A mammogram is used to screen women for breast cancer. False positives are tests that incorrectly show a positive result. 85% of positive mammograms are actually false positives. If 1,000 women receive mammograms, and 200 are told there is an abnormal finding, how many women are likely to actually have breast cancer?

Nancy can buy maximum 8 video games.

Steps to solve inequality:

The inequality will not change if the coefficient is positive.

The inequality will be the other way around if the coefficient is negative.

If Nancy wants to keep at least $120 in her account and at present, she is having $240

So, she can spend = 240-120= $120

And, one video game price= $15

Let us consider she can buy maximum 'X' games

15×X=$120

X = 8 units

Hence, she can buy a maximum of 8 video games.

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We want to study the population formula of a given US state according to exponential equation.

a) 23.1 millions.

b) in 2013 - 2014

What is exponential equation?

The exponential function may be a function denoted by f(x)=\exp or e^. Unless otherwise fixed, the term usually refers to the positive-valued operate of a true variable

Main body:

The population state is:

A = 23.1*e^(0.0153*t)

In millions.

Where t represents the number of years after 2000.

a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).

A(0) = 23.1*e^(0.0153*0) = 23.1

The population at year 2000 was 23.1 millions.

b) Now we want to solve:

A(t) = 28.3 = 23.1*e^(0.0153*t)

       28.3/23.1 = e^(0.0153*t)

      1.23 = e^(0.0153*t)

Now we can apply the natural logarithm to both sides:

ln(1.23) = ln( e^(0.0153*t) )

ln(1.23) = 0.0153*t

ln(1.23)/0.0153 = t = 13.5

Hence, 13.5 years after 2000 the population will be 28.3 million.

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Answer:

x = -2

Step-by-step explanation:

hope this will help you

Using law of logarithm and exponent rules, the value of the unknown is 5

logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation. For example, if 102 = 100 then log10 100 = 2.

Logₐ x = n  or   aⁿ = x

Where b is the base of the logarithmic function.

This can be read as “Logarithm of x to the base b is equal to n”.

In this case, we just need to solve for the value of b

4 = logₐ(625)

4 = 1 / log625(a)

multiply both sides by log₆₂₅(x)

log₆₂₅(a) / 4 = 1/4

applying log rules

a = 5

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Answer: Cory can have 6 different schedules

Step-by-step explanation:

Add them all together and divide by fifteen

to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.

[tex]\stackrel{\textit{\LARGE line of reflection}}{(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2})} \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{-2 +4}{1 +1} \implies \cfrac{ 2 }{ 2 } \implies \text{\LARGE 1}[/tex]

now, keeping in mind that perpendicular lines have negative reciprocal slopes, there are three dotted lines, each one of them, hits the line of reflection perpendicularly, so their slope must be

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{1\implies \cfrac{\boxed{1}}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{\boxed{1}}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{\boxed{1}}\implies \text{\LARGE -1}}}[/tex]

The recursive formula for the arithmetic succession will be written as aₙ = 25 - 5n.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The sequence is given below.

20, 15, 10, 5, .....

The first term is 20 and the common difference is given as,

d = 15 - 20

d = - 5

Then the recursive formula given the following sequence is given as,

aₙ = a₁ + (n - 1)d

aₙ = 20 + (n - 1) × (-5)

aₙ = 20 - 5n + 5

aₙ = 25 - 5n

The formula for the arithmetic sequence will be written as aₙ = 25 - 5n.

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Using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate.

The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

So, let's say the car's affordable price is P:

The entire payback is equal to P r/100 T + P.

In this case, P, r = 4.75, and T = 9 years.

$351,00 = P × (4.75/100 × 9 + 1)

$351,00 = P × ( 0.4275 + 1)

$351,00 = P × 1.4275

P = 351,00 / 1.4275

When you use the division operation, we receive:

P = $24588.44

Therefore, using the interest rates formula, we know that an automobile that costs $24588.44 is within our means.

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The equation in slope intercept form of the line that passes through the points (6,1) and (3,3) is y = - 2 / 3 x +5

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

y = mx + b

where

Therefore, the equation in slope-intercept form of the line that passes through the points (6,1) and (3,3) can be represented as follows;

let's find the slope

m = 3 - 1 / 3 - 6

m =  - 2 / 3

Hence, let's find the y-intercept as follows;

using (3, 3)

y = - 2 / 3 (x) + b

3 = - 2 / 3 (3) + b

3 + 2 = b

b = 5

Therefore, the equation of the line is y = - 2 / 3 x +5

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Answer:

y=3x-4

Step-by-step explanation:

-9x+3y=-12

3y=12-9x

y=3x-4

Answer:

C. DIvide both sides by -6 to get 1/9.

Step-by-step explanation:

Answer: The correct answer is D, Lines are skew if and only if they are non-coplanar.

In geometry, lines are said to be skew if they are non-coplanar, meaning they do not lie in the same plane. They also do not intersect.

Option A is incorrect because angles can be supplementary (add up to 180 degrees) even if they do not form a linear pair (meaning they do not share a common vertex and a common side).

Option B is incorrect because Valentine's Day does not always fall in February. It is February 14th, but it could fall on a different month in a different year.

Option C is correct because a number is even if and only if it is divisible by 2. An even number can be divided evenly by 2, while an odd number cannot.

Answer:

Here,

the length=8x

the width =3y-2

We know that,

Area of rectangle=l×b

or, 8x × 3y-2

8x(3y-2)

24xy-16x

Hence, the correct answer is 24xy-16x

Answer: (6,2)

Step-by-step explanation:

(7,5)     (x,2)      m=3     x=?

y=mx+b

y=3x+b   (1)

To find the coefficient b we take the coordinate that belongs to this line (7,5): x=7    y=5

5=3(7)+b

5=21+b

5-21=21+b-21

-16=b

Thus, b=-16

Hence, y=3x-16

To find the x we take the coordinate that belongs to this line (x,2): y=2

2=3x-16

2+16=3x-16+16

18=3x

Divide both parts of the equation by 3:

6=x

Thus, x=6

1) The legs of △ABC are AB and BC.

2) The name of hypotenuse is AC.

3) The legs of △PQR are PR and RQ.

4) The name of hypotenuse is PQ.

5) The legs of △HLM are LH and ML.

6) The name of hypotenuse is MH.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The right angle of △ABC is ∠ABC. Thus AB and BC meet at right angle. Therefore AB and BC are legs of △ABC.

The opposite side of ∠ABC is AC. Therefore the hypotenuse is AC.

The right angle of △PQR is ∠PRQ. Thus PR and RQ meet at right angle. Therefore PR and RQ are legs of △PQR.

The opposite side of ∠PRQ is PQ. Therefore the hypotenuse is PQ.

The right angle of △HLM is ∠HLM. Thus HL and LM meet at right angle. Therefore HL and LM are legs of △HLM.

The opposite side of ∠HLM is MH. Therefore the hypotenuse is MH.

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The graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

What is the graph of the equation?

The graph of an equation is the group of all points on a number line or the coordinate plane that are solutions of an equation (= statement that two amounts are equal).

0 hours- $0

4 hours- $32

8 hours- $64

12 hours- $96

First find the equation of this problem to represent the relationship, which is y = 8x.

Next, you substitute the number of hours into x to get y, which is the amount of money.

Hence, the graph of the relationship between x, the number of hours, and y, the total amount Andrew earns attached below, and the equation represent the relationship y = 8x.

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Answer:

the digit 1 is less than 5, so we round 54.71 down to 54.7.

Step-by-step explanation:

Answer:

The slope is -1

Step-by-step explanation:

To find the slope using two points, you must do this:

(y2-y1) divided by (x2-x1) which is -1-4 divided by 2+3 and the answer will be -5/5 or just simply -1

The required radius of the circle is given as  3.18 m.

Given that,
A circle has a circumference of 20 m. the radius of the circle is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
The perimeter of the circle = 20m
2πr = 20
r = 20/2π
r = 3.18 m

Thus, the required radius of the circle is given as  3.18 m.

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In the given congruent triangle  ΔPHS ≅ ΔCNF,  the values of x, y, and z are 24° , 37/3° , 61/4° respectively

What is a congruent triangle ?

The meaning of congruent in Maths is addressed to those figures and shapes that can be repositioned or flipped to coincide with the other shapes. These shapes can be reflected to coincide with similar shapes.

Two shapes are congruent if they have the same shape and size. We can also say if two shapes are congruent, then the mirror image of one shape is the same as the other.

Two triangles are said to be congruent if their sides have the same length and angles have same measure. Thus, two triangles can be superimposed side to side and angle to angle.

In mathematics, the term "congruent" refers to figures and forms that may be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. If two forms are similar in size and shape, they are congruent. We may also state that if two forms are congruent, then their mirror images are identical .Triangles that line up. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles may be placed side by side and angle by angle on top of one another.

Since both the triangles are congruent this means the side , angles of both the triangles are equal

therefore,

∠ H = ∠ N

∠ S = ∠ C

∠ P = ∠ F

which means,

6x-29° = 115°

6x=144°

x=24°

∠ S  = 180° - ∠ H - 36°

∠ S = 180°-6x+29°-36°

∠ S = 173°-6x

173°-6x=4z-32°

173°-144°+32° = 4z

61/4° = z

3y-1° = 36°

y= 37/3°

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(a) 2.79 seconds after its release the bag will strike the ground.

(b) At a velocity of 73.28 ft/second it will hit the ground.

What is velocity?

We are given that a balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant when the balloon is 80 feet above the ground.

Assume the acceleration of the object is a(t) = −32 feet per second.

(a) For finding the time it will take the bag to strike the ground after its release, we will use the following formula;

[tex]s=u t+\frac{1}{2} a t^2[/tex]

Here, s= distance of the balloon above the ground =-80 feet

[tex]$\mathrm{u}=$[/tex] intital velocity =16 feet per second

[tex]$\mathrm{a}=$[/tex]acceleration of the object =-32 feet per second

[tex]$\mathrm{t}=$[/tex] required time

So, [tex]$s=u t+\frac{1}{2} a t^2$[/tex]

[tex]$$\begin{aligned}& -80=(16 \times t)+\left(\frac{1}{2} \times-32 \times t^2\right) \\& -80=16 t-16 t^2 \\& 16 t^2-16 t-80=0 \\& t^2-t-5=0\end{aligned}$$[/tex]

Now, we will use the quadratic D formula for finding the value of t, i.e;

[tex]t=\frac{-b \pm \sqrt{D}}{2 a}[/tex]

Here, a=1, b=-1, and c=-5

Also, [tex]$\mathrm{D}=b^2-4 a c=(-1)^2-(4 \times 1 \times-5)=21$[/tex]

So, [tex]$t=\frac{-(-1) \pm \sqrt{21}}{2(1)}$[/tex]

[tex]t=\frac{1 \pm \sqrt{21}}{2}[/tex]

We will neglect the negative value of t as time can't be negative, so;

[tex]t=\frac{1+\sqrt{21}}{2}=2.79 \approx 3 \text { seconds. }[/tex]

Hence, after 3 seconds of its release, the bag will strike the ground.

(b) For finding the velocity at which it hit the ground, we will use the formula;

v=u+a t

Here, v= final velocity

So,[tex]$v=16+(-32 \times 2.79)$[/tex]

v=16-89.28=-73.28 feet per second.

Hence, the bag will hit the ground at a velocity of [tex]$-73.28 \mathrm{ft} / \mathrm{second}$[/tex].

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Answer:

0.60

Hope this helps, I believe in you!

Answer: The answer is C 0.60

Step-by-step explanation:

The answer is true, if radius OP intersects chord AC in point B and AB=8 units, BC=8 units.

The length of the line segments from a circle's center to its perimeter is referred to as the radius of a circle or sphere in more contemporary use. Radius has two possible plurals: the traditional English plural radiuses or radii. R or r is the most common radius abbreviation and mathematical variable name. Consequently, the diameter D is equal to double the radius.

Given,

In circle radius OP intersects chord AC in point B.

And AB=8 units, BC=8 units

So, OP is perpendicular to AC.

Due to the fact that OA and OC have equal sides and a base length of AC, OAC forms a triangle (the radius of the circle)

When you trace AC, you discover that O, a line perpendicular to AC, intersects the circle's center.

So, the answer is true.

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The additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

What is quadrilateral ?

A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.

Properties include: There are four vertices . There are four sides . 360° is the total of all interior angles. There are two diagonals in them.

Trapezium is one of the five unique quadrilateral shapes. Parallelogram. Rectangle. Rhombus. Square

These bisectors intersect each other at 90 degrees.

And it means that they are perpendicular.

Since they are perpendicular, we find that there 4 congruent triangles, XY is parallel to WZ, and WX is parallel to YZ.

Additionally, opposite angles are equal.

These two latter findings are the characteristics of the parallelogram.  

Hence, the additional fact that would prove that quadrilateral WXYZ is a parallelogram is '' XY = YZ''.

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Lines with a slope of zero can be thought of as y = 0x + b, which simplifies to just "y = b".

In this case, your equation is y = 16.

If you want to force it explicitly into standard form, you could write it at
   0x + 1y = 16

The surface area of the frustum is 1744 square units

The volume of the pyramid is 2031.33 cube units.

What is a frustum of a pyramid?

By cutting the top of a typical pyramid, the frustum is created, which is a pyramid. Because of this, it is known as a truncated pyramid. The frustum of the pyramid is that portion of a pyramid that is cut through by a plane parallel to its base and lies between the vertex and the base.

a) First, we calculate the height of the frustum.

Let height be H

The base length be L1=24

Base width be W1=12

Top length is L2=14

To width be W2=13

Side height be C=13

Using the formula, H

[tex]H=\sqrt{ C^{2} - \frac{(L1-L2)^{2}}{2}}\\H=\sqrt{ 13^{2} - \frac{(24-14)^{2}}{2}}\\H=\sqrt{ 169 -50}\\H=\sqrt{119} \\H=11[/tex]

Now, the surface area of the frustum is LSA+area of bases of a frustum

Here, P1= perimeter of the base1 of the frustum

P2 is the perimeter of the base 2 of the frustum

[tex]L.S.A=\frac{1}{2} .(P1+P2).L \\=\frac{1}{2} .(72+42).24 \\=\frac{1}{2} .(114).24 \\=1368[/tex]

Now, S1 =area of base1 of frustum =288

S2= area of base 2 of frustum=98

TSA is given by LSA+area of bases of a frustum

=1368+288+98

=1724.

Therefore the surface area is 1724 square units.

b) Volume is given by

[tex]V=\frac{1}{3}.H.(S1+S2+\sqrt{S1S2} )\\ V=\frac{1}{3} . 11.(386+168)\\V=2031.33[/tex]

Therefore the volume is 2031.33 cube units.

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Answer:

thanks.

0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

The system of equations has infinite solutions, actually, any pair (x, y) is a solution.

To solve a system by elimination, we just need to add/subtract the equations in such a way that we can remove one of the variables.

Here the system of equations is:

-2x-3y = -9

-2x-3y = -9

If we subtract the two equations we will get:

(-2x-3y) - (-2x-3y) = -9 - (-9)

0 = 0

This is a trivial equation, that happens because both equations of the system are the same one.

So the system is true for all real values of x and y.

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