How much interest would you have if you deposited $200 that if you deposited $150? ​

Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

Step-by-step explanation:

[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]

The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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The negative solution is -2.21 and positive solution is 12.21

Given the quadratic equation expressed as:

x^2-10x-27 = 0

Find the solution using the general formula

x^2-10x-27 = 0

x = 10±√(10)²-4(1)(-27)/2

x =  10±√100+108/2

x =  10±√208/2

x = 10±14.422/2

Simplify

x = 10+14.422/2 and x = 10-14.422/2

x = 24.422/2 and -4.422/2

x = 12.21 and -2.21

Hence the negative solution is -2.21 and positive solution is 12.21

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The final percent of juice is 10%

We initially have one quart that is 40% juice and 60% water.

Then initially we have:

Then we add another 3 quarts of water, so the new mixture has:

So we have 4 quarts of mixture.

The new percentage of juice will be:

P = (0.4 quarts/4 quarts)*100% = 10%

The final percent of juice is 10%

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The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.

The standard equation of a line is ax + by + c = 0.

Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.

In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.

It is given that,

The equation of the given line is 3x + 4y = 24

Rewriting the given equation into the general form,

3x + 4y - 24 =0

On comparing with ax + by + c = 0,

a = 3, b = 4 and c = -24

So,

The x-intercept of the line (-c/a) = -(-24)/3 = 8 and

The y-intercept of the line (-c/b) = -(-24)/4 = 6

Therefore, the required x and y intercepts are 8 and 6 respectively.

(The graph showing the intercepts of the given line is shown below)

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Step-by-step explanation:

Find the slope between the two points given. Then, use the slope and point ONE to write the

equation of the

Answer:

True

Number of people is dependent

Answer:

true because it's hots and people cool of by getting by getting the water

The proofing for the triangle is illustrated below.

The proofing for a² + b² = c² in the triangle is illustrated.

It should be noted that the longest side in the triangle is the hypothenuse. The hypothenuse is gotten by finding the square root of the opposite and the adjacent.

Therefore, a² + b² = c²

Let's say a = 3 and b = 4, the value of c will be:

c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = ✓25

c = 5

Also, the square and triangle is illustrated and attached.

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The annual interest rate needed to reach the given amount in five years is 4.47%.

Hence, option B) is the correct answer.

Compound interest is expressed as;

A = P( 1 + r/n )^(nt)

Making rate r the subject of the formula;

r = n[ (A/P)^(1/nt) - 1 ]

Given that;

We substitute into our formular above

r = n[ (A/P)^(1/nt) - 1 ]

r = 12[ (2500/2000)^(1/(12×5)) - 1 ]

r = 12[ (1.25^(1/60) ) - 1 ]

r = 12[ 1.0037598 - 1 ]

r = 12[ 0.0037598 ]

r = 0.447

Next we convert to percentage

r = 0.447 × 100%

r = 4.47%

The annual interest rate needed to reach the given amount in five years is 4.47%.

Hence, option B) is the correct answer.

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The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.

Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.

Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

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Considering that the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

Hence, since the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

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Answer:   About the building of his bed

cancel by 3

Answer:

[tex]\sf \dfrac{8}{21}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]

When multiplying fractions, simply multiply the numerators and multiply the denominators:

[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]

Cancel the common factor x:

[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]

Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:

[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]

Cancel the common factor 3:

[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]

Answer:

A

Step-by-step explanation:

It is the quadratic parent function

The computation of the equations is illustrated below.

a. x - y = 1 .... i

x + y = -9 ..... ii

Subtract the equations

-2y = 10

y = 10/-2 = -5

Since x - y = 1

x - (-5) = 1

x + 5 = 1

x = 1 - 5 = -4

b. 3x + 2y = -9

x - y = -13

Multiply equation i by 1

Multiply equation ii by 3

3x + 2y = -9

- 3x - 3y = -39

5y = 30

y = 6

Since x - y = 13

x - 6 = 13

x = 13 + 6 = 19

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Answer: B

Step-by-step explanation:

The vertical asymptotes are at x=-4 and x=1, so the denominator needs to have factors of (x+4) and (x-1).

This eliminates everything except for B.

The length of ladder is 30 ft.

The formula below can be used in solving the problem

Tan (∅)= [tex]\frac{opposite}{adajacent}[/tex]

∅=70°

opposite = BC

Adjacent  = 12 ft

70°= opposite/ 12

opposite= 32.96 ft

Therefore, The length of ladder is 30 ft.

NOTE; Since the actual diagram can not be found i solved another on on the same topic

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CHECK COMPLETE QUESTION BELOW:

Consider the diagram shown where a ladder is leaning against the side of a building. the base of the ladder is 12ft from the building. how long is the ladder? (to the nearest ft)

a. 25ft

b. 30ft

c. 35ft

d. 40ft

The exponential form of 6 × 6, is written as: 6².

Repeated multiplication involving base exponents and base can be written in exponential form, such as: a × a × a = a³.

Given the expression, 6 × 6, the number 6 will be the base while 2 will be the exponent if we want to express it in exponential form. Therefore:

6 × 6 = 6².

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The main difference between the two nets is the top face.

The net of a box with a closed top is a 3-dimensional figure that is made up of 6 faces. The faces are all rectangles, and they are connected to each other by flaps. The flaps are the parts of the net that fold over to create the closed top.

The net of a box with an open top is a 3-dimensional figure that is made up of 5 faces. The faces are all rectangles, and they are connected to each other by flaps. However, the top face of the net is not a rectangle. Instead, it is a trapezoid. The trapezoid is created by the flaps that fold over to create the open top.

As you can see, the main difference between the two nets is the top face. The top face of the net of a box with a closed top is a rectangle, while the top face of the net of a box with an open top is a trapezoid.

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Answer:

240 pages

Step-by-step explanation:

Let x = the TOTAL number of pages in the book. So we'll add up all her reading for the week and it should equal x, the total number of pages.

see image.

Answer:

Step-by-step explanation:

let x be the price of ticket,then

120-x=3(80-x)

120-x=240-3x

3x-x=240-120

2x=120

x=120/2=60

Price of ticket=$60

Mr.Chandra has 80-60=20 $ after buying the ticket.

Answer:

60 cubic inches

Step-by-step explanation:

You multiply 3 and 4 to get 12, then 12 and 5 to get 60

3 x 4 x 5 = 60

The volume of a solid exists the measurement of how much area an object brings up. It exists measured by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

Volume exists as a three-dimensional measurement; that exists, it measures the collective length, width, and height of a figure. Because planes, polygons, and other two-dimensional figures don't contain height, they contain no volume. Only solids and figures with dimensions more significant than or equivalent to three have volume.

The volume of a solid exists as the measurement of how much space an object brings up. It exists estimated by the number of unit cubes it brings to fill up the solid.

Volume of a solid = 5 [tex]*[/tex] 3 [tex]*[/tex] 4 = 60 cubic inches

Therefore, the correct answer is option d) 60 cubic inches.

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Answer:

C

Step-by-step explanation:

Equation 1:

[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]

Equation 2:

[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]

The value of the probability is 0.54

The given parameters are:

P(A) = 0.35

P(B) = 0.54

From the question, we understand that the events are independent.

This means that

P(B|A) = P(B)

Substitute P(B) = 0.54

P(B|A) = 0.54

Hence, the value of the probability is 0.54

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The net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

A net is a two-dimensional representation of a three dimensional solid object showing its faces.

Examples of material which can have nets are

Now, for a pyramid, we know that a pyramid is a three dimensional solid object that has one square base and four triangular sides.

So, when a pyramid is split into its net, it will have one square at the center and four triangles on the sides of the squares.

So, the net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

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Answer:

B

Step-by-step explanation:

You need to use the net that only have 1 square because a pyramid only has 1 square, it also has all the triangle sides needed which is 4. You can use a model to make a pyramid out of this net

1a.The mean is 8.

b. The median is 8.

c. The mode is 8.

2. The shape of the data is: perfectly symmetrical distribution.

To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.

Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12

Mean = (96)/12

Mean = 8

The median is the center of the data when it is ordered.

Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15

The center (median) is the average of the two center values = (8 + 8)/2 = 16/2

Median = 8

The mode of the data is 8, because 8 appeared most in the data set.

The mean is 8.

The median is 8.

The mode is 8.

Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.

Therefore the shape of the data is: perfectly symmetrical distribution.

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The simplified firm of the ratio 0.40 to 0.60 is 2 : 3

0.40 : 0.60

= 0.40 / 0.60

divide both numerator and denominator by 0.20

= 2 / 3

= 2 : 3

Therefore, the simplified form of the ratio 0.40 to 0.60 is 2 : 3

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Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]