Given p(x)=x+7/3, if p(x)=13 find x

Answer:

80

Step-by-step explanation:

x/ -4 = -20

I hope this helps!

The Probability of P(B│A) is 0.77

Independent events are those events whose occurrence is independent on any other event. For example, if we flip a coin in the air and get the outcome as tail, then again if we flip the coin but this time we get the outcome as Head, In both cases, the occurrence of both events is independent of each other. It is a type of events in probability.

If A is the event that even number will appear when a die is rolled and B is when 4 or 6 appears

P(A)= 3/6 = 1/2 and P(B) = 2/6 = 1/3

Also A and B is the event ‘the number appearing is even and a multiple of 4 or 6 so that

P(A ∩ B) = 1/6

P(B│A) = P(A ∩ B)/ P(A)

= 1/6 /1/2= 1/3 = P(B)

Therefore P(B│A) = P(B)

if A= 0.15 and P(B)= 0.77

P(B│A) = 0.77

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The value of x is 11° and measure of other two angles are 80° and 117°

A triangle can be defined as a polygon which has three angles and three sides. The interior angles of a triangle sum up to 180°, and the exterior angles sum up to 360°.

Given that, the interior angles of the triangle are 37° and (3x+47)° and an exterior angle measures (5x+ 62)°

We know that the sum of two interior angles equals to the measure of an exterior angle,

Therefore,  37° + (3x+47)° = (5x+ 62)°

x = 11°

Hence, The value of x is 11° and measure of other two angles are 80° and 117°

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Answer:

a. Given

b. thru any 2 points there exists a line (you can draw a line)

c. Definition of Regular Polygon

d. Definition of Regular Polygon

e. Given

f. Def of Midpoint

g. SAS: Side-Angle-Side congruence

h. CPCTC - Corresponding Parts of Congruent Triangles are Congruent

i. Definition of Regular Polygon

j. Reflexive

k. SSS: Side-Side-Side congruence

l. CPCTC

Step-by-step explanation:

I encourage you to look up all of the above reasons to get a better understanding of what they are!!

The maximum number of guests that can fill all the standard rooms is twice the number of the standard rooms

Information from the question

each standard room can fill 2 guests

the maximum number of guests that all standard rooms can accommodate = ?

The problem is solved by multiplication

each standard room (1) = 2 guests

all standard rooms = ?

cross multiplying

? * 1 = 2 * all standard rooms

? = all standard rooms times two

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Answer:

Alessa's car would be able to drive 337.5 miles with 15 gallons of gas.

She drinks 1/12 gallons of milk each day

From the question, we have the following parameters that can be used in our computation:

Size of milk = 1/2 gallons

Number of days = 6 days

These parameters can be represented as

(x, y) = (6, 1/2)

The number of gallons a day she drinks can then be represented as the slope/unit rate and the unit rate is then calculated as

unit rate = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (0, 0) and (6, 1/2)

Substitute the known values in the above equation

So, we have the following equation

Slope = (1/2 - 0)/(6 - 0)

Evaluate the quotient

Slope = 1/12

Hence, the number of gallons she drinks a day is 1/12

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The ratio of 6 cups of sugar to pie that Quinn needs to make 12 potato pies will be 6 cups.

Ratio basically compares quantities, that shows value of one quantity with respect to other quantity.

If a and b are two values, there ratio will be a:b.

Given that,

For 3 potato pies required sugar is 3/2,

For 5 potato pies required sugar is 5/2,

for 9 potato pies required sugar is 9/2,

From the given information,

For 1 potato pies required sugar is 1/2

⇒For 12 potato pies required sugar=12×1/2=6

To make 12 potato pies,  required sugar will be 6.

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48.4 % percent of all rodents on the ship preferred peanut butter.

acc to our question-

hence,48.4 % percent of all rodents on the ship preferred peanut butter.

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When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.

A mathematical formula known as a cost function is used to visualise how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

The following equation, C'(x)=x-3/4, tells us the marginal cost (in dollars) of printing a poster after x posters have been printed.

The given equation is :C'(x)=x-3/4

The cost of printing 133 more posters when 17 have already been printed is given by;

applying the limitations we obtain and integrating both sides of the equation;

[tex]$$\int_a^b C^{\prime}(x) d x=\int_{17}^{133} x^{\frac{-3}{4}} d x$$[/tex]

As we know that [tex]$\int x^n d x=\frac{x^{n+1}}{n+1}$[/tex], so;

[tex]$&=4\left[x^{\frac{1}{4}}\right]_{17}^{133} \\[/tex]

[tex]$&=4\left[(133)^{\frac{1}{4}}-(17)^{\frac{1}{4}}\right] \\[/tex]

= $ 5.4616

Therefore When only 17 posters have been printed, it will cost $ 5. 46to print 143 more.

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The area of the shaded region is x=245 feet for both rectangle and circle.

The quantity area expresses the extent of a region on a plane or a curved surface. The area of a plane region or plane area refers to the area of a form or planar lamina, whereas surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be defined as the amount of material of a given thickness required to make a model of the shape, or the amount of paint required to cover the surface with a single coat. It is the two-dimensional equivalent of the length of a curve or the volume of a solid.

The area of a shape can be calculated.

Area of shaded region=Area of rectangle-1/2(Area of circle)

=L×B-1/2(πr²)

=23×14-1/2((22/7)×7×7)

=322-77

=245 feet

Therefore, the area of the shaded region=245 feet

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Answer:

bla blablablablabla

Step-by-step explanation:

blablablablablabla

When is a standard normal random variable, the probability of P(–1.20 ≤ z ≤ 1.50) is 0.8181.

The probability illustrates the likelihood of events.

From the information, it's important to note that P(–1.20 ≤ z ≤ 1.50) will be:

= P(Z ≤ 1.50) - P(Z ≤ -1.20)

= P(Z ≤ 1.50) - [1 - P(Z ≤ -1.20)]

It should be noted that by using the normal z table, the probability of the corresponding z score will be 0.9332 and 0.8849.

This will be:

= 0.9332 - (1 - 0.8849)

= 0.8181

Therefore, the probability is 0.8181.

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The value of x=0.301 at the x the graph of the function have a horizontal tangent.

Given that,

The function is f(x)=eˣ-2x

We have to find the value of x does the graph of the function have a horizontal tangent.

Where the derivative of a function is zero, a graph's horizontal tangent line is a mathematical feature. This is so that the derivative, by definition, can provide the slope of the tangent line. The slope of horizontal lines is zero. As a result, when the derivative is zero, the tangent line is horizontal.

For horizontal tangent line,

f'(x)=0

The differentiation of the function is

eˣ-2=0

eˣ=2

Taking logarithm on both sides.

logeˣ=log2

We know that loge=1

So,

x loge=log2

x(1)=log2

x=log2

x=0.301

Therefore, the value of x=0.301 at the x the graph of the function have a horizontal tangent.

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The two equations combined is

Eliminating one variable gives

the variables are

The equation formed is a consistent independent set of equation with two variables solved by elimination method as follows

Elimination of one of the variable

3x + y = 20      (1)

10x + y = 55     (2)

subtracting (1) from (2)

10x - 3x + y - y = 55 - 20

7x + 0 = 35

7x = 35

x = 5

substituting to find y

3x + y = 20

3 * 5 + y = 20

15 + y = 20

y = 20 - 15

y = 5

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Answer:

[tex]-1.35[/tex] is bigger (larger)

Step-by-step explanation:

[tex]-1\frac{4}{9}=-1.\overline{44}[/tex]

Therefore, because [tex]-1.35[/tex] is less negative than [tex]-1.\overline{44}[/tex],

[tex]-1.35[/tex] is bigger (larger).

The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;

(a) The dimensions of the tiles are;

Width = 0.3 meters

Length = 0.8 meters

(b) 384 tiles are needed

(c) The fitting cost of the tiles is Kshs 51,000

An equation is a mathematical statement that consists of two expressions connected with an equals sign

Shape of the floor = Square

Shape of the tiles = Rectangular

Perimeter of the tiles = 220 cm = 2.2 m

The number of tiles in each row =  20 + The number of tiles in each column

Length of the floor = 9.6 m

(a) Let w represent the width of the tiles, the length l is found using the equation;

[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]

Let n represent the number of tiles in each row, which gives;

The number of tiles in each column = 20 + n

(20+n)·x = n·(1.1 - x)

Which gives;

[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]

The side length of the square floor, s = 9.6

(20+n)·x = n·(1.1 - x) = 9.6

Which gives;

[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]

Which gives;

0.55·n² - 1.4·n -96 = 0

n = 12 or n ≈ -14.5

The number tiles in each roe, n = 20

Which gives; n·(1.1 - x) = 9.6

20 × (1.1 - x) = 9.6

x = 0.3

The width of each tile, x = 0.3 m

The length of each tiles = 1.1 m - 0.3 m = 0.8 m

(b) The number of tiles in each row, n = 20

The number of tiles in each column = n + 20, which gives;

Number of tiles in each column = 12 + 20 = 32

The number of tiles needed = 12 × 32 = 384

(c) The cost of a dozen tiles = Kshs 1,500

The labour cost = Kshs 3,000

Number of dozens of tiles = 384 ÷ 12 = 32

The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000

The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000

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Answer:

y=x-7

Step-by-step explanation:

we know the y intercept is -7 since when x was 0 g(x) is -7

We write it in slope intercept form which is y=mx+b

m- slope

b- y- intercept

To find slope we do y2-y1/x2-x1

-5+7/2-0

2/2

1

1 is the slope so we just keep it X on the equation and the equation will be

y=x-7

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The total number of hours Donna used driving is 3 2/21 hours

A rate is a special ratio in which the two terms are in different units. For example, For 1 hour Donna is using 7/10 gallons of fuel while driving.

The two quantities there are time in hours and the quantity of fuel used in gallons.

If Donna used 7/10 gallon for 1 hour

then 1 gallon will last for 1÷7/10= 1× 10/7= 10/7

Therefore for 2 1/6 gallon = 10/7×2 1/6= 10/7×13/6

= 3 2/21 hours

Therefore the total number of hours used driving with 2 1/6 gallons is 3 2/21

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If a claim will be made against such a policy and an average claim of $4900. the insurance company should make on average off of each policy holder is $683.5.

Using this formula to find the amount

Amount = [Percentage claim × ( Base price - Average claim)] + [(1 - percentage claim) × Base price]

Let plug in the formula

Amount = [0.085 × ($1,100 - $4,900)] + [(1-0.085) × $1,100]

Amount = [0.085 ×  (- $3,800)] + [(0.915 × $1,100]

Amount = -$325+ $1,006.5

Amount = $683.5

Therefore the insurance company will make the amount of $683.5.

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The solution of the expressions are

(a) (30+10 ÷ 2)-5-10 = 20

(d) 30+ (10 ÷ 2·5)-10 = 24

What is meaning of expressions?

An expression is a combination of operations, variables, and numbers.

What is BODMAS rule?

According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right.

Given expression is

(30+10 ÷ 2)-5-10

Applying BODMAS rule:

= (30 + 5) - 5 - 10

= 35 - 5 - 10

= 30 - 10

=40

Second expression is:

30+ (10 ÷ 2·5)-10

= 30 + (10 ÷ 10) - 10

= 30 + 1 - 10

= 31 -10

= 21

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Answer:

23/5 > (sqrt(18)

Step-by-step explanation:

there are many ways you could go about this,

I subtracted (sqrt(18)) from (23/5) and because the answer i got was greater than 0, 23/5 must be bigger than sqrt18

Answer:

cubic root 10 power 1

Step-by-step explanation:

Apply the rule

x

m

n

=

n

√

x

m

to rewrite the exponentiation as a radical.

3

√

10

1

Anything raised to

1

is the base itself.

3

√

10

The result can be shown in multiple forms.

Exact Form:

3

√

10

Decimal Form:

2.15443469

…

The first term of the sequence is 12 and the common difference is -3.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Given that a formula for the nth term. 5th term is 0​; 45th term is -120. The common difference is calculated as,

a₁ + d(5-1) = 0

a₁ + d(45 - 1) = -120

Solve the above equation,

a₁ + 4d = 0

-a₁ - 44d= +120

___________

     -40d = 120

          d = -3

The value of the first term is,

a₁ + 4d = 0

a₁ + 4 x -3 = 0

a₁ = 12

Therefore, the first term of the sequence is 12 and the common difference is -3.

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Answer: The answer is 0.16638935108

Step-by-step explanation:

A number line which shows -3, 1/2, 3/4, and 1 correctly plotted on a graph is shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0). Therefore, the numerical value -3 would be plotted on the left hand side of zero (0) while the numerical values 1/2, 3/4, and 1 would be plotted on the right hand side of zero (0) using a number line.

In conclusion, a number line has been used for the comparison of the given numerical values, and they are plotted on the number line shown in the image attached below.

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Answer:

y=7

Step-by-step explanation:

-3(-3)-y=2

9-y=2

9-2=y

y=7

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The expression of the phrase " Nine increased by twice a number " is 2n + 9

The given phrase is

Nine increased by twice a number

We have to convert the the phrase to the expression

The expression is the mathematical statement that consist of different variables, numbers and mathematical operators. The mathematical operators are addition, subtraction, division and multiplication. The equal sign and inequality will not be the part of expression.

Consider the number as n

Twice the number = 2n

nine increased by twice a number = 2n + 9

Hence, the expression of the phrase " Nine increased by twice a number " is 2n + 9

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Answer:

6/7

Step-by-step explanation:

2÷3/7=2*3/7

6/7