The length of the side of a cube is represented
by x-4. Express the surface area of the cube in
terms of x.

Sides AB = 3√2 and BC = 6.

The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.

In the given right triangle ABC,

Hypotenuse of the triangle = BC

Base and height = AC and AB.

Also, we see from the diagram that ∠ACB and ∠ABC are equal.

∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.

Now, by Pythagoras' theorem,

Hypotenuse² = Base² + Height²

Or, BC² = AC² + AB²

Or, BC² = (3√2)² + (3√2)²

⇒ BC² = 36

Or, BC = 6

Hence, sides AB = 3√2 and BC = 6.

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Step-by-step explanation:

5^(x+2)  <= 3^x    

5^x  *  5^2  <= 3^x

25 <=  3^x / 5^x

25<= (3/5)^x                  LOG both sides

log 25 <= x log (3/5)

log 25 / log (3/5) <= x

- 6.3 <= x

Answer: The correct answer is (5, 11π/6). or C

Step-by-step explanation:

The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

Explanation:

Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

Plugging in the given values:

r = √((5√3/2)^2 + (-5/2)^2)

= √(75/4 + 25/4)

= √(100/4)

= 5

θ = atan2(-5/2, 5√3/2)

≈ 11π/6 radians

So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).

The chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

We can first standardize the values of 20 and 40 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize (20 or 40), μ is the expected value (30), and σ is the standard deviation (5).

For x = 20, we get:

z = (20 - 30) / 5 = -2

For x = 40, we get:

z = (40 - 30) / 5 = 2

probability of getting a z-score between -2 and 2.

Using a standard normal distribution table or calculator, we find that the probability of getting a z-score between -2 and 2 is approximately 0.9544.

Therefore, the chances of rolling between 20 and 40 aces (inclusive) in 180 rolls is approximately 0.9544 or 95.44%.

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The measure of the third angle in an isosceles triangle can be expressed using the expression of option c. 180° - 2(65°).

In an isosceles triangle,

Measure of the base angles is equal to 65°.

Let us consider the measure of the third angle in an isosceles triangle is equal to x degrees.

The two base angles are congruent.

Since each base angle measures 65°, the sum of the base angles is.

65° + 65° = 130°

The sum of the angles in any triangle is 180°.

This implies,

The measure of the third angle in the isosceles triangle is equal to,

x° + 130° = 180°

⇒ x° = 180° - 130°

⇒ x° = 50°

Therefore, the correct expression to calculate the measure of the third angle in an isosceles triangle is option (c) 180° - 2(65°).

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The above question is incomplete, the complete question is:

In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?​

a. 180° - 65°

b. 180°+ 65°

c. 180° - 2(65°)

d. 180° + 2( 65°)

Using the integers −9 to 9 at most one time each, place a digit in each box (1, 3) and (9, 3) or (-9, 3) to create endpoints for the longest possible line segment both numerically and graphically whose midpoint is (1, 3).

To find the endpoints of the longest possible line segment with midpoint (1, 3), we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is ((x₁+x₂)/2, (y₁+y₂)/2).

In this case, we know the midpoint is (1, 3), so we can set up two equations using the variables for the endpoints (x and y) and solve for them:

(x₁ + x₂)/2 = 1

(y₁ + y₂)/2 = 3

We also know that the line segment must be as long as possible, so the endpoints should be as far away from each other as possible. To maximize the distance between the endpoints, we can choose one endpoint to be -9 and the other endpoint to be 9. This gives us:

(x₁ + x₂)/2 = 1 => x₁ + x₂ = 2

(y₁ + y₂)/2 = 3 => y₁ + y₂ = 6

Now we can solve for x₁ and y₁, since x₂ and y₂ will be 2-x₁ and 6-y₁ respectively:

x₁ + (2-x₁) = 2 => x₁ = 1

y₁ + (6-y₁) = 6 => y₁ = 3

So the endpoints of the longest possible line segment with midpoint (1, 3) are (1, 3) and (9, 3) or (-9, 3), and its length is 8 units.

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

Callie can make 5 necklaces.

So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.

Now, She has a pieces of leather cord that has a length of 4 yards.

Each necklace will have a length of 28 inches.

We have to determine the how many necklaces can Callie make?

We know that :

1 yard= 36 inches

So, Multiply by 36 into 4 yards

4 yards= 36x4= 144

Length of leather cord is 4 yards

144/4 = 5.14

Callie can make 5 necklaces.

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Answer:

Step-by-step explanation:

2344

Integration of   [tex]\int\limits^6_0 {\frac{8}{1+74e^{-0.3t} } } \, dt[/tex]   is 2.199.

We can solve this integral using the substitution method, where u = 1 + 74[tex]e^{-0.3t}[/tex] . Taking the derivative of both sides, we have du/dt = -222[tex]e^{-0.3t}[/tex] .

We can rewrite the integral in terms of u:

∫[8/(1+74[tex]e^{-0.3t}[/tex] )]dt = ∫[8/u * (-1/222) * (-222[tex]e^{-0.3t}[/tex] )]du

Simplifying this expression, we have:

= (-8/222) ∫[1/u] du

= (-4/111) ln|u| + C

where C is the constant of integration.

Substituting back for u, we have:

= (-4/111) ln|1 + 74[tex]e^{-0.3t}[/tex] | + C

To evaluate the definite integral from 0 to 6, we plug in the limits of integration:

= (-4/111) [ln | 1 + 74[tex]e^{-0.3(6)}[/tex] | - ln | 1 + 74[tex]e^{-0.3(0)}[/tex] |]

= (-4/111) [ln|1 + 74[tex]e^{-1.8}[/tex]| - ln75]

≈ 2.199

Therefore, the value of the definite integral is approximately 2.199.

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Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.

A general exponential decay is:

f(x) = A*(b)^x

Where A is the initial value, b is the rate of decay, x is the variable.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

The properties of the exponents are solved and the expression is given by the relation ( 2s )⁻¹ = 1 / 2s

Given data ,

Let the expression be represented as A

Now , the value of A is

( 2s )⁻¹ = 1 / 2s

From the laws of exponents , we get

m⁻ᵃ = ( 1 / mᵃ )

So , on simplifying , we get

( 2s )⁻¹ = 1/ ( 2s )

On further simplification , we get

1/ ( 2s ) = ( 2s )⁻¹

Hence , the expression is ( 2s )⁻¹ = 1/ ( 2s )

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The complete question is attached below :

Use properties of exponents to verify that ( 2s )⁻¹ = 1/ ( 2s ) are equivalent.

Answer:

The answer is

x= -2

y= -8

Step-by-step explanation:

x=y+6

substitute into equation 1

13(y+6)-6y=22

13y+78-6y=22

13y-6y=22-78

7y=-56

divide both sides by 7

7y/7= -56/7

y= -8

x=y+6

x= -8+6

x= -2

Answer: 358 miles

Step-by-step explanation:

Answer: 385

Step-by-step explanation: 77x5

The calculated value of the area of the circle is 5544 square yards

From the question, we have the following parameters that can be used in our computation:

Radius, r = 42

Using the above as a guide, we have the following:

Area = π * r^2

Substitute the known values in the above equation, so, we have the following representation

Area = 22/7 * 42^2

Evaluate the products and exponents

Area = 5544

Approximate

Area = 5544

Hence, the value of the area is 5544 square yards

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The approximate solution to the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians is 0 <= x <= 0.75. Option 1 is correct.

To solve the trigonometric inequality tan(x/4) < 1/5 over the interval 0 <= x <= 2π radians, we can use a graphing calculator and follow these steps:

Using this method, we can see that the two graphs intersect at approximately x = 0.75, x = 4.6, and x = 8.4 (or their equivalents within the interval 0 <= x <= 2π). We can also see that the tan(x/4) function is less than 1/5 between the first two intersection points (0 <= x <= 0.75 and 4.6 <= x <= 2π), but not between the second and third intersection points. Hence Option 1 is correct.

Note: Since we are rounding to the nearest degree, the approximate values may not be exact and may need to be adjusted slightly to ensure accuracy.

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Answer:

Las dimensiones del rectángulo son:

altura = 24 cm

base = 48 cm

Step-by-step explanation:

Consideración:

La formula del perímetro de un rectángulo es:

p = 2(altura+base)

Planteamiento:

144 = 2(a+b)

b = 2a

a = longitud de la base del rectángulo

b = longitud de la altura del rectángulo

de la primer ecuación del planteamiento:

144/2 = a+b

72 = a+b

b = 72-a

igualando este último valor con el de la segunda ecuación del planteamiento:

2a = 72 - a

2a + a = 72

3a = 72

a = 72/3

a = 24 cm

b = 2a

b = 2*24

b = 48 cm

Comprobación:

144 = 2(24+48)

144 = 2*72

To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.

A key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a  line AB.

Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.

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The result when 4x³ + 15x² + 17x + 6 is divide by 4x + 3 using long dividion method will be x² + 3x + 2.

Given that:

Dividend, 4x³ + 15x² + 17x + 6

Divisor, 4x + 3

The division of the polynomial is given below.

4x + 3 ) 4x³ + 15x² + 17x + 6 ( x² + 3x + 2

         - (4x³ + 3x²)

                    12x² + 17x

                 - (12x² + 9x)

                               8x + 6

                            - (8x + 6)

                                0    0    

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The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.

Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.

If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.

The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.

So, correct option is B.

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Answer:

C. Points have no size and no dimensions.

Answer:

I think it is choice A and choice C

Answer:

14

Step-by-step explanation:

l = length, w = width, h = height.

The surface area of a rectangular prism is:

2lw + 2wh + 2lh.

If the total surface area is 1648, your equation will be:

2lw + 2wh + 2lh = 1648.

lw + wh + lh = 824.

Plug in your width and height values.

16l + 16*20 + 20l = 824.

36l = 504.

Length = 14.

[tex]\boxed{\sf l=14(in)}.[/tex]

[tex]\sf SA=2(wl+hl+hw)[/tex]

Surface area (SA)= 1,648 inches;

Width (w)= 16 inches;

Height (h)= 20 inches.

[tex]\sf 1648(in)=2((16(in))l+(20(in))l+(20(in))(16(in)))[/tex]

Let's remove the units for these steps to make the algebra a little bit easier to understand.

[tex]\sf 1648=2(16l+20l+320)\\ \\1648=2(36l+320)[/tex]

Here, we apply the distributive property of multiplication. Check attached image 1.

[tex]\sf 1648=(2)(36l)+(2)(320)\\\\1648=72l+640[/tex]

[tex]\sf 1648-640=72l+640-640\\ \\1008=72l\\ \\72l= 1008[/tex]

[tex]\sf \dfrac{72l}{72} = \dfrac{1008}{72} \\ \\\\ \boxed{\sf l=14(in)}.[/tex]

If you want to verify this answer simply take the surface area formula for rectangular prisms and calculate the value for the SA using these values of lengh, width and height:

[tex]\sf SA=2((16)(14)+(20)(14)+(20)(16))=\boxed{\sf 1648}. That's\,correct![/tex]

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Answer:

38

Step-by-step explanation:

the square root of 1444 is 38.

Answer:A,D

Step-by-step explanation:

y = [5.3, 27]

x= [-1,3]

The number of students are as follows:

To find the number of students who read comics and novels only:

Let novel and textbook = x

Let textbook and comics = y

Let comic and novel = z

y + x = 11 --- (1)

y + z = 10 --- (2)

x + z = 13 --- (3)

Make y subject of the formula in (2)

y = 10 - z

substitute for y in (1)

10 - z + x = 11 --- (4)

solve (3) and (4) simultaneously by addition

10 - z + x + x + z = 11 + 13

2x = 24 - 10

x = 7

y = 11 - 7

y = 3

z  = 13 - 7

z = 4

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To find the equation of the circle with center (0, −1) that contains the point (−8, 10), we can use the standard form of the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Since the center of the circle is given as (0, −1), we have:

(x - 0)^2 + (y + 1)^2 = r^2

We still need to find the radius, r. We know that the circle passes through the point (−8, 10), so we can substitute these values for x and y and solve for r:

(-8 - 0)^2 + (10 + 1)^2 = r^2

64 + 121 = r^2

r^2 = 185

So the equation of the circle is:

x^2 + (y + 1)^2 = 185

Alternatively, we can expand the equation to get it in standard form:

x^2 + y^2 + 2y + 1 = 185

x^2 + y^2 + 2y - 184 = 0

So another form of the equation is:

x^2 + (y + 1)^2 = 185

An example of simple random sampling is given as follows:

C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.

Samples may be classified as:

Hence the samples for this problem are classified as follows:

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