10. Determine the measure of each segment. Select the statement that is true.
A) AB = JK
B) AB = GH
C) GH = JK

Solution :

Given :

Sample mean, \($\overline x = 714.2$\)

Sample size, n = 40

Standard deviation, s = 83.2

∴ The null hypothesis is \($H_0 : \mu = 703.5$\)

   Alternate hypothesis is \($H_a : \mu > 703.5$\)

Test statistic :

\($z = \frac{\overline x - \mu}{s / \sqrt n}$\)

\($z = \frac{714.2-703.5}{83.2 / \sqrt {40}}$\)

z = 0.813

Now at α = 0.05, for a right tailed,

\($z_{critical} = 1.645$\)

Since, \($z < z_{critical}$\) , we fail to reject the null hypothesis.

Applying the steps, the result of the line integral is 99.

The curve is:

\(f(x,y,z) = xy i + 9y^2 j\)

The vector field is:

\(r(t) = (x(t), y(t)) = (16t^6, t^4)\)

Applying the vector field at the curve, we have that:

\(f(t) = (16t^{10}, 9t^8)\)

The derivative of the vector field is:

\(r^{\prime}(t) = (96t^5, 4t^3)\)

The dot product of the vector field along the curve with the derivative is:

\(f(t)r^{\prime}(t) = (16t^{10}, 9t^8)(96t^5, 4t^3) = 1536t^{15} + 36t^{11}\)

Hence, the line integral is:

\(I = \int_{0}^{1} (1536t^{15} + 36t^{11}) dt\)

\(I = 96t^{16} + 3t^{12}|_{t = 0}^{t = 1}\)

\(I = 96 + 3\)

\(I = 99\)

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Answer:

x=45

Step-by-step explanation:

a=135

x+135=180

x=180-135

x=45

Answer:

17

Step-by-step explanation:

We will use angle A as theta in our trigonometric function equation.

We are dealing with hypotenuse and opposite, so the trig ratio is sine.

\(sin(39) = x/27\)

\(27sin(39)=x\)

\(27(0.6293) = x\)

\(x=16.992\)

When rounded to the nearest tenth, \(x=17\)

Answer

b. capitalized and bold

Step-by-step explanation: CORRECT ON EDGE 2021

The angle BAC and DCA are alternate interior angles , Option D is the right answer.

What are Parallel Lines ?

The lines in a plane which never intersect and are at a same distance always are called Parallel Lines.

In the given question it is given that there are two lines FG and DE

The lines are parallel to each other , and transversal are AC and BC .

The angle BAC and DCA are alternate interior angles as AC is the transversal of the parallel lines.

Option D is the right answer.

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Answer:

19

Step-by-step explanation:

product is the answer of multiplying two numbers together

342/18=19

check

19x18=342

Answer: second integer is 88  

Step-by-step explanation:

Let the integers be x, x+1, x+2 , x+3.

An equation of the line that passes through the given point and has the given slope is y = -9.

In Mathematics, the point-slope form of any straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (9, -9) and slope, m = 0, a linear equation of this line can be calculated in slope-intercept form as follows:

y - y₁ = m(x - x₁)

y - (-9) = 0(x - 9)

y + 9 = 0

y = -9

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1/8 since 4*2=8 and there is one spot you can land on with 6.

Answer:

2/8

Step-by-step explanation:

If you are spinning it twice and there is 4 places that is where you get the 8        The 2 comes from how many times you are spinning

Answer:

37

Step-by-step explanation:

The pattern is

2 (+3 =), 5 (+5 = ), 10 (+7) = , 17 (+9) =, 26 (+11) =, 37

So the difference between terms is +3, +5, +7, +9, +11... adding 2 each time, all odd numbers

Answer:

5th term is 26.

Step-by-step explanation:

5-2 =3. 10 - 5 = 5. 17 - 10 = 7.

notice how the differences are 3, 5, 7?

there's a gap of 2 between each difference.

so, let's call our next term in the sequence a.

a - 17 = (7+2).

a - 17 =9.

a = 26.

so, 5th term is 26.

The scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable is called interaction. The correct answer is C.

Interaction refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable. In other words, interaction occurs when the effect of one independent variable on the dependent variable depends on the level of another independent variable.

This can be represented in an interaction plot, where the lines representing the relationship between the dependent variable and one independent variable have different slopes at different levels of the second independent variable.

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the result is x= 1/2[㏑1745/㏑8] as exact expression and x= 1.79 when approximation in decimal.

the equations where variables present as exponent form.

we take ㏑ or㏒ on both side of equation to solve unknown variables.

in the equation 8∧2x -4 =1741

8∧2x= 1741+4

8∧2x =1745

we take㏑ on both sides of equation

㏑8∧2x= ㏑1745

as per logarithm law

2x㏑8 =㏑1745

x= 1/2[㏑1745/㏑8]

hence, x=1.79 is the solution.

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Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole

Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.

It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.

To calculate the proportion of red marbles in each sample

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Answer:

perpendicular lines

Step-by-step explanation:

Answer:

m=x+8 because the y intercept Is 8 it takes the place of b in the equation and there is no slope so there is no thus you will have a straight line on the 8on the y axis

Answer: m=x+8

good luck

Answer:

is 15.2

Step-by-step explanation:

Answer:

100 miles

Step-by-step explanation:

Let m be the number of miles.

\(100 + .30m = 50 + .80m\)

\(100 = 50 + .50m\)

\(.50m = 50\)

\(m = 100\)

Answer:

100

Step-by-step explanation:

You can put into a graph such as desmos and see where the lines intersect. the x value of the intersection is the answer you want.

Answer:

-11

Step-by-step explanation:

Notice how

\(f(x)=x^{2} +8x+1\)

So when we have

\(f(-6)=(-6)^{2} +8(-6)+1= 36-48+1=-11\)

The answer is:

f(-6) = -11

Step-by-step explanation:

Plug in -6 for x:

\(\sf{f(x)=x^2+8x+1}\)

\(\sf{f(-6)=(-6)^2+8(-6)+1}\)

Simplify this:

\(\sf{f(-6)=36-48+1}\)

\(\sf{f(-6)=-12+1}\)

\(\sf{f(-6)=-11}\)

Answer:

=£1970

Step-by-step explanation:

10%=£360

5%=£190

40%=£1440

45%=£1630

£3600-£1630=£1970

Answer:

The height of the mountain is 2305 feet.

Step-by-step explanation:

Given that:

We are provided with the angles are in degree, minutes and seconds, we are required to convert them back to degrees.

So, 47°57′52″ in degrees only will be :

=\(47^0 + 57 \times \dfrac{1}{60}+ 52 \times \dfrac{1}{3600}\)

= \(47^0 +0.95^0+0.0144^0\)

= 47.9644°

\(\simeq\) 47.96°

For the second angle after he walked a distance if 1374 feet; we have:

73°3′35″

= \(73^0 + 3 \times \dfrac{1}{60} \times 35 \times \dfrac{1}{3600}\)

= \(73^0 + 0.05 ^0 \times 0.0097^0\)

= 73.000485°

\(\simeq\) 73

From the image attached below;

x = 180° - 73° = 107°  ( angles on a striaght line)

107° + 47.96° + y = 180°   ( sum of angles in a triangle)

y = 180° - 107° - 47.96°

y = 25.04

Using sine rule:

\(\dfrac{a}{sin \ 47.96} = \dfrac{1374}{sin \ 25.04}\)

a × sin 25.04 = 1374 × sin 47.96

\(a = \dfrac{ 1374 \times sin \ 47.96} { sin \ 25.04 }\)

\(a = \dfrac{ 1020.439} {0.4233}\)

a = 2410.68

From the figure, using trigonometry rule;

\(Sin 73 = \dfrac{h}{a}\)

\(Sin \ 73 = \dfrac{h}{2410.68}\)

h = sin 73 × 2410.68

h = 0.9563 × 2410.68

h = 2305.33 feet

To the nearest whole number , the height is 2305 feet.

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Based on the scatterplot, the form of the relationshipbetween fire spread rate and wind speed   can be described as a positive correlation.

As wind speed increases,the fire spread rate also tends   to increase.

b. Direction  -

Based on the given scatterplot,the direction of the relationship between fire spread rate and wind speed appears to   be positive.

As the wind speed   increases,the fire spread rate generally tends to increase as well.

c. Strength  -

The scatterplot suggests a   moderate to strong relationship between fire spread rate and wind speed.

The data points   exhibit a somewhat linear pattern, indicating that there is a noticeable association between these variables.

The firespread rate tends to increase consistently as the wind speed increases, suggesting a relatively strong positive correlation between the two factors.

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Full Question:

Wind and Moisture: To understand how weather and landscape affect the spread of wildfires, an experiment was conducted in a low velocity wind tunnel. A fire was started in pine litter, and the researchers measured the fire spread rate for varying wind speeds and pine litter moisture contents.

Data for fires started in pine litter that had a moisture content of 4% are shown in the table below.

Wind Speed (miles/hour) Fire Spread Rate (feet/minute)

0.76                                         0

1.78                                             2

3.34                                                4

5.38                                       6

8.10                                                8

11.75                                     10

16.70                                    12

A scatterplot of these data is shown here  -

1. Based on the scatterplot, how would you describe the following with regard to the relationship between fire spread rate and wind speed?

a. Form:

b. Direction:

c. Strength:

The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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Answer:

WX= 10.4

XY= 6

Angle W= 30

Step-by-step explanation:

I attached a picture of the work, I'm not sure if side WX is rounded correctly, but I'm definitely sure side XY and angle W are correct.

Answer:

there's no graph take a screen shot of the graph and link it to the answer pls then I can help

Step-by-step explanation:

a) The initial height of the football at t = 0 is 2 feet.

b) The ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball is approximately 23.9 feet.

d) It takes approximately 4.579 seconds for the ball to hit the ground.

a) The initial height of the football at time t = 0 can be found by substituting t = 0 into the equation \(5t^2 + 20.5t + 2:h = -5(0)^2 + 20.5(0) + 2 = 0 + 0 + 2 = 2\)

Therefore, the initial height of the football is 2 feet.

b) To find the time at which the ball reaches its maximum height, we can observe the graph of the equation h = \(-5t^2 + 20.5t + 2.\) The maximum height corresponds to the vertex of the parabolic graph. The t-coordinate of the vertex can be calculated using the formula t = -b/2a, where a and b are the coefficients of the quadratic equation.

In this case, a = -5 and b = 20.5. Plugging these values into the formula, we get:

\(t = -20.5 / (2\times (-5)) = -20.5 / -10 = 2.05\)

Therefore, the ball reaches its maximum height at approximately t = 2.05 seconds.

c) The maximum height of the ball can be found by substituting the time t = 2.05 into the equation \(h = -5t^2 + 20.5t + 2:\)

h = -5(2.05)^2 + 20.5(2.05) + 2 ≈ -20.125 + 42.025 + 2 ≈ 23.9

Therefore, the maximum height of the ball is approximately 23.9 feet.

d) To find the time it takes for the ball to hit the ground, we need to determine when the height h becomes zero. We can set the equation \(-5t^2 + 20.5t + 2 = 0\) and solve for t.

This quadratic equation can be solved using factoring, the quadratic formula, or by graphing. The solutions are t ≈ -0.179 and t ≈ 4.579. Since time cannot be negative in this context, the ball takes approximately 4.579 seconds to hit the ground.

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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