Larry Mitchell invested part of his $32,000 advance at 4% annual simple interest and the rest at 6% annual simple interest. If his total yearly interest from both accounts was $1,340, find the amount invested at each rate

Answer:

Step-by-step explanation:

To find the average speed for the round trip, we can use the formula:

average speed = total distance / total time

We know that Steve drives 5 miles to school and 5 miles back home, so the total distance is:

total distance = 5 miles + 5 miles = 10 miles

To find the total time, we need to calculate the time it takes for Steve to drive to school and the time it takes for him to return home. We can use the formula:

time = distance / speed

For the first part of the trip, Steve drives 5 miles at 10 mph, so the time it takes is:

time to school = 5 miles / 10 mph = 0.5 hours

For the second part of the trip, Steve drives 5 miles at 40 mph, so the time it takes is:

time to home = 5 miles / 40 mph = 0.125 hours

The total time for the round trip is the sum of the time to school and the time to home:

total time = time to school + time to home

total time = 0.5 hours + 0.125 hours

total time = 0.625 hours

Now we can calculate the average speed using the formula:

average speed = total distance / total time

average speed = 10 miles / 0.625 hours

average speed = 16 miles per hour (rounded to the nearest integer)

Therefore, Steve's average speed for the round trip is 16 mph.

Answer:

16 mph

Step-by-step explanation:

Answer:

y = e^-4x

Step-by-step explanation:

It might be right im not sure

The simple interest on $3,575 at 4 3/4% for 80 days is $37.22.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans.

To determine the simple interest on $3,575 at 4 3/4% for 80 days, we can use the formula: Simple Interest = Principal x Rate x Time. The Principal is $3,575, the Rate is 4 3/4% (or 0.0475 as a decimal), and the Time is 80 days.

Plugging these values into the formula. The Simple Interest will be:

= $3,575 x 0.0475 x 0.2192

= $37.2229

= $37.22.

Translated question on SI "Determine according to the banking system, the simple interest on $3575 at 4 3/4% for 80 days".

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Answer:

you shouldn't be cheating kid

Answer:

29

Step-by-step explanation:

6 + 3 x 9 - 4

6 + 27 - 4

33 - 4

=29

Answer:

The 90% confidence interval for the proportion of out of state visitors at a national park is (0.3577, 0.4723).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 200, \pi = \frac{83}{200} = 0.415\)

90% confidence level

So \(\alpha = 0.1\), z is the value of Z that has a pvalue of \(1 - \frac{0.1}{2} = 0.95\), so \(Z = 1.645\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.415 - 1.645\sqrt{\frac{0.415*0.585}{200}} = 0.3577\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.415 + 1.645\sqrt{\frac{0.415*0.585}{200}} = 0.4723\)

The 90% confidence interval for the proportion of out of state visitors at a national park is (0.3577, 0.4723).

Answer:

-14x² - x + 4

Step-by-step explanation:

(-10x² + 5x - 3) - (4x² + 6x - 7)

= (-10x² + 5x - 3) - (+4x²) - (+6x) - (-7)

= (-10x² + 5x - 3) -4x² -6x +7

= -10x²-4x² +5x-6x -3+7

= -14x²  - x + 4

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Using the same-side interior angles theorem,

\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)

Using vertical angles,

\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)

The value of the angle θ is approximately 24.2 degrees to 1 decimal place.

In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. Given that tan θ = 23/52, we can find the value of the angle θ.

To find the value of θ, we can use the inverse tangent or arctan function. Taking the inverse tangent of both sides of the equation, we have:

θ = arctan(23/52)

Using a calculator or trigonometric tables, we can evaluate the inverse tangent of 23/52. The result is approximately 24.2 degrees.

Note that in the context of a right-angled triangle, the tangent function is defined for acute angles (less than 90 degrees). Since 0 degrees is the smallest possible angle, it is considered an acute angle in this case.

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Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

See below

Step-by-step explanation:

a)

\( \frac{20}{ \sqrt{10} } = \frac{20 \sqrt{10} }{ \sqrt{10} \times \sqrt{10} } = \frac{20 \sqrt{10} }{10} = 2 \sqrt{10} \)

b)

\( \frac{ \sqrt{2} }{2 \sqrt{5} - 1 } \\ \\ = \frac{ \sqrt{2} \times (2 \sqrt{5} + 1 )}{(2 \sqrt{5} - 1)(2 \sqrt{5} + 1) } \\ \\ = \frac{ \sqrt{2} \times 2 \sqrt{5} + \sqrt{2} \times 1 }{(2 \sqrt{5} ) ^{2} - (1)^{2}} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{20 - 1} \\ \\ = \frac{ 2 \sqrt{10} + \sqrt{2}}{19} \\ \\ equating \: it \: with \: \\ \frac{ a + \sqrt{b}}{c} \\ \\ a = 2 \sqrt{10} \\ \\ b = 2 \\ \\ c = 19\)

Answer:

The above answer is correct

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

$ 22.99 × 5 = $114.95

before tax $114.95

sales tax rate= 7.25%

convert 7.25 into a decimal 0.0725

$114.95 × 0.0725 = 8.333875

114.95 + 8.33 = 123.28

sales tax converted 0.0725 = $8.33

after tax price $123.28

Answer is A. $123.28

The end behavior of the function f(n) = 3(n + 2)²(n - 3)(n - 2) is given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

The function for this problem is given as follows:

f(n) = 3(n + 2)²(n - 3)(n - 2).

Considering the degree, the function can be interpreted as follows:

\(3n^4\)

(for the limit when the input goes to infinity we consider only the term with the highest degree).

The leading coefficient is positive and the exponent is even, hence the end behavior is given as follows:

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The sequence of the number of circles indicates that for the 10th case,  the number of circles are; 111 circles on the lower left and 111 circles on the top right

Please find attached a drawing of the pattern for the 10th case, created with MS Word

A sequence is an orderly arrangement of values or objects following a specified pattern.

The first pattern indicates that the number of circles in the first column on the left are 2. The number of circles located in the second row from the left side are 3

The second pattern indicates that the number of circles in the first column on the left are 3. The number of circles located in the second row from the left side are 4

The sequence of pattern in the nth case is therefore;

The number of circles in the first column on the left in the nth case are n + 1. The number of circles located in the second row from the left side are n + 2, and the number of squares circles between the column on the left and the row of circles on the top are n each, which indicates;

The number of circles in the first column on the left in the 10th case are 10 + 1 = 11. The number of circles located in the second row from the left side are 10 + 2 = 12

The dimensions of the square of circles to the left of the first column and above which the horizontal row of circles at the top are located are each 10 units wide and 10 units in height

Please find attached the drawing of case 10 creates with MS Word

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The order of the matrices of each product is given as follows:

AB is nonexistent, BA is nonexistent.

Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.

For the product AB, we have that:

Hence the product is nonexistent.

For the product BA, we have that:

Hence the product is nonexistent.

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Answer:

21%

Step-by-step explanation:

Answer:

21%

Step-by-step explanation:

Answer:

\( \frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c\)

Step-by-step explanation:

\( \int \frac{1}{ \sqrt{x} - \sqrt{x - 1} } dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x} - \sqrt{x - 1} )( \sqrt{x} + \sqrt{x - 1} )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ (\sqrt{x})^{2} - (\sqrt{x - 1} )^{2}} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - (x - 1 )} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ x - x + 1} dx \\ \\ = \int \frac{ \sqrt{x} + \sqrt{x - 1}}{ 1} dx \\ \\ = \int (\sqrt{x} + \sqrt{x - 1}) dx \\ \\ = \int \sqrt{x} \: dx+ \int\sqrt{x - 1} \: dx \\ \\ = \int {x}^{ \frac{1}{2} } \: dx+ \int {(x - 1)}^{ \frac{1}{2} } \: dx \\ \\ = \frac{ {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + \frac{ {(x - 1)}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} {x}^{ \frac{3}{2} } + \frac{2}{3} {(x - 1)}^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \bigg[ \sqrt{ {x}^{3} } + \sqrt{ {(x - 1)}^{3} } \bigg] + c \\ \\ = \bold{\purple {\frac{2}{3} \bigg[ x\sqrt{ {x}} + (x - 1)\sqrt{ {(x - 1)}} \bigg] + c}} \)

According to the information we can infer that the change between 11 and 12 is 1.3 m/hr

To establish the value of the change in height between 11 and 12 we must look at the values of the y axis. According to this information we can establish that 11 o'clock coincides with 5.2 and 12 o'clock coincides with 3.9. So we must subtract these two values:

According to the above, we can infer that the change between these two hours is 1.3 m/hr.

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Answer:

1/4

Step-by-step explanation:

x^2 - x

Take the coefficient of x

-1

Divide by 2

-1/2

Square it

(-1/2)^2 = 1/4

Add it

x^2 -x +1/4

Answer:

300

Step-by-step explanation:

30+30+w+x+y+z = 360 (all angles round a point add up to 360)

Simplifying :

60 + w+x+y+z = 360

Subtracting 60 from both sides :

w+x+y+z = 300

Hope this helped and brainliest ?

Sum of entire angle=360°

so

Answer:

Step-by-step explanation:

y + 11 = -8(x - 9)

y + 11 = -8x + 72

y = -8x + 61

The equation of the line in slope-intercept form having the given point and slope is: y = -8x + 61.

Slope-intercept formis expressed as y = mx + b.

Given the following:

A point = (9, -11) = (a, b)

Slope = -8 = m

Substitute m = -8 and (a, b) = (9, - 11) into y - b = m(x - a)

y - (-11) = -8(x - 9)

Rewrite in slope-intercept form

y + 11 = -8x + 72

y = -8x + 72 - 11

y = -8x + 61

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