A cabinet was ordered from a carpenter with a volume of 1.08 m³. He wrote down the following measurements: 1.2 m wide and 1.8 m high, but forgot to write down the depth. Therefore, the depth measurement is

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: x=25

Step-by-step explanation:

log 10 4x = 2

10^2 = 4x

100 = 4x

25 = x

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:

To find the y-intercept, we can set x = 0 in the equation y= -2x^2 -4x -5, which gives us:

y = -2(0)^2 - 4(0) - 5 = -5

So the y-intercept is (0, -5). Therefore, the correct answer is (0,-5).

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.

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)

Answer:

63m+18

Step-by-step explanation:

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

Combine them and you get 63m+18!

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.

Step-by-step explanation:

the width is 23.5ft and the length is 47ft

Answer:

Step-by-step explanation:

subtract 20-3.50 you will get 16.50

Multiply 2.50x6 you will get 15

Subtract 16.50-15.00 you will get 1.50

If Yellow Sticker Business meets its operating income goal, the quarterly safety margin in dollars will be $4,583.33.

Budgeting, debt reduction, and setting up an emergency fund are important short-term objectives. Key insurance policies should be included in medium-term goals, whilst retirement should be the primary emphasis of long-term objectives.

Next, we deduct our break-even sales from actual sales at the goal operating income level to determine the margin of safety:

Real sales are determined by dividing target operating income by total fixed costs and contribution margin ratio.

Real sales equal $8,250 plus $15,000 / 0.60.

Real sales were $29,583.33

Safety margin = Real sales Breakeven sales

Margin of safety is calculated as $29,583.33 - ($0.50 x 50,000 units).

$25,000 - 29,583.33 is the margin of safety.

$4,583.33 is the safety margin.

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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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Step-by-step explanation:

2.2 percentage answer you silly

Answer:

Therefore, the total used car sales were $179,625.

Step-by-step explanation:

Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.

The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:

3x + 5x = 8x

So, the total sales can be expressed as:

8x = $287,400

To find the value of x, we need to divide both sides by 8:

x = $35,925

Now, we can calculate the used car sales by multiplying 5x by the value of x:

Used car sales = 5x * x = 5 * $35,925 = $179,625

Therefore, the total used car sales were $179,625.

We may be confident that this is the correct scale factor because both equation equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.

An equation is a statement in mathematics that states the equality of two expressions. An equation has two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine which variable(s) must be changed in order for the equation to be true. Simple or complex equations, regular or nonlinear equations, and equations with one or more elements are all possible. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are employed in a variety of mathematical disciplines, including algebra, calculus, and geometry.

Let (x,y) be a point on the plane and k be the dilation scale factor centred at the origin. The image of (x,y) under dilation is thus given by (kx, ky).

The dilation is given as (4,6) to (5/2,15/4). That is to say:

[tex]k(4) = 5/2 \sk(6) = 15/4\\k = 5/8 \sk = 5/8[/tex]

We may be confident that this is the correct scale factor because both equations yield the same value of k. As a result, the dilatation has a scale factor of 5/8 and is centered at the origin.

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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.

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:

P = 8g⁵ - 15g + 14

Step-by-step explanation:

This question has expressions to represent the side lengths of a triangle.

The side lengths are:

-8g⁵ - 7g

10g⁵ - 8g

6g⁵ + 14

They ask for a simplified expression for the perimeter. The purpose of this question is to combine like terms.

P = s₁ + s₂ + s₃ where s is a side length of the triangle.

P = (-8g⁵ - 7g) + (10g⁵ - 8g) + (6g⁵ + 14)

P = 8g⁵ - 15g + 14

As a result, Ava's luggage will weigh 123622200 grams more than the permitted maximum.

Weight is the force of gravity that pulls objects toward the core of the Earth. The resulting force that pulls a substance toward Earth is known as gravity. In contrast to gravity force, which occurs among any two masses, this only occurs between Earth as well as a mass.

First, we need to convert all the weights to grams, since the weight limit is given in kilograms and the weights of clothes, electrical accessories, and toiletries are given in grams.

Maximum weight limit = 2020 kg = 2020000 g

Weight of empty suitcase = 33 kg = 33000 g

Weight of clothes = 55 kg = 55000 g

Weight of electrical accessories = 44 kg = 44000 g

Weight of 55 hardback books = 55 x 720720 g = 39639600 g

Weight of toiletries = 46004600 g

Total weight of suitcase and contents = 33000 + 55000 + 44000 + 39639600 + 46004600 = 125642200 g

Amount over maximum weight limit = total weight - maximum weight limit = 125642200 - 2020000 = 123622200 g

Therefore, Ava's suitcase will be over the maximum weight limit by 123622200 grams.

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Answer:

here is your answer  attached

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can solve the equation m + 9 = 27 by subtracting 9 from both sides to isolate m:

m + 9 - 9 = 27 - 9

m = 18

Therefore, Ibrain biked 18 miles last week.

Parabola intersects x-axis at two points: (-5,0) and (-4,0)

What does a parabola actually mean?

Each point on a parabola with a U-shape is equally spaced from both the focus, a fixed point, and the directrix, a fixed line. As the topic of conic sections depends heavily on the parabola, all of the parabola-related concepts are covered here.

The x-intercepts of a parabola are where the parabola intersects the x-axis on its graph. There are a number of ways to find the x-intercepts of a parabola, and each one is usually specific to each situation.

In the case, when you are given the graph, the easiest way to find x-intercepts is to identify points at which parabola intersects the x-axis.

From your graph, parabola intersects x-axis at two points: (-5,0) and (-4,0)

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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 .

The probability that the participant either is a teen or prefers country music is given as follows:

P(C or T) = 0.55.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The desired outcomes for this problem are given as follows:

There were 520 people in the research, hence the probability that the participant either is a teen or prefers country music is given as follows:

P(C or T) = (170 + 114)/520

P(C or T) = 0.55.

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The first thing we must do for this case is to find the surface area of the rectangular prism.

We have then:

[tex]A = 2 \times (l \times h) + 2 \times (h \times w) + 2 \times (w \times l)[/tex]

Where,

w: width

l: long

h: height

Substituting values we have:

[tex]A = 2 \times (10 \times 8) + 2 \times (8 \times 8) + 2 \times (8 \times 10)[/tex]

[tex]A = 448 \ in ^ 2[/tex]

Answer:

the least amount of wrapping paper needed to wrap the gift box answer is:

A = 448 in²

Answer:

question where is the question?

Answer:0

Step-by-step explanation: just like you did on my question and stole the points :) xx

Answer:

2.25

Step-by-step explanation:

9 × 250 m = 2250 mL

1 L = 1000 m

2250 mL × (1 L)/(1000 mL) = 2.25 L