Easy 6th grade math ! Help please :)

Answer:

87.7 degrees.

Step-by-step explanation:

In triangle ABC, attached.

The height of the building |AB|=443 meters

The distance of the agent across the street , |BC|=18 meters

We want to determine the angle at C.

Now,

[tex]Tan C=\dfrac{|AB|}{|BC|} \\C=arctan (\dfrac{|AB|}{|BC|} )\\=arctan (\dfrac{443}{18} )\\=87.67^\circ\\\approx 87.7^\circ $(correct to the nearest tenth)[/tex]

The agent should sfoot his laser gun at an angle of 87.7 degrees.

Complete Question

Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?

Answer:

(B) 4x = 45

Step-by-step explanation:

The given proportion is:

[Tex]\dfrac{4}{5}=\dfrac{9}{x}[/TeX]

To find an equivalent expression, let us cross multiply:

4*x=5*9

This gives:

4x=45

The correct option is B.

Answer:

D

Step-by-step explanation:

SEX

Answer:

∠1 = 31°

∠2 = 43°

Step-by-step explanation:

All triangles have a sum of 180°

Since we know this, then we know that in the end, the sum of the two triangles should both have a sum of 180° each.

∠2 equals 43° because it corresponds to ∠C and corresponding angles have the same measurement.

Now we can find the measurement of ∠1 by using the big triangle.

180 - (106 + 43)

180 - (149)

31°

So, the measurement of ∠1 is 31°.

Now, let's check our work.

Big triangle:

106 + 43 + 31 = 180

Small triangle:

43 + 31 + 106 = 180

Answer:

0.545 = 54.5% probability that it came from machine A

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Defective.

Event B: Coming from machine A.

Machine A is responsible for 30%

This means that [tex]P(B) = 0.3[/tex]

10% of the output from machine A is defective

This means that [tex]P(B|A) = 0.1[/tex]

Probability of being defective:

Machine A is responsible for 30%. Of those, 10% are defective.

Machine B is responsible for 20%. Of those, 5% are defective.

Machine C is responsible for 100 - (30+20) = 50%. Of those, 3% are defective. Then

[tex]P(A) = 0.3*0.1 + 0.2*0.05 + 0.5*0.03 = 0.055[/tex]

Finally:

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)} = \frac{0.3*0.1}{0.055} = 0.545[/tex]

0.545 = 54.5% probability that it came from machine A

Answer:

Check the explanation

Step-by-step explanation:

Let X denotes steel ball and Y denotes diamond

[tex]\bar{x_1}[/tex] = 1/9( 50+57+......+51+53)

=530/9

=58.89

[tex]\bar{x_2}[/tex]= 1/9( 52+ 56+....+ 51+ 56)

=543/9

=60.33

difference = d =(60.33- 58.89)

=1.44

[tex]s^2=1/n\sum xi^2 - n/(n-1)\bar{x}^2[/tex]

s12 = 1/9( 502+572+......+512+532) -9/8 (58.89)2

=31686/8 - 9/8( 3468.03)

=3960.75 - 3901.53

=59.22

s1 = 7.69

s22 = 1/9( 522+ 562+....+ 512+ 562) -9/8 (60.33)2

=33295/8 - 9/8 (3640.11)

=4161.875 - 4095.12

=66.75

s2 =8.17

sample standard deviation for difference is

s=[tex]\sqrt{[(n1-1)s_1^2+ (n2-1)s_2^2]/(n1+n2-2)}[/tex]

 = [tex]\sqrt{[(9-1)*59.22+ (9-1)*66.75]/(9+9-2)}[/tex]

= [tex]\sqrt{1007.76/16}[/tex]

=7.93

sd = [tex]s*\sqrt{(1/n1)+(1/n2)}[/tex]

=[tex]7.93*\sqrt{(1/9)+(1/9)}[/tex]

=7.93* 0.47

=3.74

For 95% confidence level [tex]Z (\alpha /2)[/tex] =1.96

confidence interval is

[tex]d\pm Z(\alpha /2)*s_d[/tex]

=(1.44 - 1.96* 3.75 , 1.44+1.96* 3.75)

=(1.44 - 7.35 , 1.44 + 7.35)

=(-2.31, 8.79)

There is sufficient evidence to conclude that the two indenters produce different hardness readings.

The correct options are:

A, C and E.

Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many categories. The forms are often enclosed by an outline or border that is composed of points, lines, curves, etc.

As per the given data:

We are given some shapes in the diagram, and we are also given the type of the shape, we have to identify the correct options out of the given options.

Figure A is a cylinder.

This is correct, as the figure correctly resemble a cylinder.

Figure B is a square pyramid.

This is incorrect, as the figure resembles a cone.

Figure C has no bases.

This is correct, as the figure correctly resemble a sphere and it has no base.

Figure D is a triangular prism.

This is incorrect, as the figure resembles a rectangular prism.

Figure D has four lateral faces that are triangles.

This is correct, as the figure correctly resemble a rectangular prism with four lateral faces that are triangles.

Hence, the correct options are:

A, C and E.

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Answer:

1 and 1/30 gallons of paint

Step-by-step explanation:

Answer:

Type 1 Error: Stating 'American families owing house< 67.4%', when it = 67.4%

And, implementing the tax break for first time home buyers, due to the error

Step-by-step explanation:

Null Hypothesis [H0] : American families owing house = 67.4%

Alternate Hypothesis [H1] : American families owing house < 67.4%

Type 1 error is he rejection of an actually true null hypothesis.

In this case, it means : Results reject H0 in favour of H1 & state that 'american families owing house < 67.4% ; when actually null hypothesis, i.e 'american families owing house = 67.4%'  is true.

This would imply that city council might extend the tax breaks for first time home buyers because of the type 1 error in the case. When, it is actually not needed as per the true data status.

Answer:

0.0228, Hope that useful for you.

Step-by-step explanation:

Because of " the scores...normally distributed of a mean 310 and the standard deviation 12", we can use the Central limit theorem.

That means:

([tex]P(X>334)= P(\frac{X-E(X)}{SD(X)}>\frac{334-310}{12})= P(Z>2)= 1-P(Z\leq 2)= \\1- 0.9772= 0.0228[/tex]

Answer:

7.4

Step-by-step explanation:

To calculate the time taken to travel a certain distance at a certain speed, use the formula: Time = Distance/Speed. In this case, to travel 520 miles at 70 miles per hour, it would take approximately 7.43 hours or 7 hours and 26 minutes.

The subject of this question is about calculating time based on speed and distance in a real-world context. To find out how many hours it will take you to reach your destination travelling at 70 miles per hour for 520 miles, we use the formula: Time = Distance / Speed. In this context, the distance is 520 miles and the speed is 70 miles per hour. Insert these values into the formula, you get: Time = 520 / 70 which gives you approximately 7.43 hours. This means it would take you about 7 hours and 26 minutes to reach your destination, if you were traveling at a consistent speed of 70 miles per hour.

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Answer:

B. 280 units cubed

Step-by-step explanation:

Multiply all of the numbers together

Answer: 9

Step-by-step explanation:

In order to make the expression a perfect square, ,we ate going to add to the expression the square of the half of the coefficient of 6.

x² + 6x + c

= x² + 6x + (6/2)²

= x² + 6x + 3²

= x² + 6x + 9

Therefore, 9 is the required solution that will.make the expression a perfect square.

Answer:

9

Step-by-step explanation.

x² + 6x + 9

= (x+3)(x+3)

= (x + 3)²

it is a perfect square trinomial when c is equal to 9

To calculate the volume of the region W, set up and evaluate a triple integral over the given region. Identify the bounds, write the triple integral, find the limits of integration, and evaluate the integral.

To calculate the volume of the region W, we need to set up and evaluate a triple integral. We will integrate over the region defined by the given inequalities. Let's break it down step by step:

Identify the bounds of the region:

Write the triple integral:

∫∫∫ f(x,y,z) dz dy dx

Find the limits of integration:

Evaluate the integral:

Integrate the function f(x,y,z) over the given limits. The function f(x,y,z) will depend on the specific problem you are trying to solve.

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The volume of the region bounded by z = 100 - y², y = 10x², and the plane z = 0, is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.

To find the volume of the region W bounded by z = 100 - y², y = 10x², and the plane z = 0, we need to evaluate a triple integral in the order dz dy dx. We can start by setting up the integral:

Thus, the triple integral is:

[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} \int_{0}^{100-y^2} dz \, dy \, dx \][/tex]

First, we integrate with respect to z:

⇒ [tex]\[ \int_{0}^{100-y^2} dz = (100-y^2) - 0 = 100 - y^2 \][/tex]

This reduces our integral to:

[tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \int_{0}^{100} (100 - y^2) \, dy \, dx \][/tex]

Next, we integrate with respect to y:

⇒ [tex]\[ \int_{0}^{100} (100 - y^2) \, dy = 100y - \frac{y^3}{3} \bigg|_{0}^{100}[/tex]

⇒ [tex]100(100) - \frac{(100)^3}{3} = 10000 - \frac{1000000}{3}[/tex]

⇒ 10000 - 333333.33 = [tex]\frac{20000}{3}[/tex]

Finally, we integrate with respect to x:

⇒ [tex]\[ \int_{-\sqrt{10}}^{\sqrt{10}} \left( \frac{20000}{3} \right)[/tex] [tex]dx = \frac{20000}{3} \left[ x \right]_{-\sqrt{10}}^{\sqrt{10}}[/tex]

⇒ [tex]\frac{20000}{3} ( 2\sqrt{10})[/tex] = [tex]\frac{40000 \sqrt{10}}{3}[/tex]

Therefore, the volume of W is [tex]\(\frac{40000 \sqrt{10}}{3} \)[/tex] cubic units.

For a positive angle coterminal to 127°, select Graph B (with angle measurement of 492°). For the angle 79°, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.

A positive angle coterminal to 127° can be found by adding 360° to it, since coterminal angles are separated by full rotations:

1.First Positive Coterminal Angle:

 [tex]\( 127° + 360° = 487° \)[/tex] (This is not one of the choices provided.)

2.Second Positive Coterminal Angle:

  [tex]\( 487° + 360° = 847° \)[/tex] (This is beyond the range of the options provided.)

However, if we look for a coterminal angle between 360° and 720°, we find:

 [tex]\( 127° + 360° = 487° \)[/tex], which is closer to 492° given in Graph B.

For the angle 79°:

1.Positive Coterminal Angles:

  - Add 360° for the first positive coterminal angle:

    [tex]\( 79° + 360° = 439° \)[/tex]

  - Add another 360° for the second positive coterminal angle:

 [tex]\( 79° + 720° = 799° \)[/tex]

2. Negative Coterminal Angles:

  - Subtract 360° for the first negative coterminal angle:

   [tex]\( 79° - 360° = -281° \)[/tex]

  - Subtract 720° for the second negative coterminal angle:

    [tex]\( 79° - 720° = -641° \)[/tex] (However, this is not the nearest negative coterminal angle.)

The first negative coterminal angle is already the nearest, so the second negative coterminal angle is actually the original angle itself, which is 79° (since subtracting 0° gives us the same angle).

So, the nearest two positive coterminal angles are 439° and 799°, and the nearest two negative coterminal angles are -281° and 79°.

complete question given below:

Answer:

7, -7

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

The required value of the quadratic function which is determined by the using quadratic formula would be [tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]   which is the correct answer would be an option (B).

The quadratic function is defined as a function containing the highest power of a variable is two.

We have been given that quadratic function as

5x = 6x² – 3

⇒ 6x² - 5x  - 3 = 0

Compare the given function to the standard quadratic function

f(x) = ax² + b x + c = 0.

We get a = 6, b = -5 and c = -3

Using the quadratic formula to solve the above quadratic function

[tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 6, b = -5 and c = -3 in the quadratic formula

[tex]x = \dfrac{-(-5)\pm\sqrt{-5^2-4\times6\times-3}}{2\times6}[/tex]

[tex]x = \dfrac{5\pm\sqrt{25+72}}{12}[/tex]

[tex]x = \dfrac{5\pm\sqrt{97}}{12}[/tex]

Therefore, the correct answer would be an option (B).

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Answer:

100000

Step-by-step explanation:

[tex] {10}^{5} = 100000[/tex]

[tex]10 \times 10 \times 10 \times 10 \times 10 = 100000[/tex]

Answer:

y=2x+1

Step-by-step explanation:

A(1;3)  and m=2

y-yA=m(x-xA)

y-3=2(x-1)

y-3=2x-2

y=2x+1; or 2x-y+1=0

Answer:

solution is : x = -6 and x = 2

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Answer:

(2.5,5)

Step-by-step explanation:

The x coordinate of the midpoint is found by averaging the x coordinates

(-1+6)/2 = 5/2 = 2.5

The y coordinate of the midpoint is found by averaging the y coordinates

(5+5)/2 = 10/2 = 5

Answer:

I think it's 2,772

Step-by-step explanation:

I did

36-14=22

Then I did 22× $126

hi

if  14 = 126

   36 =  ?  

:  36*126 /14 = 324

Answer:

That should be pentagon, irregular

(5 sides which are not equal)

Hope this helps!

:)

The requried, Il. The voluntary response makes it likely that the most dissatisfied people were the ones to respond. Ill. The response suffers from under coverage. are true. Option A is correct.

The survey is defined as an activity that took the participation of the public in order to improve the service by taking feedback from the targeted public.

here,
As of the given conditions,
The number of people that returned the voluntaries is not a very large number, while the voluntary response increases the likelihood that the most dissatisfied people responded, the response also suffers from under coverage

.

Thus, Both II and III are correct statements. Option A is correct.

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Answer:

22%

Step-by-step explanation:

Answer:

22% tax bracket

Step-by-step explanation:

Answer:

Step-by-step explanation:

let width=x

length=x+4

height=x-2

A=W×L

252=(x)(x+4)

252=x^2 +4x

0=x^2 +4x -252

use quadratic formula

x=14

W=14

L=18

H=12

V=W×L×H

V=(14)(18)(12)

Final answer:

To calculate the volume of the crate, solve for the width using the base area and the relation between length and width, then find the height. Multiply length, width, and height to obtain the crate's volume.

Explanation:

To find the volume of the crate, we must first determine the dimensions of the base. We know that the area of the base is 252 square inches, and that the length (L) is 4 inches greater than the width (W).

Therefore, we can express the length as L = W + 4. Since the area of a rectangle is given by length times width (A = L × W), we can write the equation W × (W + 4) = 252.

Step 1: Find the width (w)

Substitute l=w+4 into the first equation:

w² + 4w - 252= 0

Solve the quadratic equation using the quadratic formula:

w = −b ±√ b²−4ac​​/2a

where a=1, b=4, and c=−252.

w = −4 ± √4²−4 × 1 × −252​​/2 × 1

w = −4 ± √1024​​/2

w = −4 ± 32​/2

Since the width cannot be negative, we discard the negative solution.

Therefore, w=14 inches.

Step 2: Find the length (l) and height (h)

l=w+4=14+4=18 inches

h=w−2=14−2=12 inches

Step 3: Find the volume (V)

V = l × w × h = 18 × 14 × 12 = 3024 cubic inches.

Answer:

- The integral of arctan(x)/x =

C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

- The radius of convergence is R = 1/x

Step-by-step explanation:

First note that

tan^(-1)x = arctan(x)

And

arctan(x) = Σ [(-1)^n. x^(2n+1)]/(2n+1). From n = 0 to infinity

arctan(x)/x = Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity

∫arctan(x)/x dx = ∫{Σ [(-1)^n. x^(2n)]/(2n+1). From n = 0 to infinity}dx

= ∫{Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.∫x^(2n)dx

= {Σ [(-1)^n]/(2n+1) .From n = 0 to infinity}.x^(2n+1)/(2n+1) + C

= C + Σ [(-1)^n.x^(2n+1)]/(2n+1)². (From n = 0 to infinity).

To obtain the radius of convergence, we apply the ration test

R = Limit as n approaches infinity |a_n/a_(n+1)|

a_n = (-1)^n.x^(2n+1)]/(2n+1)²

a_(n+1) = (-1)^(n+1).x^(2(n+1)+1)]/(2(n+1)+1)²

|a_n/a_(n+1)| = (2(n+1) + 1)²/(2n+1)².x

= (1/x)[1 + 2/(2n+1)]

R = Limit as n approaches infinity |a_n/a_(n+1)|

= R = Limit as n approaches infinity (1/x)[1 + 2/(2n+1)]

R = 1/x

The integration of the arctan (x)/x is C + Σ [(-1)^n x^(2n+1)]/(2n+1)² where n is from 0 to ∞. The radius of convergence is R = 1/x

It is the reverse of differentiation.

The indefinite integral is a power series that will be

[tex]\rm \int \dfrac{\tan^{-1}x }{ x} \ dx[/tex]

We know that the arctan is given as

[tex]\rm \tan^{-1} x = \dfrac{\sum [(-1)^n \ x^{2n+1}]}{(2n+1)}\\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ x^{2n})]}{(2n+1)}\\\\\\\dfrac{\tan^{-1} x }{x} = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n}[/tex]

Then we have

[tex]\rm \int \dfrac{\tan^{-1} x }{x}\ dx= \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \ x^{2n} dx\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \dfrac{\sum [(-1)^n \ ]}{(2n+1)} \ \int x^{2n}\\\\\\\int \dfrac{\tan^{-1} x }{x} \ dx = \int \dfrac{\sum [(-1)^n \ ]}{(2n+1)^2} x^{2n + 1} + C[/tex]

To obtain the radius of convergence, then the ration test

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{a_n}{a_{n+1}}\\\\\\a_n = \dfrac{(-1)^n \ x^{2n+1} }{(2n+1)^2}\\\\\\a_{n+1} = \dfrac{(-1)^{n+1} \ x^{2(n+1)+1} }{(2(n+1)+1)^2}\\\\\\ \dfrac{a_n}{a_{n+1}} = \dfrac{1}{x}(1+\dfrac{2}{2n+1})[/tex]

Then we have

[tex]\rm R = \displaystyle \lim_{n \to \infty} \dfrac{1}{x}(1+\dfrac{2}{2n+1})\\\\\\R = \dfrac{1}{x}[/tex]

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Answer:

largest area that can be enclosed = 8,000,000 m²

Step-by-step explanation:

Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.

Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.

Since we know the amount of fencing available is 8000m, we get:

8000 = x + 2y

solving for x, we have;

x = 8000 - 2y

substitute 8000 - 2y for x into the area equation to give;

A = (8000 - 2y)y distribute

A = -2y² + 8000y

Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,

Thus; y = -b/2a = -8000/[2(-2)] = 2000

x = 8000 - 2(2000) = 4000

A = 4000(2000) = 8,000,000 m²

Answer:

All the statement are true about these functions

Step-by-step explanation:

Given any monomial function where a=1 and n is even.

Attached is the graph of [tex]y=x^4 \:\&\: y=x^6[/tex] as a case study.

From the graphs, the following are observed.

To graph monomial functions where a = 1 and n is even, enter the equations into a graphing calculator and observe the graph. The graph opens up, passes through the origin, and is symmetric about the y-axis.

To graph the monomial functions where $a=1$ and $n$ is even, we can use a graphing calculator. For example, to graph $y=x^4, y=x^6$, and $y=x^8$, we can enter these equations into the graphing calculator and select an appropriate viewing window. By tracing along these functions, we can make the following observations:

Based on these observations, we can conclude that all of these statements are true about the graph of the monomial functions with $a=1$ and even $n$.

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Answer:

12.55

Step-by-step explanation:

Answer:

[tex]Area\,\,of\,\,the\,\, circle=12.56\,\, units ^2[/tex]

Step-by-step explanation:

Circumference of the circle= 12.56 units

[tex]Circumference=2\times\pi \times r[/tex]

As,

[tex]\pi =\dfrac{22}{7}=3.14[/tex]

     [tex]2\pi r=12.56\\\\2\times 3.14 \times r=12.56\\\\6.28\times r=12.56\\\\r=\dfrac{12.56}{6.28} \\\\r=2\,\,units[/tex]

Area of a circle= [tex]=\pi \times r^2[/tex]

                        [tex]=3.14\times 2^2\\\\\=3.14\times 4\\\\=12.56\,\, units ^2[/tex]