Last year, Alonzo had 30,00 to invest. He invested some of it in an account that pain 7% simple interest per year, and he invested the rest in an account that paid 5% simple interest per year. After one year, he revived a total of 1680 in interest. How much did he invest in each account?

Any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.

Here,

The n subsequent integers from -(n-1)/2 to (n+1)/2 have a sum of 0 if n is an odd number. Sum n is produced by translating the interval to the right by 1. Each positive sum is therefore a positive multiple of n.

If n is even, the sum of the next n even integers from -n/2-1 to +n/2 is n/2. Sum n+n/2 is produced by moving the interval to the right by 1. As a result, every positive sum is an odd multiple of n/2.

Therefore, any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

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Answer: x=-1

Step-by-step explanation:

1. -4(3x-7)=40

2. -12x+28=40

3. -12x=12

4. x=-1

Answer:

D

Step-by-step explanation:

if x = 0 or x = 3 the function doesn’t exist

If x = 1  Y = 0

The standard form of the number  [tex](1.5*10^(13))^2[/tex]  is  2.25×[tex]10^(26)[/tex] .

What is standard form of a number ?

 An equation, an expression, or a set of integers can all be written in standard form using the standard form approach. It is possible to express a number in a way that adheres to certain standards by writing it in its standard form. Standard form refers to any number between 1.0 and 10.0 that may be expressed as a decimal number and multiplied by a power of 10. The term "standard form" in this context refers to the act of condensing a particularly big expanded form of a number.

Here given is ,

=> [tex](1.5*10^(13))^2[/tex]

=> [tex]1.5^2[/tex] × [tex]10^(13)^2[/tex]

=> 2.25×[tex]10^(26)[/tex]

Therefore standard form of the number is  2.25×[tex]10^(26)[/tex].

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Answer:

12

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

x=12

Step-by-step explanation:

x/6=2

x=(2)(6),

x=12

A. The equations are given as follows:

B. The solutions are given as follows: x = 11, y = -5.

C. The angles are given as follows:

The two parallel lines, p and q, are cut by the transversal line, hence angles 2 and 3 are supplementary angles, and thus:

x - 9y + 1 + 11x + 2 = 180

12x - 9y = 177.

Angles 1 and 2 are alternate interior angles, meaning that they are congruent, hence:

6x + y - 4 = x - 9y + 1.

5x + 10y = 5.

x + 2y = 1.

x = 1 - 2y.

Replacing in the first equation, the value of y is given by:

12(1 - 2y) - 9y = 177

33y = -165

y = -165/33

y = -5.

Then the value of x is of:

x = 1 - 2y = 1 + 10 = 11.

The angle measures are given as follows:

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anwser

4

Step-by-step explanation:

17

Answer:

1,330.46

Step-by-step explanation:

v=h times pie times r squared.

since the diameter is 11 the radius is 5.5.

5.5x14=77

Now multiply that by pie and your answer is

1,330.46

Answer: 1330.46cm³

Step-by-step explanation:

The equation for a volumne of a cylinder is πr²h (r=radius h=height)

The radius is half of the diameter so the radius is 5.5

πx5.5²x14=1330.46

To use the delta method to approximate the standard error for the square root of the sample average g, we first need to calculate the sample average g.

A variation from precision or correctness is called an error. An error, then, is a mistake or a failure to perform an action appropriately. Errors can take place  person commits a calculation error, an equipment breaks down, or a person interprets information incorrectly.

Various factors might lead to errors. For instance, a person may make a mathematical error because they misunderstood the problem or made an error when doing the computation. A machine may break down due to a design error, normal wear and tear, or an outside event like a power loss. A person's prejudice may cause them to interpret information incorrectly.

How to solve?

This can be done by summing all the values in the sample and dividing by the total number of values in the sample. Next, we need to find the derivative of the function that describes the square root of the sample average g. This derivative will be used to approximate the standard error. To find the standard error, we then multiply the derivative by the standard deviation of the sample average g. This will give us an approximation of the standard error for the square root of the sample average g. It is important to note that this approximation will only be accurate if the sample is normally distributed and the sample size is large. Additionally, the delta method is only one way to approximate the standard error, and other methods may be more appropriate in certain situations.

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It will take 2.5 hours to make 32 1/2 cups of juice, in the fraction mode.

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.

Cye-Na is starting a juice stand. It takes her 15 minutes to prepare 3 1/4 cups of juice.

So in 15 minutes, she makes 13/4 cups of juice.

So for 1 cup she will take 15/ (13/4) minutes.

For 32 1/2 cup she will take 15 * (65/2)/ (13/4)

= 15*65*4/ 2*13

= 150 minutes.

Which is 2.5 hours

Hence, It will take 2.5 hours to make 32 1/2 cups of juice.

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Answer:

there is no value for x since there is no answer for the quetion

Step-by-step explanation:

Answer:

x = 70

Step-by-step explanation:

0.04 + 0.015x = 1.09 ( subtract 0.04 from both sides )

0.015x = 1.05 ( divide both sides by 0.015 )

x = 70

The x -intercept and y-intercept of the graph 9x + 3y = 18 are x = 2 and y  =6 respectively.

The y-intercept is the point where the graph intersects the y-axis. In other words, the y -intercept of a graph is the point where the graph crosses the y -axis. The y-intercept is the value of y when x = 0.

The x-intercept is where a line crosses the x-axis. In other words, the x-intercept of a line is the point on a graph where the line crosses an axis.

The x-intercept is the value of x when y = 0.

Therefore, let's find x-intercept of the graph

9x + 3y = 18

9x + 3(0) = 18

9x = 18

x = 18 / 9

x = 2

Hence, let's find the y-intercept.

9x + 3y = 18

9(0) + 3y = 18

3y  =18

y  =18 / 3

y = 6

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Answer:

The answer is zero.

Step-by-step explanation:

For the order of operations, division comes before subtraction, so take 8 and divide it by 4, then you have 2-2, which is zero. So your answer to the question should be zero.

Answer:

Step-by-step explanation:

BODMAS:
Brackets.Operation,division,multiplication,addition,subtraction

8/4 first = 2

2-2 = 0

The least natural number which when divided by 18,24 and 30 leaves the remainder 14,20,26 respectively is 356

To get the least natural number which when divided by 18,24 and 30 leaves the remainder 14,20,26 respectively. The steps required are as follows:

1. List the divisors:

18, 24, 30

2. Subtract the corresponding remainder of the divisors from them:

18-14 =4

24-20 = 4

30-26 = 4

3. Find the LCM of the divisors:

LCM 18, 24, 30 is 360

4. Subtract the number obtained in step 2 from the LCM:

360 - 4 = 356

Therefore, the number is 356

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The pH value of water when the H₃O⁺ is 1.0 x 10⁻⁷ will be 7.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The pH value of any ion is given as,

pH = - log [H₃O⁺]

The ions of H₃O⁺ is 1.0 x 10⁻⁷. Then the pH value is given as,

pH = - log [H₃O⁺]

pH = - log [1.0 x 10⁻⁷]

pH = - log [10⁻⁷]

pH = - (-7) log 10

pH = 7

The pH value of water when the H₃O⁺ is 1.0 x 10⁻⁷ will be 7.

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

Explanation:

We first need to find the slope

[tex](x_1,y_1) = (0,3) \text{ and } (x_2,y_2) = (4,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - 3}{4 - 0}\\\\m = \frac{8}{4}\\\\m = 2\\\\[/tex]

The y intercept is b = 3 due to the point (0,3). This is where the graph crosses the y axis. The y intercept always occurs when x = 0.

Since m = 2 and b = 3, we go from y = mx+b to y = 2x+3

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

Check:

I'll let you do these steps.

Another way to verify is to use graphing tools like GeoGebra, Desmos, or a TI83/TI84 graphing calculator.

Using the velocity - time graph given, the value of t is 180 seconds

Velocity-time graph is a plot between Velocity and Time. It shows the Motion of the object that moves in a Straight Line. Magnitude of Velocity at a given instant is equal to its Instantaneous Speed. It is drawn for 1-D motion only and can take both positive and negative values.

To calculate speed, distance and time, we can use the formula below

speed = distance / time

Harry walked back home at a constant speed of 2 m/s

This can be represented mathematically as

2 = 150 / t - 105

The value of t in the equation above

150 = 2(t - 105)

150 = 2t - 210

2t = 150 + 210

2t = 360

t = 360 / 2

t =  180 seconds

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The percentage of high school seniors and eighth grade students is the 40% and the 15%.

According to the statement

we have  to find that the percentage of high school seniors and eighth grade students.

For this purpose, we know that the

The percentage is a ratio expressed as a fraction of 100.

And with the given information,

the percentage is the used by the marijuana in the past year.

By the researchers,

the percentage of high school seniors in 2011 is 40%

And

the percentage of eighth grade students is 15%.

So, The percentage of high school seniors and eighth grade students is the 40% and the 15%.

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For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic at least as unlikely as or more unlikely than that provided by the sample.

What is two tailed test ?

In statistics, a two-tailed test is a procedure that determines whether a sample is greater than or less than a specific range of values by using the critical area of a distribution that is two-sided.

Main body:

Hence the p-value is the probability of obtaining a value for the test statistic at least as unlikely as or more unlikely than that provided by the sample.

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The distance between the two points (5,-3,-4) and (-1,-2,7) is:

d = √158

So the correct option is the last one.

The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by:

distance = √( (x₁ - x₂)² + (y₁ - y₂)² + (z₁ - z₂)²)

Here we want to find the distance between the two points (5,-3,-4) and (-1,-2,7), using the above formula we will get:

d =  √( (5 + 1)² + (-3 + 2)² + (-4 - 7)²)

d =  √( (6)² + (-1)² + (-11)²)

d =  √( 36 + 1  + 121)

d = √158

So the correct option is the last one.

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1. A = 45°         B = 110°

2. B = 88°        C = 44°

3. A = 59°        B = 48°        C= 73°

4. The measure of the exterior angle is 108°

5. The tornado's direction needs to change by 30°

The sum of interior angles of triangle is always equal to 180°.

Now let's apply it in the given questions.

1. A = x

B = x + 65

C = 25

So, x + x + 65 + 25 = 180

2x = 180 - 90

x = 90/2

x = 45°

2. x + 48 + x - 44 = 180

2x = 180 - 4

x = 176/2

x = 88°

3. x + 73 + x - 11 = 180

2x = 180 - 62

x = 118/2

x = 59°

4. Let the third interior angle be b.

2a + b = 180

b = 180 - 2a

now by applying angle sum property

a + 10 + 44 + 180 - 2a = 180

2a - a = 54

a = 54°

the exterior angle is 2a that is 54*2 = 108°

5. For the tornado to deviate and pass through radar station instead of cell phone tower the angle that needs to be made will be nothing but the third interior angle of the triangle as the tornado is at the vertex.

Let us suppose the angle to be y

so y + 75 + 75 = 180

y = 180 - 150

y = 30°

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A numeric variable is used with the VAR statement.

Given statement,

What type of variable is analyzed using a PROC TTEST? That is, what type of variable do we use with the VAR statement,

Here, we use;

→ Numeric Variable

Hence, a Numeric Variable type of variable is analyzed using a PROC TTEST.

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By using the concept of Pythagoras Theorem, the result obtained is

Distance between their tops is 13 ft.

What is Pythagoras Theorem?

Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of perpendicular and base.

The figure has been attached

Let the poles be represented by CD and AE and let AC represents the distance between their tops

Construction

A line from C parallel to DE (shown by a dotted line) is drawn

CD = 10 ft.

AE = 15 ft.

BE = 10 ft.

AB = AE - BE

     = 15 - 10

     = 5 ft.

DE = 12 ft.

BC = 12 ft.

[tex]\angle AED = 90^{\circ}[/tex] [ Angle between pole and ground is 90°]

[tex]\angle ABC = 90^{\circ}[/tex] [ Corrosponding angles are equal]

By Pythagoras Theorem,

[tex]AC^2 = AB^2+BC^2\\AC^2 = 5^2 + 12^2\\AC^2 = 25 + 144\\AC^2 = 169\\AC =\sqrt{169}\\[/tex]

AC = 13 ft.

Distance between their tops is 13 ft.

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Increasing the launch angle increases the maximum height. Increasing the launch angle increases the time of flight.

The starting vertical velocity determines the time in the air. Increasing the launch angle lengthens the duration in the air because steeper launch angles have a larger vertical velocity component.

The height of release and the angle of release is related. -The angle of release decreases as release height increases. - The angle of release rises as the height of release falls.

We observe that the projectile's maximum height is dependent on both initial speed and the angle of projection (), just as it is in the case of flight time. The projectile will rise to a larger height if its initial velocity is higher and its angle of projection from the horizontal is greater.

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The measure of the angle coterminal to - 118° is equal to 242°. (Correct choice: A)

Two angles are coterminal when they have different measures and the same direction in the terminal side. Two consecutive coterminal angles differ their measures in 360°. Then, we can determine the value of the coterminal angle by using the following formula:

θ' = θ + 360°

Where:

If we know that θ = - 118°, then the coterminal angle between 0° and 360° is:

θ' = - 118° + 360°

θ' = 242°

The measure of the coterminal angle is 242°.

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Answer:

x = - 1 ± 2[tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² + 2x = 7

solve using the method of completing the square

add ( half the coefficient ot the x- term )² to both sides

x² + 2(1)x + 1 = 7 + 1

(x + 1)² = 8 ( take square root of both sides )

x + 1 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 1 from both sides )

x = - 1 ± 2[tex]\sqrt{2}[/tex]