Kathy invested $3000 at a rate of 7% for 4 years and 6 months. Find the amount she got back.

The value of the linear correlation coefficient r is of:

m = -1.

A linear equation is a special function that has the format of the equation given as follows:

y = mx + b.

The coefficients of the equation y = mx + b are given as follows:

In this problem, the points of the function are listed as follows:

(1 , 6) , (3 , 4) and (5 , 2)

From these three points, we can gather that when x increases by 2, y decays by 2, hence the slope of the linear function is given as follows:

m = -2/2 = -1.

Meaning that the linear correlation coefficient r of the linear function is of r = -1.

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a) At t = 0days : 300insects

b) The growth rate is 5.12% each day.

c) Population after 10days: P(10) =494.61

d) The population to reach 420 is equals roughly 70.129 hours

e) The insect population double in  t=6.020 days , which is 144.48 hours.

What is Population?

Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.

Given: t in days, P(t)=300e(0.05t).

(a) The total number of insects at time t=0 days is equal to

P(0)=300(1)

P(0) =300.

(b) The growth rate is calculated as the percentage increase over time, which is equal to-

P(t+1)/P(t)=300e(0.05(t+1))/300e(0.05t)

P(t+1)/P(t) =e^(0.05(1))

P(t+1)/P(t) =1.0512

Therefore, the growth rate is 5.12% each day.

(c) Population after 10 days.

P(10)=300e^(0.05*10)

P(10) =300(1.6487)

P(10) =494.61

(d) When P(t)=420, the population will reach 420,

or 300e0.05t=420,

take log

0.05t=log(1.4), or

t = 2.922 days,

for the population to reach 420.

equals roughly 70.129 hours

(e) When P(t)=2*300=600 the population will double.

300e^(0.05t)=600

=> e^(0.05t)=600/300=2

Take log

(log 0.05t=log(2)),

t=6.020 days , which is 144.48 hours.

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Answer:

43 cm^2

Step-by-step explanation:

Area of the triangle:

A = (1/2) x base x height

A = (1/2) x (2 cm + 4 cm) x 7 cm

A = (1/2) x (6 cm) x 7 cm

A = (1/2) x 42 cm^2

A = 21 cm^2

The area of the triangle is 21 cm^2

Area of the rectangle:

A = length x width

A = 11 cm x 2 cm

A = 22 cm^2

The area of the rectangle is 22 cm^2

Area of the figure = Area of the triangle + Area of the rectangle

Area of the figure = 21 cm^2 + 22 cm^2

Area of the figure = 43 cm^2

Arithmetic proportions are those whose means are not equal and are called discrete arithmetic proportions. On the contrary, if the means of the arithmetic proportion are equal, it is called continuous.

[tex]\bf\large{\underline{\fcolorbox{blue}{aqua}{Problem:}}}[/tex]

[tex] \sf8 : 2 :: x : 6[/tex]

Since the unknown term is an extreme and as we have seen, it is equal to the product of the means divided by the other extremes, we will have:

[tex]\boxed{\: x = \frac{8 \times6}{2} = \frac{48}{2} = 24 }[/tex]

Therefore, the resulting geometric proportion would be:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red\longmapsto \sf \orange{8 : 24 :: 6}[/tex]

Given the number of trees in the orchard, the number of trees in each row is 20 trees.

Assuming that the number of rows is represented as x, the number of trees would be 2 less than the number of rows which makes it:

= x - 2

The number of trees is:

x ( x - 2) = 440

x² - 2x - 440 = 0

Solving for r can then be done quadratically which gives us:
x = (2 ± √(2² - 4(1) (- 440)) / 2 (1)

= 22, and -20

The number of rows in the orchard cannot be negative so the number of rows is 22.

The number of trees is therefore:

= Number of rows - 2

= 22 - 2

= 20 trees

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The solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

We are given:

y = 1/8 x − 1                 ..............equation i.

− 5x + 4y = − 13          ..............equation ii.

We will use the substitution method to solve the given equation.

substitute the value of y from equation i in equation ii, and we will get;

− 5x + 4(1/8 x − 1) = − 13

− 5x + 1/2 x − 4 = − 13

(-10 + 1) / 2 x = -13 + 4

-9/2 x = -9

x = -9 * 2 / -9

x = 2

Put the value of x in equation i, we will get;

y = 1/8 *2 − 1

y = 1/4 - 1

y = 1 - 4 / 4

y = -3 / 4

So, the value of x = 2 and the value of y = -3 / 4.

Thus, the solution to the system of equations y = 1/8x −1 and −5x + 4y = −13 is (2, −3/4). Option D is correct.

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From the number line √90-√40 match with D, [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C, 2√27 -√48 match with E and [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.

In the given question we have to match the each expession with its position on the number line.

The given first expression is √90-√40.

We firstly simplifying the expression.

√90-√40=√9×10-√4×10

√90-√40=3√10-2√10

Taking common [tex]\sqrt{10}[/tex] on both side

√90-√40=√10(3-2)

√90-√40=√10

√90-√40=3.16

From the number line √90-√40 match with D.

The given second expression is [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex].

We firstly simplifying the expression.

We can write it as

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{5\times7}-\sqrt{6\times7}}{\sqrt{5}-\sqrt{6}}[/tex]

Taking common √7 on both side

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\frac{\sqrt{7}(\sqrt{5}-\sqrt{6})}{\sqrt{5}-\sqrt{6}}[/tex]

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}=\sqrt{7}[/tex]

[tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] = 2.65

From the number line [tex]\frac{\sqrt{35}-\sqrt{42}}{\sqrt{5}-\sqrt{6}}[/tex] match with C.

The given third expression is 2√27 -√48.

We firstly simplifying the expression.

We can write it as

2√27 -√48=2√3×9 -√16×3

2√27 -√48=2×3√3 -4√3

2√27 -√48=6√3 -4√3

Taking √3 common on both side, we get

2√27 -√48=√3(6 -4)

2√27 -√48=2√3

2√27 -√48=2×1.71

2√27 -√48=3.42

From the number line 2√27 -√48 match with E.

The given fourth expression is [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex].

We firstly simplifying the expression.

We can write it as

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{9\times6}-\sqrt{4\times6}}{\sqrt{2\times9}-\sqrt{2\times4}}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{3\sqrt{6}-2\sqrt{6}}{3\sqrt{2}-2\sqrt{2}}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\frac{\sqrt{6}(3-2)}{\sqrt{2}(3-2)}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}=\sqrt\frac{6}{2}[/tex]

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] =√3

[tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] = 1.71

From the number line [tex]\frac{\sqrt{54}-\sqrt{24}}{\sqrt{18}-\sqrt{8}}[/tex] match with A.

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Answer: d,c,e,

ur welcomee!

Answer:

there is no picture but m∠EBD = m∠EBD would be one of the best one as a guess to what the photo might be

Step-by-step explanation:

Point E is added to the given figure so that point E lies on segment BD and it is exactly halfway between points B and D

Answer: Par affluence

Step-by-step explanation: Car chaque 3 min le nombre de client augmentera

As per the given relation between ordered mg to kg and supplied mg to ml then weighs  40kg is equal to 2ml.

As given in the question,

Relation between mg to kg as per the ordered is given by ,

0.5 mg / kg

⇒ For 1 kg   = 0.5 mg

Relation between mg to ml as per the supplied is given by ,

10 mg / ml

⇒ 1 ml = 10 mg

Now for 40 kg weighs the relation is given by,

1 kg   = 0.5 mg

⇒ 40 kg   = ( 40 × 0.5) mg

⇒ 40 kg = 20 mg  ___(1)

And

1 ml = 10 mg

⇒ ( 2 × 1) ml = ( 2 × 10 ) mg

⇒ 2ml = 20mg    ____(2)

From  (1) and (2) we get ,

For 40 kg weighs we need 2ml.

Therefore, As per the given relation between ordered mg to kg and supplied mg to ml then weighs  40kg is equal to 2ml.

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The missing statement and the reason of LN bisects ∠MLO, LM≅LO are given and ∠OLN≅∠MLO is because of definition of angle bisector, LN≅LN is because it is common to both the angles ∠LNO AND ∠LNM, LO≅LM is because ΔLNO and ΔLNM both are congruent.

Given that:

LN bisects ∠MLO and LM≅LO

Prove that: ΔLMN ≅ ΔLON

In order to prove ASA congruence between the triangles we need two angles to be congruent to each other. When we look at the figure, we see that ∠LNO ≅ ∠LNM is a common angle in both the triangles.

Hence, using this we will prove that the triangles are congruent by ASA congruence rule.

In ΔLON and ΔLMN

Side ON ≅ Side MN

∠LNO ≅ ∠LNM ( ∵ common angle)

∠ONL ≅ ∠MNL (∵ Given as LN is the angle bisector of ∠MLO)

⇒ ΔLMN ≅ ΔLON ( By ASA congruence theorem).

Statement 1: LN bisects ∠MLO

Reason: Given.

Statement 2:  LM≅LO

Reason: Given.

Statement 3: ∠OLN≅∠MLO

Reason: Definition of angle bisector.

Definition of angle bisector: An angle bisector is defined as a line segment that bisects one of the vertex angles of a triangle.

Statement 4: LN≅LN

Reason: Common to both the angles ∠LNO AND ∠LNM and also these angles are 90° because angle made by angle bisector is always 90°.

Statement 5: LO≅LM

Reason: ΔLNO and ΔLNM both are congruent.

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Answer:

False

Step-by-step explanation:

x ≤ - 2

the symbol ≤ ( less than or equal to ) means that x can equal - 2 and any values to the left of - 2 on the number line.

- 1 is to the right of - 2 and - 3 is to the left , so

the values represented are - 2, - 3

The sentence which is true is 5+3×2²=17. The correct option is D.

Given the sentences is 5+3×22=256, 5+3×22=32, 5+3×22=180 and 5+3×2²=17.

We want to choose the sentence which is true.

An operator is a wildcard symbol used to indicate a mathematical operation that results in one or more mathematical objects leading to another similar object.

The first option is 5+3×22=256.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The first option 5+3×22≠256.

The second option is 5+3×22=32.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The second option 5+3×22≠32.

The third option is 5+3×22=180.

Solve the LHS, we get

5+3×22=5+66

5+3×22=71.

The third option 5+3×22≠180.

The fourth option is 5+3×2²=17.

Solve the LHS, we get

5+3×2²=5+3×4

5+3×2²=5+12

5+3×2²=17.

The fourth option 5+3×2²=17.

Hence, the sentence which is true from the given sentences is 5+3×2²=17.

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The equation of the line is option (C) y = 2x - 1

First we have to choose two points

The first point = (1, 1)

The second point = (2, 3)

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of first point

[tex](x_2,y_2)[/tex]  is the coordinates of the second point

Substitute the values in the equation

Slope of the line = (3-1) / (2-1)

= 2 / 1

= 2  

From the graph line is intersecting on y axis at y = -1

The slope intercept form of the line

y = mx + b

where m is the slope of the line

b is the y intercept

Substitute the values

y = 2x - 1

Hence, the equation of the line is option (C) y = 2x - 1

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Answer:

When the function is to be reflected over the x and y-axis, we write it as a reflection of a function over x = y, so it is divided into two parts or two cases y = x and y = − x. When the graph of function is reflected over y = x, then we will swap the coordinates of the x and y-axis with each other while their signs remain the same.

Step-by-step explanation:

The slope of the function 5x − 3y = −3 is 5/3 and the y-intercept of the function 5x − 3y = −3 is 1.

First, let us understand the slope intercept form;

The slope intercept form is simply a way of writing a line's equation so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are obvious.

We know that the slope intercept form of a line is y = mx + c where m is the slope of the line and b is the y-intercept of the line.

We are given;

5x − 3y = −3

- 3y = -5x - 3

3y = 5x + 3

y = 5/3 x + 1

Compare with y = mx + c, we will get;

m = 5/3

b = 1

So, the slope is 5/3 and the y-intercept is 1.

Thus, the slope of the function y = 2 + 34x is 5/3 and the y-intercept of the function y = 2 + 34x is 1.

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Answer:

the sum of squares kasi yan

Explanation:

first find the squareroot of a² and 100

the squareroot of a²=a

because a×a=a²

the squareroot of 100=10

because 10×10=100

second factor

(a + 10)² or (a + 10)(a + 10)

The solved answer for the given fraction expression in will be 2.6833.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Given X = 1/3

Y = 3/5

Z = 2 1/4 = 9/4

The value of X*Y*Z = (1/3*3/5*9/4)

= (20+36+105)/60

=161/60

=2.6833

Hence the solved answer for the given expression will be 2.6833.

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The values of x that make the equation true are approximately  5.7 and  -0.7  .

The given equation is :

[tex]\frac{x+1}{x} = \frac{2}{x-4}[/tex]

Using cross multiplication this can be written as:

or, ( x + 1 ) ( x - 4 ) = 2 x

or, x² + x - 4x - 4 = 2x

Putting all the like terms together.

or, x² + x - 4x -2x - 4 = 0

or, x² - 5x  - 4 = 0

Now we will use the quadratic formula to find the values of x :

[tex]{\displaystyle x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ \ }[/tex]

or, [tex]{\displaystyle x={\frac {5\pm {\sqrt {(-5)^{2}-4(1)(-4)}}}{2(1)}}\ \ }[/tex]

or, [tex]x = \frac{5+\sqrt{41}}{2} , \frac{5-\sqrt{41}}{2}[/tex]

or, x ≈ 5.7 , -0.7

The roots or zeros of the expression, which are also on the left side of the equation, are used to indicate the values of x that satisfy the equation.

There can only be two possible solutions to a quadratic problem. One argues that if there is only one remedy, there are many different causes of the problem. There are only four possibilities: one real double root, two complex solutions that appear to be complex conjugates of one another, two real solutions, or two real solutions if each of the coefficients has a real value.

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The area of the circle with radius 33 cm is 3419.5 square centimeters.

According to the question,

We have the following information:

Radius of the circle = 33 cm

We know that the following formula is used to find the area of the circle:

Area of the circle = π[tex]r^{2}[/tex] where r is the radius of the circle

There are two approximate values of π which are 22/7 and 3.14. In this case, we will use the value of π as 3.14.

So, we have the following expression:

Area of the circle = 3.14*33*33

Area of the circle = 3419.46 square centimeters

Rounding it off to one decimal point:

3419.5 square centimeters

Hence, the area of the circle with radius 33 cm is 3419.5 square centimeters.

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Answer: 59.28

Step-by-step explanation:

your welcome :)

Answer:

837/1150=0.727

Or 73%

Step-by-step explanation:

If the graph is passes through the origin then there is no y - intercept on the graph.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Usman graphs a proportional relationship.

And, Leandro graphs a line that passes through the origin.

Now,

Since, Leandro graphs a line that passes through the origin.

That's mean the graph has no any y - intercept.

Thus, If the graph is passes through the origin then there is no y - intercept on the graph.

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Answer: A &  D

Step-by-step explanation: Multiply length times width

l x w = a

Answer: c=54

Step-by-step explanation:

Answer:

y intercept: 1

X intercept: 4

Step-by-step explanation:

to find y intercept we set x to 0

0+4y=4

   /4.  /4

  y=1

y intercept is 1

Now for x intercept we set y to 0

x+4(0)=4

x=4

X intercept is 4

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