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Let's consider the information at hand:

         ⇒ has some special property about its side length

             ⇒ look at the diagram I attached

Using the same ratios of side length as seen in the diagram:

  ⇒ we get the equation:

        [tex]\frac{1}{\frac{\sqrt{2} }{2} } =\frac{x}{3\sqrt{2} } \\\frac{\sqrt{2} }{2}*x=3\sqrt{2} \\\frac{x}{2}=3\\ x=3*2\\x=6[/tex]

Thus x = 6.

Answer: x = 6

Hope that helps!

Answer: I think

Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)

Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.

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Answer:

It is the third option

Step-by-step explanation:

Trust me

(4x−101)(2x+3)

Apply the distributive property by multiplying each term of 4x−101 by each term of 2x+3.

8x²+12x−202x−303

Combine 12x and −202x.

8x²−190x−303

Hi student, let me help you out! :)

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We are asked to find the value of x in [tex]\mathrm{(4x-101)(2x+3)}[/tex].

◈ Note:

⇛ We can't find the value of x, but we can simplify this expression.

This is how we'll simplify it:

◆ Multiply 4x times 2x and 3 first:

[tex]\large\pmb{4x\times2x=8x^2}[/tex]

[tex]\large\pmb{4x\times3=12x}[/tex]

Add the terms:

[tex]\large\pmb{8x^2+12x}[/tex]

Now, do the same thing with -101 - multiply that times 2x and 3:

[tex]\large\pmb{-101\times2x=-202x}[/tex]

[tex]\large\pmb{-101\times3=-303}[/tex]

Add the terms:

[tex]\large\pmb{-202x-303}[/tex]

Put all 4 of the terms together:

[tex]\large\pmb{8x^2+12x-202x-303}[/tex]

Combine like terms (12x and -202x):

[tex]\large\pmb{8x^2-190x-303}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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Step-by-step explanation:

Soln:-

Given,

Area of sticker=56 cm^2

Width of sticker=7 cm

Length of sticker=?

We know that,

Area of rectangle=l×b

or,56=l×7

or,l=56÷7

•°•l=8

Hence,the required length of the sticker is 8 cm.

Answer:

the answer is 48m²

Step-by-step explanation:

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Step-by-step explanation:

i answered it , and tried to give explanation too...

hope its helpful ,

Answer: 3ln4 + 3lna

Step-by-step explanation:

[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]

Answer:

C and second one is A

The answer will be x squared over 4 plus y squared over 8 equals 1.

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

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Answer:

rawrrrrrrrrrrrrrrrrr

Step-by-step explanation:

Why is P(A) •P(B/A) = P(B) • P(A/B)

P/B + P = A

P/B/P

- A

Answer:176

Step-by-step explanation:

8 x 2 x 11

Answer:

Good style in solving such problems is to notice/(to observe) immediately from the condition that the difference

   between two combinations is  the cost of 2 cookies,  and it is equal to  $9 - $7 = $2.   So  2 cookies cost  $2.

   Then subtracting $2 dollars for 2 cookies from the Greg purchase, you got the cost of two bottles - it is equal to  $7 - $2 = $5.

   Answer.  A bottle of water costs  $2.50.

Step-by-step explanation:

Answer + Step By Step Explanation:

There is no single value for y as the input could differ (x)

y = -3/4x

if x = 0, y = -3/4(0) than y = 0

if x = 1, y = -3/4(1) than y = -3/4

...

if x = 5, y = -3/4(5) than y = -15/4

On a train ride cross-country, the trees, buildings, and people appear to be speeding by the window. While traveling in a train, it appears that the trees near the track are moving whereas co-passengers appear to be stationary.

When measuring, scientists use a shared system of measurement, called the International System of Units (SI). Physical science is concerned with the study of natural but non-living objects.

If 6 tyrannosaurs weigh 30,000 kg, the weight of one tyrannosaur will be;

= 30000/6

= 5000kg

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Let A(t) denote the amount of salt (in ounces, oz) in the tank at time t (in minutes, min).

Salt flows in at a rate of

[tex]\dfrac{dA}{dt}_{\rm in} = \left(17 (1 + 15 \sin(t)) \dfrac{\rm oz}{\rm gal}\right) \left(8\dfrac{\rm gal}{\rm min}\right) = 136 (1 + 15 \sin(t)) \dfrac{\rm oz}{\min}[/tex]

and flows out at a rate of

[tex]\dfrac{dA}{dt}_{\rm out} = \left(\dfrac{A(t) \, \mathrm{oz}}{180 \,\mathrm{gal} + \left(8\frac{\rm gal}{\rm min} - 8\frac{\rm gal}{\rm min}\right) (t \, \mathrm{min})}\right) \left(8 \dfrac{\rm gal}{\rm min}\right) = \dfrac{A(t)}{180} \dfrac{\rm oz}{\rm min}[/tex]

so that the net rate of change in the amount of salt in the tank is given by the linear differential equation

[tex]\dfrac{dA}{dt} = \dfrac{dA}{dt}_{\rm in} - \dfrac{dA}{dt}_{\rm out} \iff \dfrac{dA}{dt} + \dfrac{A(t)}{180} = 136 (1 + 15 \sin(t))[/tex]

Multiply both sides by the integrating factor, [tex]e^{t/180}[/tex], and rewrite the left side as the derivative of a product.

[tex]e^{t/180} \dfrac{dA}{dt} + e^{t/180} \dfrac{A(t)}{180} = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

[tex]\dfrac d{dt}\left[e^{t/180} A(t)\right] = 136 e^{t/180} (1 + 15 \sin(t))[/tex]

Integrate both sides with respect to t (integrate the right side by parts):

[tex]\displaystyle \int \frac d{dt}\left[e^{t/180} A(t)\right] \, dt = 136 \int e^{t/180} (1 + 15 \sin(t)) \, dt[/tex]

[tex]\displaystyle e^{t/180} A(t) = \left(24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t)\right) e^{t/180} + C[/tex]

Solve for A(t) :

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) + C e^{-t/180}[/tex]

The tank starts with A(0) = 15 oz of salt; use this to solve for the constant C.

[tex]\displaystyle 15 = 24,480 - \frac{66,096,000}{32,401} + C \implies C = -\dfrac{726,594,465}{32,401}[/tex]

So,

[tex]\displaystyle A(t) = 24,480 - \frac{66,096,000}{32,401} \cos(t) + \frac{367,200}{32,401} \sin(t) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

Recall the angle-sum identity for cosine:

[tex]R \cos(x-\theta) = R \cos(\theta) \cos(x) + R \sin(\theta) \sin(x)[/tex]

so that we can condense the trigonometric terms in A(t). Solve for R and θ :

[tex]R \cos(\theta) = -\dfrac{66,096,000}{32,401}[/tex]

[tex]R \sin(\theta) = \dfrac{367,200}{32,401}[/tex]

Recall the Pythagorean identity and definition of tangent,

[tex]\cos^2(x) + \sin^2(x) = 1[/tex]

[tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

Then

[tex]R^2 \cos^2(\theta) + R^2 \sin^2(\theta) = R^2 = \dfrac{134,835,840,000}{32,401} \implies R = \dfrac{367,200}{\sqrt{32,401}}[/tex]

and

[tex]\dfrac{R \sin(\theta)}{R \cos(\theta)} = \tan(\theta) = -\dfrac{367,200}{66,096,000} = -\dfrac1{180} \\\\ \implies \theta = -\tan^{-1}\left(\dfrac1{180}\right) = -\cot^{-1}(180)[/tex]

so we can rewrite A(t) as

[tex]\displaystyle A(t) = 24,480 + \frac{367,200}{\sqrt{32,401}} \cos\left(t + \cot^{-1}(180)\right) - \frac{726,594,465}{32,401} e^{-t/180}[/tex]

As t goes to infinity, the exponential term will converge to zero. Meanwhile the cosine term will oscillate between -1 and 1, so that A(t) will oscillate about the constant level of 24,480 oz between the extreme values of

[tex]24,480 - \dfrac{267,200}{\sqrt{32,401}} \approx 22,995.6 \,\mathrm{oz}[/tex]

and

[tex]24,480 + \dfrac{267,200}{\sqrt{32,401}} \approx 25,964.4 \,\mathrm{oz}[/tex]

which is to say, with amplitude

[tex]2 \times \dfrac{267,200}{\sqrt{32,401}} \approx \mathbf{2,968.84 \,oz}[/tex]

The value of the x will be 12. The value of the x is obtained from the condition,(f – g)(x) = 0

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

Given function;

f(x) = 16x – 30

g(x) = 14x – 6

⇒(f – g)(x) = 0

⇒(16x – 30)-(14x – 6)=0

⇒16x-30-14x+6=0

⇒2x-24=0

⇒x=24/2

⇒x=12

Hence, the value of the x will be 12.

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Usando proporciones, hay que se necessita 8.42 litros de pintura para pintar 1 metro cuadrado de pared.

Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.

En este problema, se utilizan 9.01 litros de pintura para pintar 1.7 metros cuadrados, por eso, la cantidad relativa a 1 metro cuadrado es dada por:

c = 9.01/1.7 = 8.42 litros.

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Rounded to the nearest whole number, the standard deviation of the data is 29.

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where:

n = number of values = 4

x = each value

Therefore, we have:

Mean = (65 + 75 + 100 + 130) / 4 = 92.50

Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) =  2,525 / 3 = 841.666666666667

Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882

Rounding to the nearest whole number, we have:

Standard deviation = 29

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Answer:

The answer is C. 100

Step-by-step explanation:

There are 30240 different ways can he arrange the five posters out of the ten on his closet door

The given parameters are:

The number of ways is calculated as:

Ways =[tex]^nP_r[/tex]

This gives

Ways =[tex]^{10}P_5[/tex]

Apply the permutation formula

Ways = 30240

Hence, there are 30240 different ways can he arrange the five posters out of the ten on his closet door

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Answer:

3x^2

Step-by-step explanation:

Area = (length) x (width)

Area = (1x)*(3x)

Area = 3x^2

Answer:

C. 8/17

Step-by-step explanation:

Given:

Hypotenuse = 17

BC = 8

Cos (B) = leg adjacent to ∠B / hypotenuse

= BC/BA

Substitute

Cos (B) = 8/17

Hence option C is correct

When accessing your credit card information online, you cannot makes purchase.

A credit card is a card that enables a card holder to buy or purchase things online on credit.

A credit card holder can carryout the following when accessing their credit card data online:

Therefore the correct option is C.

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Answer:

Volume

For the rectangle, h = 3cm, l = 8cm, w = 6cm
V = length x width x height
V = 8cm x 6cm x 3cm
V = 144cm^3

For the semi circle, we need to find the radius. The radius is width/2, so 6cm/2 = 3cm. r = 3cm, [tex]\pi[/tex] = 3.14
V = radius^2 x height x [tex]\pi[/tex]
V = 3cm^2 x 3cm x 3.14
V = 84.8 cm^3/2 (because the cylinder needs to be divided to form a semi-circle)
V= 42.4cm^3 (there are two cylinders though so we will multiply this by 2 in the total volume)

Total volume:
V = 144cm^3 + 42.4cm^3(2)
V = 186.4cm^3

Surface Area

Rectangular prism:
A = 2[w(l) + h(l) + h(w)]
A = 2[6cm(8cm) + 3cm(8cm) + 3cm(6cm)]
A = 180cm^2
But there are two sides that are covered by the semi-circular prisms, so we will have to calculate those sides and remove them.
A = l x w
A = 6cm x 3cm
A = 18cm^2(2) (2 being the two faces)
A = 36cm^2

A = 180cm^2 - 36cm^2
A = 144cm^2 (the area of the rectangle)

Semi-circular prism:
A = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex]r^2
Earlier, we found out that the radius of the circle is 3cm, so we will plug that in.
A = 2(3.14)(3cm)(3cm) + 2(3.14)(3cm)^2
A = 113.09cm^2

Total surface area:
A = 144cm^2 + 133.09cm^2
A = 277.09cm^2

Therefore the total volume of the prism is 186.4cm^3 and the total surface area is 277.09cm^2.

Answer:

50

Step-by-step explanation:

90+40= 130

There are 180 degrees in a triangle.

180- 130 = 50

Answer:

Step-by-step explanation:

The profit = 150 000 - 120 000 = 30 000

………………………………………………………

The profit percentage is :

[tex]=\frac{30000}{120000} \times 100=0.25 \times 100 = 25 \%[/tex]

Answer:

+12 percentage points

Step-by-step explanation:

All options have positive percentage in themselves

So lesser marginal error should be more applicable as lower the marginal errors lower the probability of doing mistakes so higher marks .

Option B

Step-by-step explanation:

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