Marsha deposited $10,000 into a savings account five years ago. The simple interest rate is 4%. How much money did Marsha earn interest

The magnitude of vector is 8.24 and angle is 75.9638.

What is vector?

A vector could be a amount that not solely describes the magnitude however additionally describes the movement of an object or the position of an object with reference to another purpose or object.

Main body:

we know that the magnitude of vector is found out by,

| u | = [tex]\sqrt{i^{2}+j^{2} }[/tex]

so here , u = 2i + 8j

|u| = [tex]\sqrt{2^{2} +8^{2} }[/tex]

|u| = [tex]\sqrt{68}[/tex]

|u| = 8.24

now to find the direction , angle

tan∅ = j/k

tan∅ = 8/2

∅ = tan⁻¹ (4)

∅ = 75.9638°

Hence , direction angle of the following vector is ∅ = 75.9638°

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Answer: 3 11/15  please mark brainliest If I helped you.

the question is kayar and 12 by 5 miles on Monday and 21 by three miles on Tuesday what is the total distance in miles kayuren during those two days first phone on Monday how much run that was 12 by 5 miles on Tuesday Shirin to 1 by 3 minus now this whole part and fractional part are written separately so this can be converted into a mixed fraction like when a number is of the form of p by see that is one whole number and fraction then it is written as a + b by c so we can write Monday that was 12 by 5 miles that is

12 by 1 + 2 by 5 that will be 5 will be LCM of 5 + 2 will be 7 by 5 MI and Tuesday it will be 21 by 3 that is 2 + 1 by 3 3 will be the LCM of 3 and 22 will be 6 plus one that is 7 by 3 minus in question is asked that what was the total distance kayar and thus during today's so Monday plus Tuesday will be the total total 27 by 5 + 7 by 3 that will be equal to LCM will be 15 this will be X 307 into 3 + 7 and 25 that

is 21 + 45 upon 15 that will be equal to 56 upon 15 Now since we have to give answer in mixed fraction in whole number and fraction this a bi bi can be divided into a whole number and fraction part when divided by be the remainder is remainder is written here b is written here and question is written here so 56 by 15 can be written as 15 and 23 is 45 three years question remainder will be 11:00 that is 56 - 45 and below will be the denominator will be 15 so this is our answer and the correct

Therefore ,the water level is rising  by 0.1388 ft/min when h is 1.2 feet deep and  the water is being pumped at rate of 0.8625 cubic feet per min when water is rising at 3/8 inch/min

A three-dimensional space's occupied volume is measured. It is typically quantified using a variety of imperial or US-standard units as well as SI-derived units. The concept of length and volume are related.

Here,

Given: A trough has a 12 foot length and a 3 foot top width. Three-foot-high isosceles triangles make up its ends. 12f 3 ft 31

So the first case:

using this we find the rate of Volume,

So,

=> dV/dt = length * height *dh/dt

=> dV/dt = 12 * 1.2 *dh/dt

=> 2 = 12*1.2* dh/dt

=> 2 = 14.4 * dh/dt

=>dh/dt = 2/14.4

=>dh/dt = 0.1388 ft/min

Therefore ,the water level is rising  by 0.1388 ft/min when h is 1.2 feet deep .

Second case:

Since water level is rising by 3/8 inch per min =0.03125 feet/min

=> dV/dt = length * height *dh/dt

=> dV/dt = 12 * 2.3 *0.03125

=>dV/dt = 0.8625 cubic feet per min

Therefore , the water is being pumped at rate of 0.8625 cubic feet per min.

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Answer:

You did not provide the choices, but the first step to find the result of the operation using standard algorithm is to set up a long division

Analyzing the events a and b given in the question , the events are not mutually exclusive events, which are also called intersecting events in terms of venn diagram.

Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events. The probability of an occurrence if A and B are mutually exclusive is indicated by P(A Or B) or P. (A U B).

Mutually inclusive events permit the occurrence of both occurrences simultaneously or inside a single trial. It refers to events that are required to take place simultaneously by a rule or a natural law. When two occurrences are mutually inclusive, they cannot happen separately.

Here, the events a and b can occur simultaneously, since we can get a number greater than 3 and less than 5 at the same time while rolling a dice randomly.

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Continental glacier ice flows from the region where it is thickest toward the edges where it is thinner. In the central thickest parts, the ice flows almost vertically down toward the base, while at the edges of the glacier, it flows horizontally out toward the margins.

Glaciers generally advanced from the direction where the contour lines on the landforms are closest together (steep slope) toward the direction where the contour lines on the landforms are farther apart (gentle slope).

A continental glacier originating in far Northern Canada began to move South towards the Northeastern United States. The ice sheet crept slowly forward, scraping off the loose rock materials and gouging the bedrock beneath the ice as it advanced.

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Answer: 19/7

Step-by-step explanation:

Your goal is to isolate x or get x by itself.

Move all other variables to the opposite side.

70x+10-10=200-10

70x=190

Divide both sides by 70

x= 19/7

Answer:

[tex]x= \frac{19}{7}[/tex]   OR   [tex]2 \frac{5}{7}[/tex]

Step-by-step explanation:

To do this you need to:

  1. Subtract 10 from both sides {As shown below}

[tex]70x+10-10=200-10[/tex]

  2. Simplify {As shown below}

[tex]70x=190[/tex]

   3. Divide both sides by the same factor {As shown below}

[tex]\frac{70x}{70} = \frac{190}{70}[/tex]

    4. Simplify {As shown below}

        {a. Cancel terms that are in both the numerator and the denominator}

        {b. Divide the numbers}

[tex]x= \frac{19}{7}[/tex] OR [tex]2 \frac{5}{7}[/tex]

{Please give Brainliest}

Answer:

Step-by-step explanation:

Answer:

Slope of the line, [tex]m_{1} = -\frac{1}{2}[/tex]

Slope of parallel line, same as the slope above

Slope of perpendicular line, [tex]m_{2} = 2[/tex]

Step-by-step explanation:

Parallel line: [tex]m_{1} = m_{2}[/tex]

Perpendicular line: [tex]m_{1} * m_{2} = -1[/tex]

[tex]y = mx +b[/tex]

Where, m = slope

Thus, in the equation provided, the slope is [tex]-\frac{1}{2}[/tex]

Finding the slope of perpendicular line:

[tex]m_{1} * m_{2} = -1\\m_{2} = \frac{-1}{m_{1}}\\m_{2} = -1 * -2\\m_{2} = 2[/tex]

(a) Determinant: det(A) = -18; Rank: rank(A) = 4. The determinant and rank are non-zero, so the vectors are linearly independent.(b) Determinant: det(A) = 0; Rank: rank(A) = 3. The determinant is zero and the rank is less than 4, so the vectors are linearly dependent.

(a)

2 4 5 -3

-3 2 7 0

9 2 4 6

3 2 -6 5

Det = -18

(b)

1 -1 3 2

-1 2 4 -5

3 -4 2 9

7 2 1 3

Det = 0

The determinant and rank of the vectors can be used to determine whether or not they are linearly dependent. If the determinant is non-zero and the rank is equal to the number of vectors, then the vectors are linearly independent. If the determinant is zero and the rank is less than the number of vectors, then the vectors are linearly dependent.

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The function  y = x⁴ + 7 is decreasing on (-∞ , 0) and increasing on (0 , ∞) .

In the question ,

it is given that ,

the function is y = x⁴ + 7 ,

we have to show that function y  is decreasing on (-∞ , 0) and increasing on (0 , ∞) .

differentiating the function y = x⁴ + 7 , with respect to x ,

we get ,

y'(x) = d/dx(x⁴ + 7) = 4x³

putting y'(x) = 0 , then 4x³ = 0 ;

x³ = 0 that means , x = 0 .

thus , the critical number is ⇒ x = 0 .

y'(-1) = 4(-1)³ = -4   So , it is decreasing

y'(1) = 4(1)³ = 4    So , it is increasing .

Therefore , the function y is decreasing in (-∞ , 0) and increasing in (0 , ∞) .

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Answer:

The area of the square is larger than the area of the rectangular field.

This hypothesis is a false positive.

What is a false positive result?

When a scientist concludes something is real when it is actually wrong, this is known as a false positive (also called a type I error). A "false alarm" is a false positive. Saying something is false when it is truly true is known as a false negative (also called a type II error). A false negative indicates that something was missed or that something that was present was not discovered.

A false positive is getting a positive result that should be negative (this is also known as a “type I error”). A false negative is getting a negative result that should be positive (this is also known as a “type II error”).

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Answer: 50.24

Step-by-step explanation:

The formula to find the circumference of a circle is two pi r. So we just have substituted value into our formula. So we have To multiply by pi, so let's use 3.14 multiplied by our sequence to eight, so this is equal to 16, multiply by 3.14, which is equal to 50.24.

Answer:

Square Root of 80 in Radical Form: 4√5.

Step-by-step explanation:

√80 = 4√5. Meaning that the square root of 80 in radical form 4 √ 5.

OR Decimal form: 8.944

(Not sure if you wanted it in radical form... I also included it in decimal form)

The height of Jane will be 38 9/30 inches.

The process of combining two or more numbers is called the Addition.

Given that;

Trina is 54 3/4 inches tall. Morgan is 1 1/2 inches taller than Trina and Jane is 1 1/5 inches taller than Morgan.

Now,

Since, Trina is 54 3/4 inches tall.

And, Morgan is 1 1/2 inches taller than Trina.

Hence, The height of Morgan = 54 3/4 + 1 1/2

                                              = 219/4 + 3/2

                                              = 219/4 + 6/4

                                              = 225/4

And, Jane is 1 1/5 inches taller than Morgan.

Hence, The height of Jane = 225/4 + 1 1/5

                                          = 225/4 + 6/5

                                          = (1125 + 24)/30

                                          = 1149/30

Thus, The height of Jane = 38 9/30 inches

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The fraction of the package of raisins Ashley left with will be equal to 7/18.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Amount of raisins used for fruit cake = 1/2

Amount of raisins used for muffins = 1/9

Then, the amount of raisins left will be,

1 - (1/2 + 1/9)

= [18 - (9 + 2)]/18

= (18 - 11)/18

= 7/18

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To determine the maximum or minimum value of a given function, Lagrange multipliers are used.

What is langrange multipliers?

Let's set up everything now. We want to optimize (i.e., find the minimum and maximum value of) a function, f, under the condition that g (x, y, and z) = k. (x, y, and z). Once more, the equation that describes the boundary of a region may or may not be the constraint. Although the process is actually quite simple, there are times when the workload seems quite overwhelming.

Solve the following system of equations.

∇f(x,y,z) = λ

∇g(x,y,z)

g(x,y,z)= k

If there are minimum and maximum values, enter them into f(x,y,z) along with all of the solutions (x,y,z) from the first step.

∇ g ≠ → 0 at the point.

The constant, λ, is called the Lagrange Multiplier.

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All the possible values for the number 'x' will be less than or equal to 1,350.

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 remainder of a number and 5 in addition to 25 is something like 45.

Let the number be 'x'. Then the inequality is given as,

x / (5 + 25) ≤ 45

x / 30 ≤ 45

x ≤ 1,350

All the possible values for the number 'x' will be less than or equal to 1,350.

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Step-by-step explanation:

1/2×2 sin 5x. cosx

=1/2×sin (5x+x)+cos (5x-x)

=1/2 sin 6x +sin 4x

The representation table given indicates that the function is linear, as the difference between consecutive y-values (9-8, 8-7, and 7-6) is constant. Therefore, we can represent the function with a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the function, we can use the x- and y-values given in the table to solve for m and b. For example, using the x- and y-values (-3,9) and (-2,8), we can solve the equation 9 = m(-3) + b for m and b:

9 = -3m + b

8 = -2m + b

Subtracting the second equation from the first equation gives us:

1 = -m

So the slope of the function is -1. Substituting this value back into either equation gives us:

9 = -3(-1) + b

9 = 3 + b

6 = b

So the y-intercept of the function is 6. Therefore, the equation of the function is y = -1x + 6.

The other two representations can be solved in the same way to find the equations of those functions.

Answer:

Step-by-step explanation:

You could use 1 3/4's of a cup and 8 1/4's of a cup.

1 of the 3/4 cups is 3/4 so that covers the 3/4 of the cups of how much flour is needed.

8 of the 1/4 cups is 8/4 which is equal to 2 so that covers the rest of the flour needed.

And 2 + 3/4 is 2 3/4 which is the amount of flour that is needed.

OR

You could use 3 3/4's of a cup and 2 1/4's of a cup.

3/4 + 1/4=4/4

3/4+1/4=4/4

4/4 + 4/4 is the same thing as 1+1 which is 2, so that covers the 2 cups of the flour that is needed, and then you add another 3/4, now you have

2 3/4, which is the amount of flour needed.

(I think that there might be other ways/combinations but I only included 2..)

∛8.1 = 2.00829885025 it has accuracy up to 6 places which means the error is less than at least 8 decimal places .

For example ,

Using the first three terms of the Taylor series expansion of

f(x)=∛x  centered at

x = 8, approximate inmate ∛8.1 :

f(x) = ∛x≈2  + (x-8) / 12 - (x-8)² / 288

the first three terms shown will be sufficient to provide a good approximation for ∛x . Evaluating this sum at x = 8.1 gives an approximation for ∛8.1

f(8.1) = ∛8.1 ≈2 + (8.1 -8)/ 12 - (8.1 - 8 )² / 288

       = 2.00829861111

   ∛8.1 = 2.00829885025  

With just three terms, the formula above was able to find the approximate accuracy in ∛8.1 to six decimal places .

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We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

What is Normally distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

results obtained are 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15

            [tex]\overline {X} = \frac{0.06 + 0.11 + 0.16 + 0.15 + 0.14 + 0.08 + 0.15}{7}\\\\ \overline {X} = 0.1214\\[/tex]

            [tex]S=\sqrt[2]{\frac{0.0091}{n-1} } \\\\S= \sqrt[2]{\frac{0.0091}{7-1} }\\\\S=0.039\\\\n-1 = 6\\\\E= 3.143 * \frac{0.039}{\sqrt[2]{7} } \\\\E= 0.0462\\\\[/tex]

The confidence interval ⇾ 0.0752 < µ < 0.1676

We cannot safely conclude that this requirement is being met because 0.165 is contained in the confidence interval.

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Answer:

Step-by-step explanation:

its 2

Answer:

-11

Step-by-step explanation:

To find f(3), we simply need to plug 3 in for x in the function f(x) = -3x-2. This gives us:

f(3) = -3(3) - 2 = -9 - 2 = -11

Therefore, the value of f(3) is -11.

Answer:

DF is congruent to FG

Step-by-step explanation:

segment subractive property means to subract a part of a segment from another if they are equal. If we do this in this situation, we will see that DF is congruent to FG

       Statement                                        Reason                          

By using p-value hypothesis test,we find that the mean delivery time actually exceeds 34 minutes.

It is a number calculated from a statistical test that describes how you are found a particular set of observation ,if the null hypothesis were true.P-values are used in hypothesis testing to help to decide whether to reject the null hypothesis .The lower the p-value the greater the statistical significance of observation differences.

The null hypothesis states that as the assumption that there is no change , no difference and no relationship between two variables.The alternate hypothesis stated that there is a change, difference and relationship between two variables or group.

let we use p-value test

Let u=average time spend on deliveries

so,null hypothesis H0;u[tex]\leq[/tex]34 minutes

    alternate hypothesis HA; u >34

Now the decision rule based on the p-value to whether null hypothesis should be accepted or rejected is given by;

.If hypothesis p-value of test statistical is less than the level of significance,then we will our null hypothesis.

.If the p-value of test statistical is more than the level of significance.then we will not reject our null hypothesis.

Here, we assume that the level of significance is 5%.

Since the p-value test statistics is less than the level of significance as 0.029<0.05.

so,we have evidence to reject our null hypothesis.

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Answer:

  -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

Step-by-step explanation:

You want to simplify (7x+5y)^3–(7x–5y)^3–30y(7x+5y)(7x–5y)^3.

We recognize that there are some repeated expressions here that may make it easier to simplify this without multiplying it all out.

Let a = 7x+5y, b = 7x -5y. Then the expression becomes ...

  a³ -b³ -30y·a·b³

  = (a³ -b³) -30yb²(ab)

  = (a -b)(a² +ab +b²) -30yb²·ab

Now ...

  a -b = (7x +5y) -(7x -5y) = 10y

  a² +b² +ab = (7x +5y)² +(7x -5y)² +(7x +5y)(7x -5y)

     = (7x)² +2(7x)(5y) +(5y)² +(7x)² -2(7x)(5y) +(5y)² +(7x)² -(5y)²

     = 3(7x)² +(5y)² = 147x² +25y²

So the first pair of terms expands to ...

  a³ -b³ = 10y(147x² +25y²) = 1470x²y +250y³

The last term becomes (with a positive sign) ...

  30yb²(ab) = 30y(7x -5y)²((7x)² -(5y)²)

     = 30y((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) . . . . see comment below

     = 30y((7x)⁴ -(5y)⁴ -70xy((7x)² -(5y)²))

     = 72030x⁴y -18750y⁵ -102900x³y² +52500xy⁴

Putting it all together gives ...

  = -72030x⁴y +18750y⁵ +102900x³y² -52500xy⁴ +1470x²y +250y³

__

Additional comment

The difference of squares form is used several times here:

  p² -q² = (p -q)(p +q)

The expression ((7x)² -2(7x)(5y) +(5y)²)((7x)² -(5y)²) is decomposed to ...

  ((7x)² +(5y)²)·((7x)² -(5y)²) - 2(7x)(5y)((7x)² -(5y)²)

This lets us use the difference of squares form to simplify at least part of the expression. This whole thing gets multiplied by -30y.