Two different antibiotics can be used to treat an infection. Treatment with antibiotic 1 is known to be successful 80% of the time. This treatment costs $80. Antibiotic 2 is successful 90% of the time and costs $100. The two treatment plans are: Plan A: Treat with antibiotic 1. If not effective, treat with antibiotic 2. Plan B: Treat with antibiotic 2. If not effective, treat with antibiotic 1. Based on the data provided, what is the probability that a patient treated under plan A will be successfully treated?
A. 0.98
B. 0.72
C. 0.80
D. 0.90

Answer:

[tex]\large\boxed{\dfrac{7x^2}{6x-10}}[/tex]

Step-by-step explanation:

[tex]\dfrac{7x^2}{2x+6}\div\dfrac{3x-5}{x+3}=\dfrac{7x^2}{2(x+3)}\cdot\dfrac{x+3}{3x-5}\\\\\text{cancel}\ (x+3)\\\\=\dfrac{7x^2}{2}\cdot\dfrac{1}{3x-5}=\dfrac{(7x^2)(1)}{(2)(3x-5)}\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=\dfrac{7x^2}{6x-10}[/tex]

Answer:

Step-by-step explanation:

If you flip coins, you can get,

HT TH HH TT

There are 4 possible outcomes.

Out of these 4, Matt has to do chores if two heads are flipped. It is 1/4 chance.

Out of these 4, Mark has to do chores if two tails are flipped. Again, 1/4 chance.

The method of decision is far since both guys have the same chance of being picked to do chores.

To flip again, they would have to get either HT or TH out of the 4 choices. So 2/4=1/2 is the likeihood they must flip again.

Answer: X = 8 And Y = 5 "First Choice Letter A"

Step-by-step explanation: x + y = 13......x = 13 - y

2x - 3y = 1

2(13 - y) - 3y = 1

26 - 2y - 3y = 1

-2y - 3y = 1 - 26

-5y = -25

y = -25/-5

y = 5

x + y = 13

x + 5 = 13

x = 13 - 5

x = 8

so, x = 8 and y = 5

Answer:

4

Step-by-step explanation:

An angle of depression is measured from the horizontal downwards

From the given diagram this is represented by angle 4

Answer:

C. Black grapes cost more per pound than green grapes.

Step-by-step explanation:

Verify each statement

A. Three pounds of green grapes cost $6.00

The statement is False

Because

For x=3 pounds

y=1.5x

y=1.5(3)=$4.5

B. Black grapes cost less per pound than green grapes

The statement is False

Because

For x=1 pound

The green grapes cost ----> y=1.5(1)=$1.5

Observing the graph

For x=1 pound

The black grapes cost $2

C. Black grapes cost more per pound than green grapes.

The statement is True

D. Two pounds of black grapes cost $3.00.

The statement is False

Because

Observing the graph

Two pounds of black grapes cost $4

An equation is formed of two equal expressions. The third statement is true.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

A.) The cost of a pound of green grapes is,

Y = 1.5X = 1.5×3 = 4.5

Hence, the first statement is false.

B.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the second statement is false.

C.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the third statement is true.

D.) As per the graph, the cost of 2 pounds of grapes is $4. Thus, the fourth statement is wrong.

Hence, the third statement is true.

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Answer: 6 units

Step-by-step explanation:

Area = 1/2 (base1 + base2) X height <-------- Formula for a trapezoid

24 = 1/2 (2 + 6) X h <----- We know that the area of the trapezoid is 24 units

squared and that both of the bases are 2 units and 6 units.

24 = 1/2 (8) X h <------- Add 6 + 2

24 = 4 X h <-----  Half of 8 is 4

h = 6 <------  6 X 4 = 24 , therefore the height is 6 units.

Hope this helps!

Answer:

5

Step-by-step explanation:

total sum of the 6 numbers

= 4 ×6

= 24

sum of numbers without the two 2s

= 24 - 2(2)

= 20

average of other 4 numbers

= 20 ÷ 4

= 5

The average of the other four numbers is 5.

How to find the average?

The average of six numbers is 4. If the of two of those numbers is 2.

The total sum of the 6 numbers

= 4 ×6

= 24

The sum of numbers without the two 2s

= 24 - 2(2)

= 20

The average of other 4 numbers

= 20 ÷ 4

= 5

Hence, The average of the other four numbers is 5.

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Answer:

  650 kg/m³

Step-by-step explanation:

The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.

  density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³

  = 650 kg/m³

Answer:

  650 kg/m³

Step-by-step explanation:

Divide the total inches by the scale inches:

7.5 / 3 = 2.5

Multiply that by the scale feet:

2.5 x 2 = 5 feet.

Answer: 5

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

Same x coordinates with different y values is considered undefined

[tex]

s=\frac{-2-6}{-4-(-4)}=\frac{-8}{0}=\boxed{undefined}

[/tex]

Answer:

A

Step-by-step explanation:

The degree of a polynomial is determined by the largest exponent in the terms of the polynomial. The leading coefficient is the coefficient of the term with the largest exponent.

Given

f(x) = 2x³ + 2x² - [tex]\frac{1}{x}[/tex]

The term - [tex]\frac{1}{x}[/tex] means that f(x) is not a polynomial

Since terms with division by a variable are not allowed.

Answer:

1. the cost of the computer (c)

2. > (greater than)

3. how much ($300)

4. c > 300

The variable in the inequality represents the cost of the computer.

The inequality symbol needed is > (greater than)

The constant is how much ($300)

The inequality that correctly represents the problem is cost of the computer  > 300

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

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0=1/2(2x²+13x+20)

0=x²+6,5x+10

[tex]x = \frac{ - 6.5 + \sqrt{2.25} }{2} \\ x = - 2.5 \\ x = - 4[/tex]

Answer:

x = - 2.5, x = - 4

Step-by-step explanation:

To find the zeros, set y = 0, that is

[tex]\frac{1}{2}[/tex](2x + 5)(x + 4) = 0

Equate each of the factors to zero and solve for x

2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - 2.5

x + 4 = 0 ⇒ x = - 4

Answer:

The length of the line segment is 13 units

Step-by-step explanation:

The line segment joining the two points is horizontal since the y co-ordinate is the same.

For a horizontal line, the length of the line segment is simply the difference between the x co-ordinate values.

In this case we have;

7 - (-6) = 7 + 6 = 13

Therefore, the length of the line segment is 13 units

Answer:

your answer is 13 units

Step-by-step explanation:

I do K12

Answer: -8n^4 + 3n^2

(The ^ is the exponent)

The answers are:

First box: 7 times the cube of the sum of x and 8

Second box: 8 added to the cube of 7x.

Third box: 8 added to 7 and x cubed.

Fourth box: the cube of the sum of 7x and 8.

We are given the expression and we need to macth to the correct verbal description, so we have:

First box:

[tex]7(x+8)x^{3}[/tex]

It's 7 times the cube of the sum of x and 8

Second box:

[tex](7x)^{3}+8[/tex]

We have that "7x" is cubed and then, added to 8, so,  it's 8 added to the cube of 7x.

Third box:

[tex]7x^{3}+8[/tex]

We have "7" times "x" cubed and added to 8, so it's 8 added to 7 and x cubed.

Fourth box:

[tex](7x+8)x^{3}[/tex]

We have "7x" added to 8, and the expression is cubed, so, it's the cube of the sum of 7x and 8.

Have a nice day!

Answer:

a and f

Step-by-step explanation:

Vertical angles are directly opposite each other, created by two lines intersecting.

∠A and ∠F are congruent to each other because they are vertically opposite angles. Then the correct option is D.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

∠A and ∠F, ∠B and ∠E, ∠C and ∠H, and ∠D and ∠G are congruent to each other because they are vertically opposite angles.

Then the correct option is D.

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Perimeter: 2(l+w)

2•l+2•w

l+w+l+w

Area: l•w

wl

Neither: l+w

Answer:

Step-by-step explanation:

[ (x + 7) / 6 ] − [ (x + 5) / (x + 3) ]

First, we must find the common denominator.  In this case, that's 6 (x+3).  Multiply the first fraction by (x+3)/(x+3) and the second fraction by 6/6.

[ (x + 7)(x + 3) / (6 (x + 3)) ] − [ 6 (x + 5) / (6 (x + 3)) ]

Now distribute the numerators:

[ (x² + 10x + 21) / (6 (x + 3)) ] − [ (6x + 30) / (6 (x + 3)) ]

Now we combine the fractions:

((x² + 10x + 21) − (6x + 30)) / (6 (x + 3))

(x² + 10x + 21 − 6x − 30) / (6 (x + 3))

(x² + 4x − 9) / (6 (x + 3))

So the simplified form is:

[tex]\frac{x^{2} + 4x - 9}{6 (x + 3)}[/tex]

Answer:

Second Option

f(x) − 2

Step-by-step explanation:

The function [tex]y=3 (2) ^ x[/tex] passes through point (0, 3) because:

[tex]f (0) = 3 (2) ^ 0 = 3 (1) = 3[/tex]

Then, if the transformed function passes through the point (0, 1) then this means that the graph of [tex]y = 3 (2) ^ x[/tex] was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

[tex]y = f(x) + k[/tex]

Where k is a negative number. In this case [tex]k = -2[/tex]

Then the transformation is:

[tex]y = f(x) -2[/tex]

and the transformed function is:

[tex]y = 3(2) ^ x -2[/tex]

Answer:

f(x − 2)

Step-by-step explanation:

thats the right answer

Answer:

a) 235.62in³

b) 904.78in³

Step-by-step explanation:

a) The formula to find the volume of a cylinder is:

[tex]V = \pi r^2h[/tex]

We are given that r = 5 and h = 3, so we can just plug in and solve:

[tex]V = \pi(5)^2(3) = 235.62in^3[/tex]

b) The formula to find the volume of a sphere is:

[tex]V = \frac{4}{3}\pi r^3[/tex]

We are given that the diameter is 12in, which means that the radius (r) must be 6in (half the diameter). Now, we can plug in and solve:

[tex]V = \frac{4}{3}\pi (6)^3 = 904.78in^3[/tex]

Answer: The mean

Step-by-step explanation: a) The mean:

To find the mean, we just simply need to add the hours spent by the students playing games and divide by the number of hours.

Mean =  = 2.85

b) The median:

We will arrange the number of hours for in ascending order and the middle value will be the median.

Median = 3

c) The mode:

Mode is the number which occurs most frequently. So in this case Mode = 2, 3.

d)Percentage of the students play video games for more than 4 hours in a month  =  = 45%

ANSWER

The coordinates of the image are (2,2)

EXPLANATION

The mapping for a reflection across the line y=k is :

[tex](x,y)\to (x,2k-y)[/tex]

We want to find the image of the point (2,-4) after a reflection in the line y=-1.

In this case k=-1.

[tex](2, - 4)\to (2,2( - 1)- - 4)[/tex]

This simplifies to,

[tex](2, - 4)\to (2, - 2 + 4)[/tex]

[tex](2, - 4)\to (2, 2)[/tex]

Hence the image is (2,2)

ANSWER

D. 135 m^2

EXPLANATION

The area of a kite is half the product of the diagonals.

The first diagonal is

9m+6m=15m

Note that the vertical diagonal is the axis of symmetry of the kite.

This diagonal bisect the kite

Therefore the second diagonal is

2(9m)=18m

The area of the kite

[tex] = \frac{1}{2} \times 18 \times 15[/tex]

[tex] = 9 \times 15[/tex]

[tex] = 135 {m}^{2} [/tex]

Answer:

[tex]A_{T}=135 m^{2[/tex]

Step-by-step explanation:

Hello

To solve this problem we can divide the kite into simpler geometric figures to find its area, we have four triangles

the area of a triangle =(b*h)/2

b is the base and his the heigth

Step 1

triangle 1 (LEFT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{1} =40.5\ m^{2}[/tex]

Step 2

triangle 2 (RIGHT UP)

[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{2} =40.5\ m^{2}[/tex]

Step 3

triangle 3 (LEFT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{3} =27\ m^{2}[/tex]

Step 4

triangle 4 (RIGHT DOWN)

[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{4} =27\ m^{2}[/tex]

Step 5

Total Area

the total area is

[tex]A_{T}=A_{1}+A_{2}+A_{3}+A_{4}   \\A_{T}=(40.5+40.5+27+27)m^{2} \\A_{T}=135 m^{2}[/tex]

Have a great day

I do not see an illustration.

Answer: -30

I really hope this helped you

To solve 3 3/5 x (-8 1/3), we convert the mixed numbers into improper fractions, multiply them, and simplify to get the answer -30.

The student is asking to perform multiplication between a mixed number and a mixed number with a negative sign. To compute 3 3/5 x (-8 1/3), we first convert the mixed numbers into improper fractions. The number 3 3/5 can be converted to 18/5 (since 3*5 + 3 = 18) and -8 1/3 can be converted to -25/3 (since -8*3 + 1 = -25). Multiplying these two improper fractions gives us (18/5) * (-25/3). To multiply fractions, we multiply the numerators together and the denominators together, giving us -450/15. Simplifying this fraction, we get the final answer, which is -30.

Check the picture below.

The answer is a=8 btw

I believe that it has two solutions

Answer:

The given equation has just one solution

Step-by-step explanation:

To find the solution to the problem given, we will follow the steps below;

5x + 3x - 4 = 10

We will first start by simplifying

8x - 4 = 10

Add 4 to both-side of the equation

8x - 4 + 4 = 10 + 4

8x = 10

Divide both-side of the equation by 8

8x/8 = 10/8

At the left-hand side of the equation, 8 will cancel-out 8 leaving us with just x while at the right-hand side of the equation 10 will be divided by 8

x=1.25

Therefore the given equation has just one solution

Answer:

Angle addition postulate and 2x=56

Step-by-step explanation:

The value of x is 28 degree.

Linear pair of angles are formed when two lines intersect each other at a single point.

Given:

m∠ELG = 124

as, m∠ELG and m∠ELD are in linear pair.

So, 124 + 2x =180

2x =56

x -28

Hence, the value of x is 28 degree

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Answer:

The numbers are 44 and 46

Step-by-step explanation:

Let

x, x+2 ----> the two consecutive positive even integers

we know that

[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]

Solve the quadratic equation using a graphing calculator

The solution is x=44

see the attached figure

x+2=44+2=46

therefore

The numbers are 44 and 46