To test if an observed frequency distribution with five classes is normally distributed, we need to find _____.a. The t-statisticb. The expected, normally distributed class frequenciesc. The class marksd. The class relative frequencies

Answer:

60

Step-by-step explanation:

3/2t-16=4/3t-6

       +16      +16

3/2t=4/3t+10

      -4/3t

(t/6)6/1= 10(6/1)

t=60

Answer:

\(t=60\)

Step-by-step explanation:

To get both variables on one side, do the opposite of their current form and move them over (I'm not sure how else to explain this, so I'm just going to show you).

\(\frac{3}{2} t-16=\frac{4}{3} t-6\)

You see that the \(\frac{4}{3} t\) is positive, so you subtract it. The same goes for the -16 (do the opposite). You would add the -16 to the other side.

You need to do the opposite of them because only one number exists. If you move it, you need to cancel it out so that there is always only one of that number. (so when you add the -16 to the other side, the one on the left cancels out, but the same value (16) is still present on the right side and is added).

\(\frac{3}{2} t-\frac{4}{3} t=-6+16\)

Now you have this after moving like terms to their coinciding sides (you could do this any way, btw. It doesn't matter what order you add everything, so long as you get t on one side and by itself).

\(\frac{9}{6} t-\frac{8}{6}t =-6+16\\\frac{1}{6} t=10\\(\frac{6}{1} )(\frac{1}{6} t)=(\frac{6}{1} )(10)\\t=60\)

** Everything you do on one side, you need to do on the other side. This is a very important rule (and it goes hand in hand with the idea that there can only be one of each value, unless the exact same value appeared on both sides in the given equation).

Answer:

use this info to help answer it

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.

Answer:

Step-by-step explanation:

You want the area and volume ratios when two figures have a similarity ratio of 2 : 7.

The ratio of areas is the square of the similarity ratio:

  2² : 7² = 4 : 49

The ratio of volumes is the cube of the similarity ratio:

  2³ : 7³ = 8 : 343

__

Additional comment

It can help to think about the units of area and volume. For linear dimensions in inches, area dimensions are in square inches, and volume dimensions are cubic inches. Any ratio of inches will be squared when those inch dimensions are used for area, and will be cubed when volume is computed.

  side length of a square or cube: smaller: 2", larger: 7"

  area of the square: smaller: 2² in², larger: 7² in² or 4 in² and 49 in²

  volume of the cube: smaller: 2³ in³, larger: 7³ in³ or 8 in³ and 343 in³

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The margin of error for a 95% confidence interval assuming the previous study enrolled 600 individuals is C . E = ± 4.00

Based on the information, the following can be deduced:

n = 600

mean = 490.

standard deviation = 50.

At 95% confidence interval, z will be:

= 1 - 95%

= 0.05

Using the distribution table, the value will be Z(0.05/2) = Z value of 0.025 = 1.96

Therefore, the margin of error for a 95% confidence interval assuming the previous study enrolled 600 individuals will be:

= ± 1.96 × 50/✓n

= ± 4.00

In conclusion, the correct option is C.

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Answer:

f(-7) = -19

Step-by-step explanation:

Let us solve the problem

∵ f(x) = 2x - 5

∵ g(x) = -3x - 1

∵ h(x) = 2x² + x - 7

→ We need to find f(-7), that means substitute x in f(x) by -7

∵ x in f(x) = -7

∵ f(x) = 2x - 5

∴ f(-7) = 2(-7) - 5

→ Calculate 2 × (-7)

∴ f(-7) = -14 - 5

→ Add them

∴ f(-7) = -19

BC is tangent to circle A, and the value of r is 10.

Given,

BC=24

CD=16

AD=AB=r

To find the value of r, we can use the fact that a tangent line to a circle is perpendicular to the radius at the point of tangency. So we know that angle ABD is a right angle, and we can use the Pythagorean theorem

The Pythagorean theorem can be used to calculate the value of r:

\(AB^2+BC^2=AC^2\)

\(r^2+24^2=(r+16)^2\)

\(r^2= (r+16)^2-24^2\)

\(r^2\)= \(r^2\)+256+32r-576

\(r^2\)=\(r^2\)+32r-320

\(r^2-r^2\)-32r=-320

-32r=-320

r=320/32

r=10

Therefore the correct answer is r=10.

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Answer:

The common denominator will be 70

Step-by-step explanation:

To set the fractions to a common denominator, we need to know what number they both share. In this case, both 7 and 10 share the number 70, since 7 * 10 is 70.

Therefore, we can multiply 2/7 by 10/10 and 3/10 by 7/7:

\(\frac{2}{7}\) * \(\frac{10}{10}\) = \(\frac{20}{70}\)

\(\frac{3}{10}\) * \(\frac{7}{7}\) = \(\frac{21}{70}\)

Answer: Common denominator = 70

Step-by-step explanation: In order to find a common denominator, we need to find what number they have in common. That'd be 70. So, now rewrite the fractions like this:

\(\frac{2}{7} = \frac{?}{70}\)

\(\frac{3}{10} = \frac{?}{70}\)

Now, we need to find the equivalent fractions on the right. To do that, use this formula for part 1:

Right denominator / left denominator

Then, what you get after dividing those 2, you multiply by the left numerator.

So, let's plug the numbers in:

70 / 7 = 10

10 * 2 = 20

Therefore, \(\frac{2}{7} = \frac{20}{70}\)

70 / 10 = 7

3 * 7 = 21

Therefore, \(\frac{3}{10} = \frac{21}{70}\)

I hope this helped!

The approximate volume of the cylinder to the nearest hundredth is 3799.40 in³.

The complete question is:

What is the approximate volume of the cylinder?

Use 3.14 as your approximation for π.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

From the diagram:

Radius of the cylinder r = 11 in

Height h = 10 iin

Volume V = ?

Plug these values into the above formula and solve for V.

V = π × r² × h

V = 3.14 × ( 11 in )² × 10 in

V = 3.14 × 121 in² × 10 in

V = 3799.40 in³

Therefore, the volume is approximately 3799.40 in³.

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\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Answer:79

Step-by-step explanation:

The measure of the missing side length x in the right triangle is 1.5.

The figure in the image is a right triangle having one of its interor angle at 90 degree.

From the diagram;

Let angle θ = 30 degree

Opposite angle θ = x

Hypotenuse = 3

To solve for the missing side length x, we use the trigonometric ratio.

Note that: sine = opposite / hypotenuse

Hence:

sin( θ ) = opposite / hypotenuse

Plug in the values:

sin( 30 ) = x / 3

x = sin( 30 ) × 3

x = 1.5

Therefore, the value of x is 1.5.

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Answer:

The answer is below

Step-by-step explanation:

The height of tank = 12 m = 1200 cm, the diameter of the tank = 8 meters, hence the radius of the tank = 8/2 = 4 m = 400 cm

Let h represent the water level = 8 m = 800 cm. The radius (r) of the water level at a height of 8 m is:

r/h = radius of tank/ height of tank

r/h = 400/1200

r = h/3

\(\frac{change\ in\ volume}{change\ in \ time}=water\ in-water\ out\\ \\\frac{dV}{dt=} water\ in-water\ out\\\\V=\frac{1}{3}\pi r^2h\\ \\r=\frac{1}{3}h \\\\V=\frac{1}{3}\pi (\frac{1}{3}h )^2h\\\\V=\frac{1}{9} \pi h^3\\\\\frac{dV}{dt} =\frac{1}{3} \pi h^2\frac{dh}{dt}\\\\\frac{dh}{dt}=2\ cm/min,h=8\ m=800\ cm\\\\\)

\(\frac{dV}{dt} =\frac{1}{3} \pi (800)^2(2)=426666.7\ cm^3/min\\\\\frac{dV}{dt=} water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-water\ out\\\\426666.7\ cm^3/min= water\ in-20000\ cm/min\\ \\water\ in=426666.7\ cm^3/min+20000\ cm/min\\\\water\ in=446666.7 \ cm^3/min\)

mp=n+x the P on the right side cancels out now you want to shift the n to the left side by subtracting it from both sides x=mp-n so that leaves us with the solution. m=n+x/p first you want to move the P over to the left side by x P so that leaves us with the answer. ...

mp=n+X  X=mp-n, where m=n+x/p multiplies p on both sides.

How can you change the formula so that x is the subject?

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x = mp - n ( x as the subject of m= n+ x/p)

How to make x the subject of m = n +x/p ?

\(m =\frac{n+x}{p} \\\\mp = n+ x\\\\mp - n = x\\\\x= mp -n\)

What is making x the subject?

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1) Gathering the data

221 people = 65%

2) To find the 100% people surveyed let's set a direct proportion. And then cross multiply to have an equation:

% people

65-----------221

100-------- y

65y = 22100 Dividing both sides by 65

y =340

So, 340 people were surveyed.

Answer:

Step-by-step explanation:

1)  DE = 6/sin63 = 6.7

DF = 6/tan63 = 3.1

m∠E = 180 - 90 - 63 = 27°

2)  tan30 = 1/√3 = UV / (27√10)

UV = (27√10) / √3 · (√3/√3) = (27√30) / 3 = 9√30

3)  cosV = 3/8

cos⁻¹(3/8) = 68

m∠V = 68°

Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides

The correct answer is option b. When the homoskedasticity assumption is violated, The beta parameter estimates are biased while the rest of the OLS assumptions are correct.

When the homoskedasticity assumption is violated, the ordinary least squares (OLS) estimator is still consistent but no longer efficient. This means that the estimates of the regression coefficients (beta parameters) are still unbiased, but they have higher variances and covariances.

In other words, the OLS estimator is no longer the best linear unbiased estimator (BLUE) and it may be biased when the errors are heteroscedastic. Therefore, option b is correct.

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Answer:

13.1 cm² (nearest tenth)

Step-by-step explanation:

Use the sine rule for area of a triangle with 2 sides and an included angle (SAS).

Sine rule for area

\(\textsf{Area ABC}=\dfrac12ab \sin C\)

(where \(a\) and \(b\) are the side lengths and \(C\) is the included angle)

Given:

\(\implies \textsf{Area}=\dfrac12\cdot 8 \cdot 7 \cdot\sin (28\textdegree)\)

               \(=13.14520376...\)

               \(= 13.1 \textsf{ cm}^2 \textsf{ (nearest tenth)}\)

Use sine rule

Area:-

\(\\ \sf\longmapsto \dfrac{1}{2}Base\times Height sin\theta\)

\(\\ \sf\longmapsto \dfrac{1}{2}(8)(7)sin28\)

\(\\ \sf\longmapsto 28sin28\)

\(\\ \sf\longmapsto 13.1cm^2(Approx)\)

The third graph or option 3 represents the function f(x) = - l x l - 2.

Given:

f(x) = - l x l - 2

Table

x            y = - l x l - 2

0            -2

1             -3

2            -4

3            -5

-1            -3

-2           -4

-3           -5

On plotting above points or the above points shown in figure 3 or third graph.

Therefore the third graph or option 3 represents the function f(x) = - l x l - 2.

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Given

To find

we know that

Inserting the value of radius

Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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Answer:

C.

Step-by-step explanation:

use the division rule of exponents. 7 is your base and exponents is going to be 3 - 9 which is -6

Answer:

y ≥ 14

Step-by-step explanation:

y - 27 ≥ -13

y ≥ -13 + 27

y ≥ 14

Answer:

$62.20

Step-by-step explanation:

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

34 yd²

Step-by-step explanation:

Area of the shaded region = area of the outer rectangle - area of the inner rectangle

Area of outer rectangle = L*W = 13*6 = 78 yd²

Area of inner rectangle = L*W = 11*4 = 44 yd²

Area of the shaded region = 78 - 44 = 34 yd²

Answer:    4 apples in 1 lb

Step-by-step explanation:

Since there are twice as many apples as large apples, you would multiply

2 x 84 = 168

To find the apples per pound we want to divide the total number of apples, which is 168 by the weight of the bushel which is 42 lbs.

168/42=4

Therefore, there is 4 apples in 1 lb.

Hope this helped!, come back if i am wrong! :) ( I can redo the problem if it is)

Have a nice day! :)

The radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.

What is an angle ?

The length of an arc of a circle is given by the formula:

length of arc = radius * angle in radians

Let x be the radian measure of the angle that forms an arc of length 38 inches in Circle O. Then we can write:

38 = 20x

Solving for x, we get:

x = 38/20

x = 1.9 radians (to the nearest tenth)

Therefore, the radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.

What is an arc?

In geometry, an arc is a segment of a curve, such as a circle or an ellipse. It is defined as the portion of the curve that lies between two distinct endpoints. An arc is named based on its endpoints, and it can be classified as a minor arc, major arc, or semicircle depending on its length. A minor arc is an arc that measures less than 180°, a major arc is an arc that measures more than 180°, and a semicircle is an arc that measures exactly 180°. The measure of an arc is typically given in degrees or radians, and it can be calculated using the formula:

measure of arc = (central angle/360) * 2πr

where r is the radius of the circle, and the central angle is the angle that the arc subtends at the center of the circle.

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