5. (01.06 MC)
Solve the following equation for x: 5x + 3y = 15.

Answer:

- 3b + 21

Step-by-step explanation:

- 3(b - 7) ← multiply each term in the parenthesis by - 3

= - 3b + 21

There is 0.329 probability or chance that the software really has a virus.

The calculation will be based on Bayes' theorem which relates the probability and statistics, as is mentioned in the given question. The values provided are True positive = 97%, False positive = 2% and Prevalence = 1%.

Probability = (True positive × user) ÷ (True positive × user) + (false positive × non user)

Keep the values in formula to find the probability

Probability = (0.97 × 0.01) ÷ (0.97 × 0.01) + (0.02 × 0.99)

Probability = 0.0097 ÷ (0.0097 + 0.0198)

Probability = 0.0097 ÷ 0.0295

Probability = 0.329

Thus, there is 0.329 chance that the software really has a virus.

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The vertex (the common end point for the two rays) in the angle SRQ is the point R as it is in the middle and common.

The angle is SRQ with sides SR and RQ. The common point is R.

A vertex of an angle is the endpoint where two line or rays come together. The vertex of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place.

Here two sides are SR and RQ the end point to both the sides is common which is R. So the vertex to the angle SRQ is R.

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The solutions of the expression are;

a. - 5 - 2 = -7

b. 6 - (-5) = 11

What is Addition?

A process of combining two or more numbers are called Addition.

The given expression are;

a. -5 - 2

b. 6 - (-5)

Now, Solve the expression as;

-5 - 2 = - 7

And, 6 - (-5) = 6 + 5 = 11

So, The solutions of the expression are;

- 5 - 2 = -7

6 - (-5) = 11

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The equation of the line is  y= 3 - 2x.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

Coordinates (0, 3) and (2, -1)

So,

slope = -4/2=-2

and equation of line is

(y- y1) = m (x- x1)

y-3 = (-2)(x-0)

y-3 = -2x

y= 3 - 2x

Hence, the equation of line is y= 3 - 2x.

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Answer: i feel like all of them but dont go by my word

Step-by-step explanation:

Answer:

The symbol should be equal to.

They are the same when the first expression is multiplied.

Answer:

=

Step-by-step explanation:

6.738 × 10^-11 = 0.00000000006.738

0.00000000006738 = 0.00000000006738

Answer:

I'm not completely sure, but it does look similar to a Florida Mockingbird to me, I'll do more research and comment on any new finds. Hope this helps.

Step-by-step explanation:

Answer:

yeah it might be a florida mocking bird i got a lot around where i live

Step-by-step explanation:

Step-by-step explanation:

To find a line perpendicular to one another and passing through the point we take the slope of the original line and apply its reciprocal in point slope form.

Reciprocal of [tex]\frac{1}{4}[/tex] is [tex]\frac{-4}{1}=-4[/tex]

Now plug the slope into point-slope form with the known x and y values:

[tex]x-(-2)=-4(y-4)\\x+2=-4(y-4)\\x+2=-4y+16\\x+2+4y=16\\4y=16-x-2\\y=4-\frac{x}{4}-\frac{2}{4}\\y=3.5-\frac{x}{4}[/tex]

A counterexample that disproves her conjecture is that Easter date fell outside the first 22 days in April in the year 2024, 2027, 2032 and 2038.

Easter Sunday might come between March 22 and April 25. Easter is always celebrated on the Sunday immediately following the Paschal Full Moon date of the year. The Paschal Full Moon is the first Ecclesiastical Full Moon date after March 20. So, in Western Christianity, Easter is always celebrated on the Sunday immediately following the Paschal Full Moon.

Her conjecture over 2018 to 2021 is not a full reflection of the changes that occurs in these dates. To draw a more concrete assumptions, a wider range of year would need to be considered. Hence, the date variations between 2018 and 2021 is not enough for such conjectures.

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Answer:

that the greatest common factor of 24 and 32

Answer:

24 and 32

Step-by-step explanation:

Using the description, area of triangle ACE is solved to be 150 square units

from the given data we fine AE using Pythagoras rule, as AE is the hypotenuse of the triangle AEM. So we solve as:

AE^2 = ME^2 + AM^2

AE^2 = 10^2 + 22^2

AE = √(100 + 484)

AE = √584

note AM is half of AB which is 44, it was given that M is the mid point of line AB, this makes AM = AB / 2 = 22

Area of triangle ACE

area of triangle when two sides and one angle is given is solved by the formula

= a b sin ∅ / 2

angle at A/2 = arc tan (10/22) = 24.44

= AC * AE * sin A/2 / 2

= 30 * √584 * sin 24.44 / 2

= 299.95 / 2

= 149.98 ≅ 150

Hence area of triangle ACE is solved to be 150 square units

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The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

The actual length of the car is 12 feet and is represented by 5 inches in the model.

The equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is as follows:

12 feet = 5 inches

Hence,

m = 5 / 12 a

a = 2.4m

where

or

m = a / 2.4

Therefore, the  equation that can be use to represent the relationship between the actual length(a) in feet, and the length of the model (m), in inches is a = 2.4m or m = a / 2.4

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Answer:

x = 8 and x = 2 are both valid solutions.

There are no extraneous answers.

Step-by-step explanation:

Given absolute value function:

[tex]|2(x-5)|+11=17[/tex]

To solve an equation containing an absolute value, isolate the absolute value on one side of the equation:

[tex]\implies |2(x-5)|+11=17[/tex]

[tex]\implies |2(x-5)|+11-11=17-11[/tex]

[tex]\implies |2(x-5)|=6[/tex]

Set the contents of the absolute value equal to both the positive and negative value of the number on the other side of the equation, then solve both equations.

Equation 1 (positive)

[tex]\implies 2(x-5)=6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{6}{2}[/tex]

[tex]\implies x-5=3[/tex]

[tex]\implies x-5+5=3+5[/tex]

[tex]\implies x=8[/tex]

Equation 2 (negative)

[tex]\implies 2(x-5)=-6[/tex]

[tex]\implies \dfrac{2(x-5)}{2}=\dfrac{-6}{2}[/tex]

[tex]\implies x-5=-3[/tex]

[tex]\implies x-5+5=-3+5[/tex]

[tex]\implies x=2[/tex]

Therefore, the solutions are x = 8 and x = 2.

Check if the solutions are valid by substituting them into the original equation:

[tex]\begin{aligned}x=8 \implies |2(8-5)|+11 & =17\\|2(3)|+11 & =17\\|6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

[tex]\begin{aligned}x=2 \implies |2(2-5)|+11 & =17\\|2(-3)|+11 & =17\\|-6|+11 & =17\\6+11 & =17\\ 17 & = 17\end{aligned}[/tex]

Therefore, both solutions are valid and there are no extraneous answers.

Note:  An extraneous solution is a solution that is produced by solving the problem, but is not a valid solution to the problem.

The value of logarithmic equation log₂ (x+3) + lox₂ (3) = log₂(27) which is taken as an example is x = 6.

Step 1: Isolate a logarithmic expression (with the same base) on both sides of the equation using exponentiation rules.

Step 2: equalize the arguments.

Step 3: Solve the resultant equation.

Step 4: Verify your responses.

Let us consider an example -

log₂ (x+3) + lox₂ (3) = log₂(27)

using logₐ(m.n) = logₐ(m) + logₐ(n)

log₂(3(x+3)) = log₂(27)

log₂(3x + 9) = log₂(27)

3x+9 = 27

x = 27 - 9 / 3

x = 6

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Answer: $96.27

Step-by-step explanation: 15x5=75, 75+21.27=96.27

Answer: $96.27

Step-by-step explanation:

If five of Carries' family members donated $15 we would have 15x5.

15+15+15+15+15=$75.

Carrie, herself, donated $21.27.

$75+$21.27

75+21=96

Add the .27 to 96.

Answer= $96.27 in total

Answer:

option D is the correct option

The total number of cupcakes sold by the bakery on that day were 200.

Here, we are given that a bakery sold 26 vanilla cupcakes in a day.

This was 13% of the total number of cupcakes sold that day.

Let the total number of cupcakes sold that day be x

Then 13% of x is given to be 26. Mathematically this can be represented as-

(13/100)x = 26

solving the equation to find the value of x, we get-

x = 26 × 100/ 13

x = 26/13 × 100

x = 2 × 100

x = 200

Thus, the total number of cupcakes sold by the bakery on that day were 200.

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Answer:

∠2 = 35 degrees because it is the vertical angle of ∠3

∠6 = 35 degrees because it corresponds with ∠2

∠4 = 145 degrees because when added to ∠2 145 + 35 = 180

A straight line equals 180 degrees. ∠4 and ∠2 are on the same line which means they have to add up to 180 degrees.

Step-by-step explanation:

The number of students in the group = 13

for this question,

Let n be the number of students.

Each student received a bacon cheeseburger and milkshake, and the total bill was $104.00

We need to find the total number of students in the group.

A Bacon Cheeseburger costs $4.75 and Milkshake costs $3.25.

Total cost of a bacon cheeseburger and milkshake is:

$4.75 + $3.25 = $8

The total bill was $104.00

So, we get an equation,

⇒ 8 × n = 104

By unitary method,

⇒ n = 104/8

⇒ n = 13

Therefore, the number of students in the group = 13

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Answer: its 56

Step-by-step explanation:

plug #'s in

t=72-8x2

t=56

Answer:

64

Step-by-step explanation:

Angles DBF and EBF form a linear pair, so:

[tex]5x+6+3x-2=180 \\ \\ 8x+4=180 \\ \\ 8x=176 \\ \\ x=22 \\ \\ \implies m\angle DBF=116^{\circ}[/tex]

Similarly, because angles DBF and DBC form a linear pair, the answer is 64°.

Answer:

A) "If q, then p."

B) "If not p, then (not) q."

C) "If (not) q, then not p."

Solution of logarithmic eq. log (3 - 2x) = -1 is , [tex]x = \frac{29}{20}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .

where, a is the base of function or equation

           x is expression equation

Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as  [tex]log_aN = x[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms :

According to given statement,

log (3 - 2 x)= -1

now convert this equation to exponential form

=> 3 - 2x = 10^-1

=> 3 - 2x = 1/ 10

=> x = 29 / 10

Thus solution for this equation is x =29/20.

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If we solve the expression 4 log m-log n,then it will look like log([tex]m^{4}/n[/tex]) as single logarithm.

Given that the expression is 4 log m-log n.

We are told to write the expression as a single logarithm.

logarithm is basically the exponent or power to which a base must be raised to yield a given number. It is opposite to exponential function.

The expression is 4 log m-log n.

We know that log [tex]a^{b}[/tex]=b log a and log (m/v)=log m-log n.So,

4 log m-log n=log [tex]m^{4}[/tex]- log n

=log ([tex]m^{4}/n[/tex])

Hence if we solve the expression 4 log m-log n,then it will look like

log([tex]m^{4}/n[/tex]) as a single logarithm.

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The school that Ming goes to sell their tickets as follows: price of a senior citizen ticket is $6 and the price of a student ticket is $9

Given data

first day 8 senior citizen tickets and 4 student tickets for a total of $84

second dat 8 senior citizen tickets and 2 student tickets for a total of $66

let the price of a senior citizen ticket be x and the price of a student ticket be y. The equation is written as:

8x + 4y = $84    equation 1

8x + 2y = $66    equation 2

subtracting equation 2 from equation 1

( 8x - 8x ) + 4y - 2y = 84 - 66

0 + 2y = 18

2y = 18

y = 9

substituting y = 9 into equation 1

8x + 4y = 84

8x + 4 * 9 = 84

8x + 36 = 84

8x = 84 - 36

8x = 48

x = 6

Hence the price of a senior citizen ticket is $6 and the price of a student ticket is $9

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The cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

The relation between speed, distance and time is as follows -

Speed = distance ÷ time. The maximum and minimum number of hours will depend on the distance. The maximum number of hours will be spent when maximum distance is covered, and minimum number of hours will be spent when minimum distance is covered.

Maximum distance = 35 + 10

Maximum distance = 45 miles

Minimum distance = 35 - 10

Minimum distance = 25 miles

Maximum number of hours = 45 ÷ 20

Maximum number of hours = 2.25 hours

Minimum number of hours = 25 ÷ 20

Minimum number of hours = 1.25 hours

Thus, cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

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We get the product -9 9/20 after multiplying the given two mixed numbers  -1 3/4 and 5 2/5.

Mixed numbers: A mixed number is a whole number, and a proper fraction represented together.

Multiplication: In simple algebra, multiplication is the process of calculating the result when a number is taken times. The result of a multiplication is called the product.

Given are two mixed numbers  -1 3/4 and 5 2/5.

Explanation:

= -1 3/4 * 5 2/5

converting both the mixed numbers into improper fractions, we get

= -7/4 * 27/5

multiplying numerator by numerator and denominator by denominator, we get

= -189/20

= -9 9/20

Therefore, we get the product -9 9/20 after multiplying the given two mixed numbers  -1 3/4 and 5 2/5.

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