocity or angle, we cannot calculate the exact time. However, we can estimate it by assuming a reasonable range of velocities.

Let's assume the drop was traveling between 5 and 20 meters per second. With a distance of 1.554 meters, the estimated time of flight would be between 0.0777 and 0.311 seconds.

Next, we need to calculate the vertical displacement. We have the dimensions of the blood drop, with a width of 0.8 mm and a length of 2.1 mm. Assuming the drop maintained a spherical shape while in motion, we can take the average of the width and length to find the diameter. So, the diameter is approximately 1.45 mm, which is 0.00145 meters.

Using the estimated time of flight, we can calculate the vertical displacement using the formula:

Vertical displacement = (1/2) * g * t^2

where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the estimated values, the vertical displacement ranges from 0.0038 to 0.0301 meters (3.8 to 30.1 mm).

Therefore, based on the given information, the person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

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Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

The standard form is y= 1/2x+ 4.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

(2,5) and (-4,2)

So, slope

= (2- 5)/ ( -4 - 2)

= -3 / (-6)

= 1/2

and, using slope- intercept form

y- 5 = 1/2( x - 2)

y-5 = 1/2x -1

y= 1/2x + 4

Hence, the standard form is y= 1/2x+ 4.

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Answer:

(-7,0) and (-5,0)

Step-by-step explanation

1. 0= (x + 7)

  -7        -7

    -7=x

(-7,0)

2. 0= (x + 5)

    -5         -5

      -5=x

(-5,0)

Answer:

yes

Step-by-step explanation:

yes but not a postitive one

Answer:

i think so yeah

Step-by-step explanation:

The equation of the line in slope-intercept form is y = (3/5)x + 2. This form allows us to easily identify the slope and y-intercept of the line and to graph it on a coordinate plane.

To write the equation of a line in slope-intercept form, we use the formula:y = mx + b

where:

- y represents the dependent variable (the vertical axis)

- x represents the independent variable (the horizontal axis)

- m represents the slope of the line

- b represents the y-intercept, the point where the line intersects the y-axis.

In this case, we are given the slope as 3/5 and the y-intercept as 2. Plugging these values into the formula, we get:

y = (3/5)x + 2

This equation represents a line with a slope of 3/5, indicating that for every 5 units we move horizontally (along the x-axis), the line moves 3 units vertically (along the y-axis). The y-intercept of 2 tells us that the line intersects the y-axis at the point (0, 2).

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Answer:

$1,657.82

Step-by-step explanation:

435.20 + 510.20 + 345.12 + 142 + 225.30 = total checking balance

1,657.82

Answer:

14.4 units

Step-by-step explanation:

In Trigonometry

\(\cos \theta =\frac{Adjacent}{Hypotenuse}\\\)

In Triangle DEF,

\(\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).\)

Answer:

add the number on the bar graph to get the answer so add all of the charts numbers together

Step-by-step explanation:

Answer:

RANGE: y greater than or equal to -5 (b)

Graph the function

Attached

Then

We know

Vertex form of parabola

vertex:-

Range:-

Answer:

The linear equation relating price to demand is Q=-0.5*P + 30

Step-by-step explanation:

The demand for a good is the quantity of that good that the demanders are willing to purchase at a given price.

Then, the Demand Curve relates the quantity that a consumer would be willing to buy as a function of price.

You seek to determine the linear equation that relates the price to the demand Q = m * P + b where Q is the quantity demanded at a price P, and compared with the equation of the straight line y = mx + b, m is the slope and b is the ordinate to the origin.

On a line of the form y = m * x + b, the value of m, having two points, is calculated by:

\(m=\frac{y2-y1}{x2-x1}\)

And the ordinate to the origin b is calculated, taking the value of m, replacing any of the two points (replacing any of the two because it must give the same value of b) in the expression y = m * x + b and solving its value.

In the case of Q=m*P+b, the value of m, having two points, is calculated by:

\(m=\frac{Q2-Q1}{P2-P1}\)

Being:

and replacing:

\(m=\frac{10-5}{40-50}\)

you get:

m= -0.5

So, being Q=-0.5*P+b,  b is calculated by:

5= -0.5*50 + b → 5= -25 + b → 5+25= b → b= 30

10= -0.5*40 + b → 10= -20 + b → 10+20= b → b= 30

Then, the linear equation relating price to demand is Q=-0.5*P + 30

Elena can make 20/3 cups of purple paint

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

WE are given that Elena makes her favorite shade of purple paint by mixing 3 cups of blue paint, 1 1/2 cups of red paint, and 1/2 cup of white paint.

Since Elena has 2/3 cup of white paint. then;

1 1/2 cups of red paint (1 1/2=1.5)

1/2 cup of white paint (1/2=0.5)

Then the ratio is 3:1.5:0.5

Means every 0.5 cups of white paint Elena makes 5 cups of purple paint (3+1.5+0.5)

Let x the number of cups of purple paint

5/ 0.5 = x / (2/5)

x = 20/3 cups of purple paint

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9514 1404 393

Answer:

  A, C

Step-by-step explanation:

You know that the product (-1)×(-1) = 1. This is true for any number of minus signs. The end result is that a product or quotient is ...

This means expressions with an odd number of minus signs will not be equivalent to the given value.

Equivalent values are ...

  -(1/(-8))

  (-1)/(-8)

At x =6 the function has a positive slope.

A function is a mathematical expression, rule, or law that describes the relationship between an independent variable and a dependent variable. At x = 2 and x = 6, the function y(x) is zero, and it has a value of 1 for all other values of x. the dependent variable. Functions are essential for building physical relationships in both math and science.

A function, which generates one output from a single input, is an illustration of a rule. origin of the image. An illustration of this is Y=X2.

But

At x = 2, the function starts to decline and has a negative slope. negative derivative

while

At x = 6, the function increases with a positive slope, producing a positive derivative.

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The value of the S & P 500 before the open on June 22nd, 2010 is 1,113.20 points.

The percent change points is -1.61%/

The value of the S & P 500 before the open would be higher than the value at the close of June 22nd, 2010. This was because the index declined over the day.

Value before the open of June 22nd, 2010 = value at the close + change

17.89 + 1095.31 = 1,113.20 points

Percentage change = (change in points / points before open) x 100

(-17.89 /1,113.20) x 100 = -1.61%

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Answer:

8

Step-by-step explanation:

Ashley is going to use 12 bags of flour each week. 12x8 = 96. This means that it will take 8 weeks to use 96 bags of flour.

Answer:

It would take her 8 weeks.

Step-by-step explanation:

144 / 12 = 12

12 x 8 = 96

therefore, it would be 8 weeks.

(to find the 8, just use process of elimination for example, I just kept multiplying different numbers until I ended up with 96.)

Step-by-step explanation:

35% of 19.99 is 6.99. so subtract 6.99 from 19.99

19.99-6.99= 13.00

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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The equation of the parabola is\((y + 6)^2 = 4(x - 13)\), where the vertex is (13, -6) and the distance between the directrix and focus is 14.

To determine the equation of the parabola, we need to use the standard form for a parabola with a horizontal axis:

\((x - h)^2 = 4p(y - k)\)

Where (h, k) represents the vertex of the parabola, and p is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given that the parabola opens to the right, the vertex will be on the left side. Let's assume the vertex is (h, k).

We know that the focus of the parabola is at (13, -6), so the distance from the vertex to the focus is p = 13 - h.

We are also given that the focal diameter is 28, which means the distance between the directrix and the focus is twice the distance from the vertex to the focus.

Therefore, the distance from the vertex to the directrix is d = 28/2 = 14.

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Discriminant and The real roots are exits only for D≥0.

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

Discriminant D = \(\sqrt{4ac - b^{2} }\)

D = 0 (The roots are equal and Real)

D > 0 (The roots are unequal, Real and Rational)

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Answer:

Step-by-step explanation:

The distributive property tells us that the term in the inside the parentheses will by multiply by the term on the outside of the parentheses first.  Example:

3(x + 5) means that (x + 5) + (x + 5) + (x + 5) = 3x + 15

So 7(x + 5) - x = 42 ; without the distributive property you would have to write what is inside the parentheses seven times then complete solving the problem

7( x + 5) -x = 42

(x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) + (x + 5) - x = 42   by definition

(x + x + x + x + x + x + x) + (5 + 5 + 5 + 5 + 5 + 5 +5) -x = 42  (x + 5) Associative and Commutative

7x + 35 - x = 42      Addition

6x + 35 = 42           Associative and Commutative

6x = 7                     Subtraction

x =7/6                     Division

Now with the Distributive property

7(x + 5) - x = 42

7·x + 7 · 5 - x = 42        Distributive property

7x + 35 - x = 42           Multiplication

6x + 35 = 42                Associative and Commutative

6x =  7                          Subtraction

x = 7/6                          Division      

Answer:

2/14, 4/28, 5/35, 7/49

Answer:

it is 5/35 and 4/28 , 2.14, and 7/49

Step-by-step explanation:

Hopes this helps you out

have a nice day

Answer:

x = 6

Step-by-step explanation:

\(\frac{x}{1.5} =4\\\\\)

We can multiply both sides by 1.5 to isolate x

\(x=4*1.5\\x=6\)

Answer:

x = 6

Step-by-step explanation:

x / 1.5 = 4

x = 1.5 x 4

x = 6

Hope that helps!