The diagram shows a cuboid. 4 cm 12 cm x cm the volume of the cube is 120cm² calculate the value of x​

Answer:

Step-by-step explanation:

The relevant relations here are ...

The given arc CD is part of the semicircular arc CDA. The remaining arc, DA, is the supplement of CD:

  arc DA = 180° -CD = 180° -125° = 55°

Central angle AOD has the same measure, 55°. That is one of the acute angles in right triangle AOB, so the other one is the complement of 55°.

 ∠ABO = 90° -∠AOB = 90° -55°

  ∠ABO = 35°

In right triangle ABC, angle ABC is given as 55°. The other acute angle, ACB, will be the complement of this.

  ∠ACB = 90° -∠ABC = 90° -55°

  ∠ACB = 35°

In the figure, angles ABO and ACB have measures of 35°.

Answer:

1/8

Step-by-step explanation:

say the bar has 20 pieces. he has 10 pieces. and he gave away 1/4 of those 10

1/4 x 10 = 2.5

20 / 2.5 = 8

So his friend recieved 1/8

you could also just do 1/2 x 1/4 which is 1/8

Answer:

1/8 of the candy bar.

Step-by-step explanation:

Elias has 1/2 of a candy bar.

He gave 1/4 of 1/2 to his friend.

[tex]\sf Friend's s\ share = \dfrac{1}{4} \ of \ \dfrac{1}{2}[/tex]

                      [tex]\sf =\dfrac{1}{4}*\dfrac{1}{2}\\\\=\dfrac{1}{8}[/tex]

Answer:

6

Step-by-step explanation:

The growth factor is the same as the base of the exponential factor.

The value of the function [tex]$f(x)=(1/3)(6)^x[/tex] growth factor exists 6.

function [tex]$f(x)=(1/3)(6)^x[/tex]?

Given: [tex]$f(x)=(1/3)(6)^x[/tex]

For any equation [tex]$ f(x)=ab^x[/tex]

Let, 'a' exists the initial value

b exists the growth or decay factor.

When the value of b exists greater than 1 then its growth factor

when the value of b exists between 0 and 1 then it exists a decay factor

Let x exists the number of years

Given function, [tex]$ f(x)=(1/3)(6)^x[/tex]

The value of b exists 6.

So the growth factor exists 6.

Therefore, the correct answer is option c. 6.

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Using the Laplace transform to solve the given integral equation  f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is [tex]\frac{4(1-2e^-5s)/}{s}[/tex]

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

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Applying the angle of intersecting chords theorem, the value of z is: D. 100.

According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.

Applying the angle of intersecting chords theorem, let's find x first:

73 = 1/2(96 + x)

Multiply both sides by 2

2 × (73) = 1/2(96 + x) × 2

146 = 96 + x

Subtract both sides by 96

146 - 96 = 96 + x - 96

50 = x

x = 50°

Therefore:

x + z + 96 + 114 = 360° [full circle measure]

Plug in the value of x

50 + z + 96 + 114 = 360

z + 260 = 360

Subtract both sides by 260

z + 260 - 260 = 360 - 260

z = 100°

The answer is: D. 100°.

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No, we can only suppose that the observed distribution deviates from the expected distribution when we reject the null hypothesis.

The null hypothesis exists as a specific mathematical theory that claims that there exists no statistical relationship and significance between two sets of observed data and estimated phenomena for each set of selected, single observable variables. The null hypothesis can be estimated to define whether or not there exists a relationship between two measured phenomena, which creates it useful. It can let the user comprehend if the outcomes exist as the product of random events or intentional manipulation of a phenomenon.

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The width on the blueprint is 4 inches.

The blueprint is a scale drawing of the building. A scale drawing is a reduced form in terms of dimensions of an original image / building / object

The scale of a drawing is usually written in this format - length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 inch 12 feet. This scale means that 1 inch of the blueprint represents 12 feet of the building.

Width of the building on the blueprint = 48 / 12 = 4 inches

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Answer:

x=0, x= -9

Step-by-step explanation:

First we simplify the equation into the form

ax^{2}+bx+c=0

By adding 4x+3 on both sides, we form the equation

x^{2}+9x=0

Now, we factor out the common factor: x.

x(x+9)=0

The only values that allow x(x+9) to be equal to 0 are:

x=0  or

x+9=0

The solutions are x=0 or x= -9

Answer:

A = 0; B = -9/2

Step-by-step explanation:

To have no solutions, you need parallel lines with equal slopes and different y-intercepts.

3x + 4y = A      Eq. 1

Bx - 6y = 15     Eq. 2

In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.

We must have the same ratio for the coefficients in Eq. 2.

B/(-6) = 3/4

4B = -6(3)

4B = -18

B = -9/2

Now we have

3x + 4y = A      Eq. 1

-9/2 x - 6y = 15     Eq. 2

How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2

To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.

If we divide 15 by -3/2 we get -10.

The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.

To have no equations, the y-intercepts must be different, so A can be any number other that -10.

Answer: A = 0; B = -9/2

The perimeter of the rhombus FGHJ is 20 units

The coordinates are given as:

F = (-2, -2)

G = (-2, 3)

H = (2, 6)

From the question, we understand that vertex J is directly below vertex H.

This means that vertices H and J have the same x coordinate.

So, we have

J = (2, y)

The distance between F and G is 5 units,

So, we have

J = (2, y - 5)

Where

y = 6 i.e. the y coordinate of H

This gives

J = (2, 6 - 5)

Evaluate

J = (2, 1)

See attachment for the graph of the rhombus

In (a), we have:

The distance between F and G is 5 units,

This means that

FG = 5

The side lengths of a rhombus are equal.

So, the perimeter is

P = 4 * FG

This gives

P =4 * 5

Evaluate

P = 20

Hence, the perimeter of the rhombus is 20 units

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Answer:

175 cal

Step-by-step explanation:

if 12oz = 300 cal

then, 7 oz = ?

cross multiplication

12×?= 7×300

? = 2100/12

? = 175 cal

NB: you can replace the question mark with any variable.

Answer:

[tex]y=\frac{-x}{78} -\frac{220}{78}[/tex]

Step-by-step explanation:

Remember to create a line perpendicular to one another the slope has to be the reverse reciprocal of the first line.

Given the current slope is [tex]\frac{-78}{1}[/tex] the new slope would be [tex]\frac{1}{78}[/tex].

To find the line that passes through a point with a given slope we must use point slope form, remember the default equation of point slope form:

[tex]y-y1=m(x-x1)[/tex]

Where y1 is the y value of the point, m is the slope, and x1 is the x value of the point.

Lets substitute in our values

[tex]y-(-3)=\frac{-1}{78} (x-14)[/tex]

Simplify the equation

[tex]y+3=-\frac{1}{78}\left(x-14\right)\\y+3=\frac{-x}{78}+\frac{14}{78}\\y=\frac{-x}{78}-\frac{220}{78}\\[/tex]

The summary of the given data is are as follows :-

Minimum: 11

Lower quartile:11

Median:24

Upper quartile:34

Maximum:45

Interquartile range:23

Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45

Minimum = The smallest number of data

Thus Minimum = 11

Maximum = The largest number of data

Thus Maximum = 45

Median = The middle number of the data if data consists of odd number of elements

Thus Median = 45

Lower quartile = The median of the lower half of data

Thus Lower quartile = 11

Upper quartile = The median of the upper half of data

Thus Upper Quartile = 34

Interquartile range = The difference of upper and lower quartiles,

Thus Interquartile range = 34 -11 = 23

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The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

simplifying the equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

A random sample of 15 men exists selected. The mean weight exists at $165.2 pounds and the standard deviation exists at $13.5 pounds. The population exists normally distributed.

So, [tex]$n=15, \bar{X}=165.2, s=13.5$[/tex]

where n exists the sample size, [tex]$\bar{X}$[/tex] exists the sample size

s exists the sample standard deviation.

The degrees of freedom will be n - 1 i.e.15 - 1 = 14.

For a 95% confidence interval, the level of significance will be [tex]$\alpha=0.05$[/tex].

The 95% confidence interval for the population standard deviation will be,

[tex]$\sqrt{\frac{(n-1) s^{2}}{\chi^{2}} \frac{\alpha}{2}} & < \sigma < \sqrt{\frac{(n-1) s^{2}}{\chi^{2}}} \\[/tex]

substitute the values in the above equation, we get

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi^{2}} 0.05} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0}^{2}}} \\[/tex]

[tex]$\sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.975}^{2}}} & < \sigma < \sqrt{\frac{(15-1)(13.5)^{2}}{\chi_{0.025}^{2}}} \\[/tex]

simplifying the above equation, we get

[tex]$\sqrt{\frac{2551.5}{26.1}} & < \sigma < \sqrt{\frac{2551.5}{5.63}} \\9.887 & < \sigma < 21.288[/tex]

The 95% confidence interval exists (9.887, 21.288).

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Answer:

1441.503 square inches

Step-by-step explanation:

155×60cm=9300square centimeter

9300 divide 6.452 to change to square inches.

Ans=1441.503

Answer:

64.58 sq.in

Step-by-step explanation:

[tex]y = 2x {}^{2} - 4x - 16 \\ \delta = b {}^{2} - 4ac \\ \delta = ( - 4) {}^{2} - 4(2)( - 16) \\ \delta = 16 + 128 \\ \delta = 144 > 0 [/tex]

[tex]x = \frac{ - b + \sqrt{ \delta} }{2a} = \frac{4 + 12}{2 \times 2} = \frac{16}{4} = 4[/tex]

[tex]x = \frac{ - b - \sqrt{ \delta} }{2a} = \frac{4 - 12}{2 \times 2} \frac{ - 8}{4} = - 2[/tex]

[tex]x = 4 \: \: \: \: \: or \: \: \: \: x = - 2 \\ (x - 4) = 0 \: \: \: \: \: or \: \: \: \: \: (x + 2) = 0[/tex]

Answer: (f+g)(x)=2(x-2)(x+1).

Step-by-step explanation:

[tex]f(x)=x^2-3x-4\ \ \ \ \ g(x)=x^2+x\\(f+g)(x)=(x^2-3x-4)+(x^2+x)\\(f+g)(x)=x^2-3x-4+x^2+x\\(f+g)(x)=2x^2-2x-4\\(f+g)(x)=2*(x^2-x-2)\\(f+g)(x)=2*(x^2-2x+x-2)\\(f+g)(x)=2*(x*(x-2)+(x-2))\\(f+g)(x)=2*(x-2)*(x+1).[/tex]

Answer:

1/311875200.

There is exactly 1 way to have all 5 of these cards.  For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:

(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.

Step-by-step explanation:

The mode of the set of 10 observations is 2.

What is the mode?

Mode refers to a value that appears most frequently in a data set. Mode is a measure of central tendency of a data set. Other measures of central tendency are mean and median.

According to the information in the question, 6 appears twice in the data set and all other values are different. Thus, 6 has the frequency of 2 which is the highest. 6 is the mode.

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Answer:

2

Step-by-step explanation:

Your slope is your change in y over your change in x.  The ordered pair is in the form of (x,y), so you subtract the y's and put that in your numerator (top)and subtract your x's and put that in your denominators (bottom).

2 - (-4) would be your top number.  To subtract a negative number is the same as adding a positive, so 2 - (-4) is the same as 2 +4, so your top number is 6.  

Now, to find the bottom number, you subtract the x's.

5-2 which is 3.

We now have the top and the bottom number

6/3 which is the same as 2.

1/2 value can be used as the common ratio in an explicit formula that represents the sequence.

Definition of sequence -

A sequence that progresses geometrically has the first term as 12.

Each number is the previous number divided by 2.

so the sequence will be 12, 6, 3, 1.5...........

Explicit formula of a geometric sequence is given by

[tex]T_{n} = ar^{n-1}[/tex]

Where [tex]T_{n}[/tex]  = nth term of the sequence

a = first term

r = common ratio

and n = number of term

In this sequence common ratio = [tex]\frac{Successive term }{previous term}[/tex]

            = 6/12

            =  1/2

Therefore, common ratio will be 1/2.

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The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

In this question we have a kind of recursive function known as Fibonacci's function, where a value of the series is generated from at least immediately previous elements. In this case, we need to find the first three elements from the fifth and fourth elements of the series:

[tex]a_{n-2} = a_{n-1} - a_{n} + 4[/tex]

a₄ = a₅ - a₆ + 4

a₄ = - 2 - 0 + 4

a₄ = 2

a₃ = a₄ - a₅ + 4

a₃ = 2 - (- 2) + 4

a₃ = 8

a₂ = a₃ - a₄ + 4

a₂ = 8 - 2 + 4

a₂ = 10

a₁ = a₂ - a₃ + 4

a₁ = 10 - 8 + 4

a₁ = 6

The first three elements of the recursive series are 6, 10, 8. (Correct choice: B)

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Step-by-step explanation:

1 meter = 100 centimeter = 1000 millimeter

therefore, 1 cm = 10 mm

4.6 m = 4.6 × 1000 = 4600 mm

88 cm = 880 mm

and so, they cut off

880 mm + 1630 mm = 2510 mm

that means

4600 - 2510 = 2090 mm = 2.09 m

are left.

Answer:

22.05

Step-by-step explanation:

First, convert 63% into a decimal.

To do this, divide it by 100.

[tex] \frac{63}{100} = 0.63[/tex]

Multiply 0.63 by 35.

[tex]35 \times (0.63) = 22.05[/tex]

Answer:

Step-by-step explanation:

.63(35)= 22.05

Multiply .63(35)

Answer: 4.0 * 10^0 kg = 4.0 kg essentially

Step-by-step explanation:

No need to convert these to numbers...

Weight of 1 bee: 1 * 10^-4 = (0.0001 kg)

Number of bees: 4 * 10^4 = (40000 bees)

(1 * 10^-4) * (4 * 10^4) =

(1 * 4) * (10^-4 * 10^4) =

(10^0 because when multiply exponential numbers, you add the exponents)

4 * 10^0 =

4 * 1 = 4 kg

Answer:

Step-by-step explanation:

3 units

Answer:

3 units.

Step-by-step explanation:

Opposite sides of a parallelogram are equal in length,

So side OD = side WS.

We see from the diagram that OD is 3 units long so

WS = 3 also.

The average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

The function is given as:

[tex]h(x) = \frac 18x^3 - x^2[/tex]

The interval is given as:

−2 ≤ x ≤ 2

Calculate h(2) and h(-2)

[tex]h(2) = \frac 18 * 2^3 - (2)^2[/tex]

h(2) = -3

[tex]h(-2) = \frac 18 * (-2)^3 - (-2)^2[/tex]

h(-2) = -5

The average rate of change is then calculated as:

[tex]m = \frac{h(-2) - h(2)}{-2-2}[/tex]

This gives

[tex]m = \frac{-5 + 3}{-4}[/tex]

Evaluate

m = 1/2

Hence, the average rate of change of the function over −2 ≤ x ≤ 2 is 1/2

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Complete question

[tex]h(x) = \frac 18x^3 - x^2[/tex]

What is the average rate of change of h over the interval −2 ≤ x ≤ 2