What is the solution set for the following inequality? 4x – 3 + 6x > 5x + 7

Answer:

sorry

Step-by-step explanation:

a) 2/8 = 1/4

b) There are 3 females who can speak French and 2 males who can speak French, so the probability is 3/5

Answer:

The answer is 3.2

The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

The value of a savings account can be found using the equation =

= 300(1.03)²⁴

From the function:

F(x) = a(1+r)ˣ

On compare:

1 + r = 1.03

r = 0.03

or

r = 3% monthly

r = 3×12 = 36% yearly

Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

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Let's prove that (sec x)(csc x) is equal to cot x + tan x

[tex]\Longrightarrow \sf (sec(x) )(csc(x))[/tex]

[tex]\Longrightarrow \sf \dfrac{1}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)+\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)} + \dfrac{\sin ^2\left(x\right)}{\cos \left(x\right)\sin \left(x\right)}[/tex]

[tex]\Longrightarrow \sf \dfrac{\cos\left(x\right)}{\sin \left(x\right)} + \dfrac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]

[tex]\Longrightarrow \sf cot(x) + tan(x)[/tex]

Hence student A did correctly prove the identity properly.

Also Looking at student B's work, he verified the identity properly.

So, Both are correct in their own way.

Identities used:

[tex]\rightarrow \sf sin^2 (x) + cos^2 (x) = 1[/tex]       (appeared in step 3)

[tex]\sf \rightarrow \dfrac{cos(x) }{sin(x) } = cot(x)[/tex]               (appeared in step 6)

[tex]\rightarrow \sf \dfrac{sin(x )}{cos(x) } = tan(x)[/tex]               (appeared in step 6)

The irrational number in the given options is √11

Irrational numbers are set of all real numbers in mathematics that are not rational numbers in nature. By the word rational, we mean that they cannot be expressed or represented in a fraction of a/b.

where;

In other words, it is impossible to describe an irrational number as the ratio of two integers.

From the given options, the square root of 11 is the only number that cannot be expressed as a fraction, therefore, we can conclude that it is considered the only irrational number in the given options.

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The number of ways to choose the colors is 36

The given parameters are:

Colors = 9

Colors to choose = 7

Since order does not matter, then it is combination

This is calculated using:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^nC_r = \frac{9!}{7!2!}[/tex]

Evaluate

[tex]^nC_r = 36[/tex]

Hence, the number of ways is 36

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The recurrence relation is dn = 0.4d(n-1) where d1 = 75

The given parameters are:

Since, the medication is eliminated from the blood; then it means that the function is an exponential decay function.

This is represented as:

d(n) = d(n - 1) * (1 - r)

Substitute r = 60%

d(n) = d(n - 1) * (1 - 60%)

Evaluate the difference

d(n) = d(n - 1) * 0.4

Evaluate the product

dn = 0.4d(n-1)

Hence, the recurrence relation is dn = 0.4d(n-1) where d1 = 75

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After divide, the solution of the expression is, 285

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

190 divided by 2/3.

Now, We can simplify as;

⇒ 190 ÷ 2/3

⇒ 190 × 3/2

⇒ 95 × 3

⇒ 285

Thus, The solution of the expression is, 285

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Answer: 1

Step-by-step explanation:

[tex]f(8+h)=8+h+10=18+h\\\\f(8)=8+10=18[/tex]

So, the average rate of change is:

[tex]\frac{(18+h)-18}{(8+h)-8}=\frac{h}{h}=\boxed{1}[/tex]

The question is wrong, the expression will not be in terms of h since it is a linear function.

An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal. The number of term 107 is 17th.

What is Arithmetic Sequence?

An arithmetic sequence is a sequence in which the difference between any two consecutive terms of the sequence is equal.

a_n = a₁ + (n-1)r

where,

a_n is the nth term of the sequence,

a₁ is the first term of the sequence,

r is a common difference between every two terms.

Given the formula for the nth term of the arithmetic sequence is,

[tex]a_n = 11+6(n-1)[/tex]

Now, the number of term that 107 will be,

107 = 11 + 6(n-1)

96 = 6(n-1)

16 = n- 1

n =17

Hence, the number of term that 107 is 17.

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Answer:  Choice D)  All rhombuses are squares

=============================================================

Explanation:

Let's go through the answer choices to see which are true and which are false.

Check out the venn diagram below showing the connection between the geometric shapes mentioned. The large outer rectangle represents the set of all quadrilaterals. Inside this is the oval representing all parallelograms. Then inside the oval is the set of rectangles and the set of rhombuses. The overlapping region of the rectangles and rhombuses is the set of squares, marked in blue.

As you can see, picking any square will get us a rhombus and a rectangle automatically. However, picking any rhombus will not guarantee it's a square.

Using the sine and cosine ratios, the true statement is: D. sin(J) = cos(L).

Sine ratio: sin ∅ = opp/hyp.

Cosine ratio: cos ∅ = adj/hyp.

In the image given, find sin(J) using the sine ratio:

∅ = J

Opposite = KL = √(219² - 178²) = 127.6 [Pythagorean theorem]

Hypotenuse = LJ = 219

Sin(J) = 127.6/219

Find cos(L) using the cosine ratio:

∅ = L

Adj = KL = 127.6

Hypotenuse = LJ = 219

Cos(L) = 127.6/219

Therefore, the true statement is: D. sin(J) = cos(L).

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Answer:

x=1

Step-by-step explanation:

20(3x-3/5) = 20(2x-2/4)

12x-12= 10x-10

12x-10x =12-10

x= 1

Answer:

Step-by-step explanation:

Solution

3x - 3       2x - 2

=====  =  ======                       Cross Multiply

5              4

4(3x - 3) = 5(2x - 2)                   Remove the brackets. Distributive Property

12x - 12 = 10x - 10                     Subtract 10 x from both sides

12x-10x - 12 = 10x-10x - 10       Combine

2x - 12 = - 10                             Add 12  to both sides

2x-12+12 = -10 + 12                   Combine  

2x = 2                                       Divide by 2

2x/2 = 2/2                                

Answer

x = 1

Step-by-step explanation:

1) the required equation in common form is:

(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;

According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:

(x+5)²+(y-2)²=6².

2) if the distance between two friends is:

[tex]d=\sqrt{(-5-1)^2+(2-1)^2}=\sqrt{37}, \ then[/tex]

this distance is longer than social (6 ft). For more info see the attachment.

Answer: (I am copying and pasting my answer from the same question you did before in case you are waiting for an answer on this instead.)

1/2

Step-by-step explanation:

To find the x-int of any equation, you will need to replace the y with a 0 since when the x-int is when y is 0.

8x+2y = 4 ➨ 8x+2*0 = 4

Now I will do 2*0 which anything times 0 is equal to 0. And we are left with the equation of:

8x = 4

Now I will divide both sides by 8, which isolates our x.

x = 1/2

The x-int is 1/2.

Answer:

(0.5 , 0) or (1/2 , 0)

Step-by-step explanation:

Any x-intercept must be at (x,0), so we substitute y=0 into the equation.

8x + 2(0) = 4

8x = 4

x = 1/2 = 0.5

Therefore, the x-intercept is at (0.5 , 0) or (1/2 , 0)

Answer:

The value of x is 200 in the equation 1/5x - 2/3y = 30, when y = 15

Step-by-step explanation:

Given

equation: x - 2/3y = 30

when y = 15

Plug in y:

1/5x - 2/3(15) = 30

1/5x - 10 = 30

add 10 to both sides,

1/5x - 10 + 10 = 30 + 10

1/5x = 40

multiply both sides by 5

1/5x * 5= 40 * 5

x = 200

Answer:

x = 200

Step-by-step explanation:

[tex]\frac{1x}{5} -\frac{2y}{3} =30[/tex]

Given that, y = 15.

So, to find the value of x you have to replace y with 15 and make the x the subject.

Let us do that now.

[tex]\frac{1x}{5} -\frac{2*15}{3} =30\\[/tex]

[tex]\frac{1x}{5} -\frac{30}{3} =30\\[/tex]

[tex]\frac{1x}{5} =30+ \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{30}{1} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{30*3}{1*3} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{90}{3} + \frac{30}{3}\\[/tex]

[tex]\frac{1x}{5} =\frac{120}{3}[/tex]

Use cross multiplication.

[tex]1x*3=120*5\\3x=600[/tex]

Divide both sides by 3.

x = 200

The length of the diagonal of the state of Wyoming is 457 miles.

The length of the diagonal of the diagonal can be determined using Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where:

√365² + 275² = 457 miles

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Answer:

if angle 2 is congruent to 6 them the slope of line o and q is equal

that is line o is parallel to q

the answer should be 5 inches I guess

Answer:

133 sodas

87 hot dogs

I've completed the work in the photo, just trying to reach the letter count lol

The fraction of the total number of marbles is left in the bag after removing and giving part to her friend is 3/8

let

Remaining marbles = x - 1/2x

= (2x-x) / 2

= x/2

= 1/2x

Number of marbles given to her friend = 1/4 of 1/2x

= 1/4 × 1/2x

= 1/8x

Number of marbles left in the bag = Remaining marbles - Number of marbles given to her friend

= 1/2x - 1/8x

= (4x-x) / 8

= 3x/8

= 3/8x

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Answer:

[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Step-by-step explanation:

Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ.  There are a few ways to go about this:

All of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.

Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle).  You might remember this through SohCahToa

[tex]sin(\theta)=\frac{opp}{hyp}[/tex]

In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so  [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] .  While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse.  So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].

While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)

This triangle represents the triangle for the unknown θ in the original sine function.  We're tasked with finding the secant of that particular unknown θ.

Working toward Secant

Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].

I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex].  From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).

Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse.  We already know the length of the hypotenuse, so we just need the length of the adjacent side.

Applying the Pythagorean Theorem

Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex]  (where c is the length of the hypotenuse, and a & b are the lengths of the legs)

Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]

...isolating "adj" by subtraction...

[tex](adj)^2=4-1\\(adj)^2=3[/tex]

...applying the square root property...

[tex]adj=\sqrt{3}[/tex]  or  [tex]adj=-\sqrt{3}[/tex]

Identifying which Quadrant the triangle is in

Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.

Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].

Finding the final solution

From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]

Note:  This method did not require knowing what the angle θ was.

If you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex]  is associated with [tex]\theta=30^o[/tex].  If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that  [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].

This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].

Answer:

Step-by-step explanation:

I answer for what I understand, the question is not clear.

2 divided by what times what equals 7

2 : x = 7

x = -2/-7

x = 2/7

-------------

check

2 : 2/7 = 7

2 * 7/2 = 7

7 = 7

the answer is good

When faced with an unknown variable in a maths problem, it is advised to find the subject formula and then use it to solve the equation to find the answer.

This refers to the type of variable in a given equation that has to be solved for because its properties or value is not known.

Hence, we can see that when faced with an unknown variable in a given math problem, it is better to find the subject formula, then input the value of this into an equation, to find the value of the variable.

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Answer:

21 grandchildren

Explanation:

2/7ths + 5/7th = all

5/7ths = 15   <- divide both sides by 3 to get 1/7th

1/7th = 3 (multiply both sides by 7 to get "1")

  7/7ths    = 21

so, eva has 21 grandchildren

Answer:

21

Step-by-step explanation:

If 2/7th of Eva's grandchildren live in one location, we know that 5/7th (the remaining portion of Eva's grandchildren) must live in the other location

Wales + Australia = all of the kids (100% = 1/1  (which is equal to 7/7) )

Wales + Australia = 7/7ths

{x is the total number of kids}

Australia = 5/7ths

15 = [tex]\frac{5}{7}x[/tex]   {multiply both sides by 7 to get rid of fraction}

105 = 5x   {divide both sides to find 1x}

21 = x

check:

2/7th of 21 = 6

5/7th of 21 = 15  {which we know}

6 + 15 = 21

21 = 21

(TRUE)

So, Eva has 21 grandchildren

hope this helps!!

Solution: Below! ^^

Detailed explanation:

Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.

First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!

This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.

Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!

What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.

_________

Hope I helped, best wishes & happy studies!

Please reach out to me if any queries arise.

_________

Answer:

Image attached below

Step-by-step explanation:

The line should cross y axis as -8 and should have a point of (0,-8)

The line should have a gradient / slope of 1/4

The multiplication of the expression will be 1215 cubic yd 2295 cubic inches.

It is also known as the product. If the object n is given to m times, then we just simply multiply them.

The expression is given below.

(9 cubic yd and 17 cubic in) × 135

On multiplication, we have

135 × 9 cubic yd and 135 ×  17 cubic in

1215 cubic yd and 2295 cubic inches

1215 cubic yd 2295 cubic inches

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The multiplication is 56,689,335 cu in

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

9 cu yd 17cu in

1 cu yard = 46656 cu inches

9 cu yard = 9*46656 = 419904 cu inches

Now, total inches

= 419904 cu inches + 17 cu in

= 419,921 cu inches.

and, the multiplication is

=56689335

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Answer:

5th or 6th grade

Step-by-step explanation:

The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.