The Hillmans have $12,000 in a savings account. The bank pays 1.25% interest on the savings account, compounded continuously. Find the total balance after four years.

Given:-

To find:-

Answer:-

In the given right angled triangle, we may use the trigonometric ratios. We can see that the measure of the longest side is "x" which is hypotenuse and it needs to be find out. The perpendicular in this case is "2" .

We may use the ratio of sine here as , we know that in any right angled triangle,

[tex]\implies\sin\theta =\dfrac{p}{h} \\[/tex]

And here , p = 2 and h = x , so on substituting the respective values, we have;

[tex]\implies \sin\theta = \dfrac{2}{x} \\[/tex]

Again here angle is 60° . So , we have;

[tex]\implies \sin60^o =\dfrac{2}{x} \\[/tex]

The measure of sin45° is √3/2 , so on substituting this we have;

[tex]\implies \dfrac{\sqrt3}{2}=\dfrac{2}{x} \\[/tex]

[tex]\implies x =\dfrac{2\cdot 2}{\sqrt3}\\[/tex]

Value of √3 is approximately 1.732 . So we have;

[tex]\implies x =\dfrac{4}{1.732} \\[/tex]

[tex]\implies \underline{\underline{\red{\quad x = 2.31\quad }}}\\[/tex]

Hence the value of x is 2.31 .

Answer:

The length of side x to the nearest tenth is 2.3.

Step-by-step explanation:

From inspection of the given right triangle, we can see that the interior angles are 30°, 60° and 90°. Therefore, this triangle is a 30-60-90 triangle.

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is b: b√3 : 2b where:

We have been given the side opposite the 60° angle, so:

[tex]\implies b\sqrt{3}=2[/tex]

Solve for b by dividing both sides of the equation by √3:

[tex]\implies b=\dfrac{2}{\sqrt{3}}[/tex]

The side labelled "x" is the hypotenuse, so:

[tex]\implies x=2b[/tex]

Substitute the found value of b into the equation for x:

[tex]\implies x=2 \cdot \dfrac{2}{\sqrt{3}}[/tex]

[tex]\implies x=\dfrac{4}{\sqrt{3}}[/tex]

[tex]\implies x=2.30940107...[/tex]

[tex]\implies x=2.3\; \sf (nearest\;tenth)[/tex]

Therefore, the length of side x to the nearest tenth is 2.3.

Answer:

question where is the question?

The total cost to fence the rectangular yard is given as follows:

$1,610.28.

The perimeter of a rectangle is the total distance around its outer boundary. To find the perimeter of a rectangle, you need to add up the lengths of all four sides.

If a rectangle has length l and width w, then its perimeter P is given by the equation presented as follows:

P = 2l + 2w

Considering the scale factor of 0.75, the distance represented by each unit on the graph is given as follows:

0.75 x 12 = 9 yards.

Hence the dimensions of the rectangle are given as follows:

The perimeter of the fence is then given as follows:

2 x (72 + 54) = 252 yards.

It costs $6.39 per yard, hence the total cost to fence the yard is given as follows:

252 x 6.39 = $1,610.28.

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Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Answer:

here is your answer  attached

Step-by-step explanation:

Answer:

Step-by-step explanation:

To determine the amount that Buggiero Brothers Oil must deposit today in order to have enough money to pay the R85 000 liability four years from today, we can use the present value formula:

Present Value (PV) = Future Value (FV) / (1 + r)^n

where:

- FV is the future value, which is R85 000

- r is the annual interest rate, which is 6%

- n is the number of years until the liability needs to be paid, which is 4

To calculate the future value of the annual deposits of R16 000, we can use the future value of an annuity formula:

FV = PMT x [(1 + r)^n - 1] / r

where:

- PMT is the annuity payment, which is R16 000

- r is the annual interest rate, which is 6%

- n is the number of years of the annuity, which is 3 (since the first payment is made one year from today)

Plugging in the numbers:

FV = R16 000 x [(1 + 0.06)^3 - 1] / 0.06

FV = R61 719.56

Therefore, the total future value that Buggiero Brothers Oil will have in four years, including the initial deposit and the annual payments, will be:

FV = R85 000 + R61 719.56

FV = R146 719.56

Plugging in the numbers to the present value formula:

PV = R146 719.56 / (1 + 0.06)^4

PV = R116 442.12

Thus, Buggiero Brothers Oil needs to deposit R116 442.12 today to have enough money to pay the R85 000 liability four years from today, assuming a 6% rate of return.

The successor of -34 is -33 using the formula "n+1".

A phrase that follows or is right after a specific number, term, or value is known as a successor.

The successor of n is "n+1" if n is a number (and n belongs to any whole number).

The terms just after, immediately after, and next number/next value are also used to describe a successor.

As is common knowledge, integers are collections of numbers that range from negative infinity to positive infinity.

The integers are.........., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,.................. The preceding and following numbers will also be negative integers if the provided number is a negative integer.

So, the successor of -34:

= -34 + n

= -34 + 1

= - 33

Therefore, the successor of -34 is -33 using the formula "n+1".

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The amounts of each substance needed to obtain a mixture of 20 pounds at a price of $5.4 per pound is given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

The mixture has a total of 20 pounds, hence:

x + y = 20.

y = 20 - x.

The total cost of the mixture is of $108, as 108/20 = 5.4, hence:

7x + 3y = 108

Replacing the second equation into the first, the value of x is given as follows:

7x + 3(20 - x) = 108

4x = 48

x = 12.

Then the value of y is given as follows:

y = 20 - 12

y = 8.

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Answer:

To add mixed numbers, we need to add the whole numbers separately and fractions separately.

Starting with the whole numbers, we have:

9 1/2 − 3 7/8 + 4 4/5 − 1 1/2

= (9 + 4) − (3 + 1) + (4/5 − 1/2) + (1/8 − 7/8) (grouping the terms)

= 10 − 4 + (8/10 − 5/10) + (−6/8) (converting fractions to have a common denominator)

= 6 + 3/10 − 3/4 (simplifying fractions and adding whole numbers)

= 5 7/20 (expressing the result as a mixed number in simplest form)

Therefore, the value of the expression is 5 7/20.

The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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Answer:

1250/500

=2.5

Multiplied by interest rate (30)

2.5 times 30

= $75.00

Step-by-step explanation:

Hope I helped.

Roderick earns an interest of $30 per year for every $500 deposited in his savings account. This means that the interest rate per $500 deposit is:Interest rate per $500 = $30/$500 = 0.06 or 6%To calculate the interest earned on Roderick's savings account, we first need to determine how many $500 deposits he has. We can do this by dividing his total savings by $500:Number of $500 deposits = $1,250/$500 = 2.5

Answer:

60:61.8 OR 10:10.3

Step-by-step explanation:

Cant be simplified - unless your in advanced classes. If so

10:10.3

Answer:

Step-by-step explanation:

1/3 or 0.3 or 33.333333% or 3^-1 or 3.333333 x 10^-1

An angle is  a geometric figure formed by two rays or line segments that share  a common endpoint, called the vertex. Angles are measured in degrees or radians and are typically denoted by  symbol ∠ followed by the name of the vertex, like ∠ABC.

The size of angle is determined by  amount of rotation needed to bring one of  rays or line segments into coincidence with others.

Angles can be acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (exactly 180 degrees), or reflex (greater than 180 degrees).

Angles are fundamental to geometry and have many applications in physics, engineering, and other fields.

This is because the sum of the angles in a triangle must always be 180°, and 40° + 60° + 80° = 180°.

However, the angles do not satisfy the conditions of the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, It is not possible to construct a triangle with angle measures of 40°, 60°, and 80°.

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Answer:

We can use the half-angle formula for sine to find the exact value of sin(a/2) in terms of sin(a):

sin(a/2) = ±√[(1 - cos(a))/2]

where the ± sign depends on the quadrant of a/2.

To use this formula, we first need to find cos(a). We can do this using the identity:

sin^2(a) + cos^2(a) = 1

Substituting sin(a) = 7/9, we get:

(7/9)^2 + cos^2(a) = 1

Simplifying and solving for cos(a), we get:

cos(a) = ±4/9

Since a is in quadrant I, we take the positive value of cos(a):

cos(a) = 4/9

Now we can use the half-angle formula for sine to find sin(a/2):

sin(a/2) = ±√[(1 - cos(a))/2]

Substituting cos(a) = 4/9, we get:

sin(a/2) = ±√[(1 - 4/9)/2]

Simplifying, we get:

sin(a/2) = ±√(5/18)

Since a is in quadrant I, a/2 is also in quadrant I, so we take the positive value of sin(a/2):

sin(a/2) = √(5/18)

Therefore, the exact value of sin(a/2) is √(5/18)

The value of the trigonometric functions for the right triangle is tan(29) = 0.518. cos(29) = 0.838. sin (29) = 0.435.

The sine, cosine, and tangent trigonometric ratios are the three most important ones. These are their definitions:

Sine (sin) is the proportion of a right triangle's hypotenuse to the length of the side that faces an angle.

The length of the side next to an angle in a right triangle divided by the length of the hypotenuse is known as the cosine (cos).

In a right triangle, the tangent (tan) is the ratio between the lengths of the sides that face each other and the angle.

These ratios are used in trigonometry to connect the angles and sides of right triangles, and they may be used to a number of triangle- and other geometric shape-related problems.

In the given triangle using the sum of interior angle of triangle we have:

180 - 90 - 29 = 61

The measure of the third angle is 61 degrees.

Now, tan(61) = XZ/XY

XZ = XY * tan(61)

XZ = 18 * 1.927 = 34.686

Now, using the Pythagoras theorem we have:

ZY² = XZ² + XY²

ZY² = 34.686² + 18²

ZY² = 1712.3996

ZY = 41.38

Now, the value of:

sin(29) = opposite/hypotenuse = XY/ZY = 18/41.388 = 0.435

cos(29) = adjacent/hypotenuse = XZ/ZY = 34.686/41.388 = 0.838

tan(29) = opposite/adjacent = XY/XZ = 18/34.686 = 0.518

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Answer:

63m+18

Step-by-step explanation:

9*7m is 63m and 9*2 is 18

Combine them and you get 63m+18!

Answer: 9 3/10

Step-by-step explanation:

6 + 2/5 + 2 + 9/10= 6 + 2 = 8 = 2/5 + 9/10= 4/10 + 9/10= 13/10= 1  3/10= 8 + 1 + 3/10= 9 3/10

Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

Answer:

1 solution

Step-by-step explanation:

Y = 4

Y = 4x - 1

Substitute value of Y here,

4 = 4x - 1

4 + 1 = 4x

5 = 4x

5/4 = x

1.25 = x

•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.

______

hope this helps!

Answer: 0.24z

Step-by-step explanation: If you make 24% a decimal you will get 0.24. Then you make your equation 0.24z or 0.24 x z .

Answer: We can simplify the expression step by step:

3/4 − x(1/2 − 5/8) + (−3/8)x

3/4 − x(-1/8) + (−3/8)x

3/4 + x/8 − 3/8x

Multiplying everything by 8 to get rid of the fractions:

6 − x + (−3x)

6 − 4x

Therefore, the equivalent expression is D) 34 - 14x / (4/3).

Step-by-step explanation:

Answer: D

Step-by-step explanation: so if we look at the picture, youll notice 2 things right off the bat, firstly, the top shape goes over the y axis, so that wont work, secondly, the shapes are on the same side of the x axis (the positive side) so that wouldnt work, the last thing we now have to look at is making the shapes even, essentially if you were to flip one shape over a certain distance, the mirrored shape needs to be the same distance you flipped the first shape. In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

side note: reflecting over the x axis or y axis, means the line of reflection is equal to 0 on either the y axis or x axis

To try to make this less confusing, another way to find the reflection is by evenly counting the shapes to the middle, how-ever many squares/spaces it takes for both shapes to reach the center of the two in this case, is how many spaces they are reflected.

The image undergoes a reflection at y=-3, Option D is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

Reflections are congruence transformations that generate a mirror image of an object, without changing its size or shape.

In the given figure the above image is original and it is flipped to form the image which is below the x axis.

In this case, if we flip shape 1, over -3, the other shape will be 6 spaces away from the 1st shape, because you need to also move the second shape 3 spaces away from where you flipped the first shape.

Hence, the image undergoes a reflection over y axis which is at y=-3.

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Step-by-step explanation:

the width is 23.5ft and the length is 47ft

Answer: 19 tickets

Step-by-step explanation:  $45 - $7 = 38      38 divided by $2 = 19 tickets

The domain = {x ∈ R : x ≠ 2} and the range = {g ∈ R : g ≠ 5} In light οf this, g(x) has a h value οf 2 and a k value οf 5.

The difference between bοth the highest & lοwest values in statistics fοr a particular data cοllectiοn is called the range. Fοr instance, if the data set is 2, 5, 8, 10, 3, then the range is 10 - 2 = 8.

The definitiοn οf the functiοn g(x) is.

g(x) = 1/(x - 2) + 5

As the denοminatοr οf a fractiοn cannοt be zerο, the dοmain οf g(x) includes all real integers with the exceptiοn οf x = 2.

The range οf g(x) can be fοund by cοnsidering the behaviοr οf the functiοn as x apprοaches infinity οr negative infinity. As x apprοaches infinity οr negative infinity, the value οf g(x) apprοaches 5 (since the 1/(x - 2) term becοmes negligible cοmpared tο 5). Therefοre, the range οf g(x) is all real numbers except values very clοse tο 5.

It is pοssible tο rewrite the functiοn g(x) as fοllοws:

g(x) = (1/(x - 2)) + 5

This is in the fοrm:

g(x) = a/(x - h) + k

Where a = 1, h = 2, and k = 5.

Therefοre, the h value fοr g(x) is 2, and the k value fοr g(x) is 5.

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Answer:

To multiply 1 3/3 by 1 2/6, we can first convert these mixed numbers to improper fractions, then multiply them together, and finally simplify the result to its simplest form.

1 3/3 can be written as 4/3 (since 1 whole and 3/3 is equivalent to 4/3)

1 2/6 can be written as 8/6 (since 1 whole and 2/6 is equivalent to 8/6)

Now, we can multiply these two fractions together:

4/3 x 8/6 = (4 x 8) / (3 x 6) = 32/18

To simplify this fraction, we can divide the numerator and denominator by their greatest common factor, which is 2:

32/18 = (2 x 16) / (2 x 9) = 16/9

Therefore, the product of 1 3/3 and 1 2/6 is 16/9, or 1 and 7/9 in mixed number form, in its simplest form.

The maximum height reached after the 13th bοunce is 6.14 cm.

The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.

Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:

[tex]h = (3/4)^{{n}} \times H[/tex]

where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.

We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.

Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:

[tex]h = (3/4)^{{13}} \times 187.00[/tex]

h ≈ 8.18 cm

Nοw we can find the maximum height:

maximum height = (3/4) × h

maximum height = (3/4) ×8.18

maximum height ≈ 6.14 cm

Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.

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Answer: 64°

Step-by-step explanation:

Had this problem and got it right

Answer:

D. A triangle with sides measuring 5 inches, 7 inches, and 9 inches. This is because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In option A, the side lengths satisfy this condition since 50 + 35 > 25. In option B, the side lengths do not satisfy this condition since 5 + 10 < 15. In option C, the side lengths satisfy this condition since 8 + 12 > 85. In option D, the side lengths do not satisfy this condition since 5 + 7 < 9, 7 + 9 > 5, and 5 + 9 > 7.