at a school, 43% of students attend the homecoming football game, 48% of students attend the homecoming dance, and 23% of students attend the game and the dance. a. what is the probability that a student who attends the football game also attends the dance? express your first answer as a simplified fraction and your percent answer rounded to the tenths place.

If the data of the research subjects are presented in a frequency distribution graph, a histogram-type graph should be used.

If the data are presented in a frequency distribution graph, then the type of graph that should be used is a histogram. A histogram is a type of bar graph that displays the distribution of a continuous variable by dividing the range of values into intervals, and bins, and counting the number of observations that fall within each bin.

If the academic majors were nominal a bar graph could also be used to display the frequency of each major. In a bar graph, each category would be plotted on the horizontal axis, and the frequency of students in each category would be plotted on the vertical axis.

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Answer:

29

Step-by-step explanation:

29-17= 12

12x-5=-60

Answer:

Today: Thursday, 15 October 2020

Hour: 04.13 WIB (in Indonesian)

____________________________

√121 + ³√125

= 11 + ³√5³

= 11 + 5

= 16

The system of equations that can be used to determine the amount each player earned, in million of dollars is the option;

(4) m + f = 3.95

f + 0.005 = m

A system of equation consists of two or more equations that have the same variables.

The details in the question indicates;

The earnings of football player McGee's in 2010, m = 0.005 million dollars more than those of his teammate Fitzpatrick's earnings, f

The amount earned by the two players = 3.95 million dollars

Therefore, we get;

m + f = 3.95

f + 0.005 = m

The correct option is therefore, option 4

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To determine the minimum required diameter (D) of the cross-section of the beam, we need to consider the maximum bending moment and the maximum allowable bending stress.

The bending stress in a beam is given by the formula:

σ = (M * c) / I

Where σ is the bending stress, M is the maximum bending moment, c is the distance from the neutral axis to the outermost fiber (which is equal to half of the diameter for a circular cross-section), and I is the moment of inertia of the cross-section.

Rearranging the formula, we have:

D = (2 * M) / (σ * π)

Substituting the given values, with M = 80 kNm (converted to Nm) and σ = 500 MPa (converted to N/m²), we can calculate the minimum required diameter (D):

D = (2 * 80,000 Nm) / (500,000,000 N/m² * π)

D ≈ 0.255 meters or 255 mm

Therefore, the minimum required diameter of the cross-section of the beam is approximately 0.255 meters or 255 mm to resist the maximum bending moment of 80 kNm within the allowable bending stress of 500 MPa.

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Answer:

Angle E is 43 degrees.

Step-by-step explanation:

So we know that AB is parallel to CD.

We also know that Angle CHF is 119 degrees and that Angle B is 18 degrees.

First, let's find Angle DHF. It is the supplementary angle to Angle CHF. Thus, they must total 180:

\(\angle DHF+\angle CHF=180\)

We already know that Angle CFH is 119. Substitute:

\(\angle DHF+119=180\)

Subtract 119 from both sides:

\(\angle DHF=61\)

Therefore, Angle DHF is 61 degrees.

Since Angle DHF is 61 degrees, then angle BGH must also be 61 degrees. This is because they are corresponding angles, and corresponding angles have the same measure.

Also, Angle BGE is the supplementary angle to Angle BGH. In other words:

\(\angle BGE+\angle BGH=180\)

Find Angle BGE. Substitute 61 for BGH:

\(\angle BGE+61=180\)

Subtract 61:

\(\angle BGE=119\)

So, angle BGE is 119 degrees.

Recall that a triangle's interior angles sum to 180. This means that Angle B plus Angle BGE plus Angle E must equal 180. Thus:

\(\angle B+\angle BGE+\angle E=180\)

Substitute 18 for B and 119 for BGE. Thus:

\(18+119+\angle E=180\)

Add:

\(137+\angle E=180\)

Subtract:"

\(\angle E=43\textdegree\)

And we're done!

Remarks:

I just realized that you can just use the fact that alternate exterior angles have the same measures to figure out that BGE is equivalent to CHF. Regardless, we will arrive at the same answer :)

Answer:

1323

Step-by-step explanation:

i did the math

The area found by Missy is wrong.

A polyhedron with three faces connecting corresponding sides, a triangle base, and a translated copy is known as a triangular prism. If the sides of a right triangular prism are not rectangular, the prism is oblique. Right triangle prisms with square sides and equilateral bases are known as uniform triangle prisms.

It is, in essence, a polyhedron with two parallel sides and three surface normals that are all in the same plane.

Given a triangular prism,

area of prism is given by

2 x area of triangle + sum of area of 3 rectangles

area for given prism is

area of triangle = 1/2bh = 1/2 x 5 x 9 = 22.5 cm²

2 x area of triangle = 45 cm²

area of each rectangle = (10.3 x 3) + (3 x 5) +(9 x 3)

rectangle area = 30.9 + 15 + 27 = 72.9 cm²

so the total area of prism is  2 x area of triangle + 72.9 cm²

Hence the area found by Missy is wrong.

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Therefore , the solution of the given problem of graphs comes out to be  graph of y  = 2ˣ .

Graphs are used by theoretical physicists to visually or analytically vertices chart assertions rather than values. Typically, a graph point shows the relationship between several different objects. A graph is a particular kind of  train assembly consisting of groups and lines. The networks, also known as the borders, should be joined with glue. The edges of this network had the digits 1, 2, 3, and 4, along with the numerals (2.5), (3.5),

Here,

y =  logₐ(x); logarithmic function (x)

The matching points that must appear on the graph x = bx can be found using the procedure below.

Step 1: In the equation  

=> x = bˣ

=> 2= b¹

=> b =2

replace (2,1) with the value of x and y.

Step 2: Now change the number of b in the equation to make

=> y = 2ˣ

Step 3: The above equation becomes y=2 at (x = 1).

Step 4 - The equation (2) becomes: at (x = 2)

Step 5 - The equation (2) becomes: y = 16 at (x = 4)

The graph of y  = 2ˣ

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Answer:

slope = gradient...

gradient (m) = ∆y

∆x

= -4 - -2

2 - -3

= -4 + 2

2 + 3

= -2

5

Answer:

2. is not an equation

Step-by-step explanation:

An equation always has an equal sign. An expression doesn't

(a) Yes, T is a linear transformation.

(b) No, T is not a linear transformation.

(c) Yes, T is a linear transformation.

(a) To determine whether T is a linear transformation, we need to check two conditions: additivity and homogeneity. In this case, T(x, y, z) = (x + 1, y + 1, z + 1) satisfies both conditions.

It preserves addition since T(x₁ + x₂, y₁ + y₂, z₁ + z₂) = (x₁ + x₂ + 1, y₁ + y₂ + 1, z₁ + z₂ + 1) = (x₁ + 1, y₁ + 1, z₁ + 1) + (x₂ + 1, y₂ + 1, z₂ + 1) = T(x₁, y₁, z₁) + T(x₂, y₂, z₂). It also preserves scalar multiplication since T(c⋅x, c⋅y, c⋅z) = (c⋅x + 1, c⋅y + 1, c⋅z + 1) = c⋅(x + 1, y + 1, z + 1) = c⋅T(x, y, z). Therefore, T is a linear transformation.

(b) For T to be a linear transformation, it should preserve both addition and scalar multiplication. However, in this case, T(A) = trace(A) = a11 + a22 + · · · + ann only satisfies the condition of preserving addition. It fails to preserve scalar multiplication because T(c⋅A) = c⋅(a11 + a22 + · · · + ann) ≠ c⋅T(A). Hence, T is not a linear transformation.

(c) Similar to part (a), we need to verify additivity and homogeneity for T to be a linear transformation.

T(x, y) = (1 + x, y) satisfies both conditions. It preserves addition since T(x₁ + x₂, y₁ + y₂) = (1 + (x₁ + x₂), y₁ + y₂) = (1 + x₁, y₁) + (1 + x₂, y₂) = T(x₁, y₁) + T(x₂, y₂). It also preserves scalar multiplication since T(c⋅x, c⋅y) = (1 + c⋅x, c⋅y) = c⋅(1 + x, y) = c⋅T(x, y). Therefore, T is a linear transformation.

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Answer:

3 wholes, each person gets 3/5 of a loaf

Step-by-step explanation:

They have 3 loaves of bread. If you divide each loaf into 1/5s you get a total of 15/5. 15/5 divided by 5 = 15/25 = 3/5 of a loaf each.

There are 5 people in Edgar's family. They have 3 loaves of pumpkin bread to share equally. 3/5 of a loaf each needed for the model.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

There are 5 people in Edgar's family. They have 3 loaves of pumpkin bread to share equally.

Edgar wants to know how much pumpkin bread he will get.

The total share of loaves of pumpkin bread in Edgar's family = 15

Each loaf into 1/5s = 15/5.

       = 15/25

        = 3/5 of a loaf each.

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Answer:

96π cubic feet

Step-by-step explanation:

Surface area of a cylinder
A = 2πr(h+r)

where r = radius, h = height

Here

r = diameter/w = 8/2 = 4 feet

h = 8 feet

A = 2π · 4 (8 + 4)

= 8π (12)

= 96π cubic feet

The probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

Denote S= Event that a purchase bought a basic camera, then P(S)=0.32

Denote D= Event that a purchase bought a deluxe camera, then

S and D are mutually exclusive.

P(D)=1-P(S)=0.68

P(W/S)=0.4

P(W/D)=4.9

We need to calculate the probability that a randomly selected purchaser who bought an extended warranty has a basic model. By notations, this is equivalent to finding P(S/W).

P(S/W)=P(W/S)*P(S)/P(W)

Since S and D are disjoint and P(S)+P(D)=1,

P(W)=P(W∩S)+P(W∩D)

P(W)=[0.4*0.32]+[4.9*0.68]

=3.61

Hence, our required probability is: P(S/W)=P(W/S)*P(S)/P(W)

\(=\frac{0.4*0.32}{3.61}\\=0.0354\)

Hence, the probability that a randomly selected purchaser with an extended warranty has a basic model camera is approximately 0.0354

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Answer:

angle BAD= angle BCD = 100

then,

angle BCD + angle ECD = 180

100+ angle ECD = 180

angle ECD= 180-100 = 80

angle ECD =80

Answer:

x= 92 degrees

Y=44 degrees

If the region R bounded by the functions f(x) = 2 and g(x) = x + 1 is rotated around the x axis , then the volume of the resulting solid is (7/3)π cubic units .

The region R is bounded by the functions f(x) = 2 and g(x) = x + 1 , and is between x = 1 and x = 2 .

Region-R between the lines x = 1 and x = 2 is rotated ,  

So , The volume of the solid can be calculated as :

⇒ Volume = π × \(\int\limits^2_1\) (2)² - (x+1)²dx  ;

⇒ Volume = π × \(\int\limits^2_1\) 4 - (x+1)²dx  ;

⇒ Volume = [4x - (x+1)³/3]²₁ × π ,

⇒ Volume = π × [(4×2 - (2+1)³/3) - ((4×1) - (1+1)³/3)]

= [(8 - 27/3) - (4 - 8/3)]π

= [(8 - 9) - (4/3)]π

= [ -1 - 4/3]π  = -7/3π  ,

On taking the modulus of the volume ,

we get , that the Volume is 7/3π cubic units .

Therefore , the volume of the resulting solid is (7/3)π cubic units .

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The given question is incomplete , the complete question is

Define R as the region bounded by the functions f(x) = 2 and g(x) = x + 1 between x=1 and x=2. if R is rotated around the x-axis, what is the volume of the resulting solid?

The given equation is

When the equation is in slope-intercept form, the coefficient of x is the slope. So, the slope of the given equation is 6.

It is important to know that parallel lines have equal slopes.

To parenthesize an arithmetic expression with n nonnegative numbers and n-1 addition and multiplication operators, determine the different ways to parenthesize the expression and evaluate each expression to find the different possible values.

To parenthesize an arithmetic expression with a given sequence of n nonnegative numbers separated by n-1 addition (+) and multiplication (x) operators, follow these steps:

1. Identify the sequence of numbers and operators: In the example provided, the sequence is 2x3x0+6+2x5+4.

2. Determine the possible parenthesizations: You can parenthesize the expression in different ways to get different results, such as:
  - ((2x3)x(0+6))+(2x(5+4)) = 54
  - (2x3)((0+(6+2))(5+4)) = 432
  - (2x(3x0))+(6+((2x5)+4)) = 20

3. Evaluate each parenthesized expression: Calculate the values of each expression by following the order of operations (PEMDAS) - Parentheses, Exponents, Multiplication, and Division (from left to right), and Addition and Subtraction (from left to right).

In summary, to parenthesize an arithmetic expression with n nonnegative numbers and n-1 addition and multiplication operators, determine the different ways to parenthesize the expression and evaluate each expression to find the different possible values.

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Given:

The two numbers are 6788678 and 1234567 .

To find:

The numbers that must be taken away from the sum of 6788678 and 1234567 to make it equal to the difference of the given numbers.

Solution:

Let x be the required number.

Sum of given numbers is:

\(6788678+1234567=8023245\)

Difference of the given number is:

\(6788678-1234567=5554111\)

The number x is taken away from the sum of 6788678 and 1234567 to make it equal to the difference of the given numbers.

\(8023245-x=5554111\)

\(8023245-5554111=x\)

\(2469134=x\)

Therefore, the required unknown number is 2469134.

Answer:

x=9

Step-by-step explanation:

Since vertical angles are congruent to each other, we can put the two expressions equal to each other in this equation: 4x=x+27

With simple algebra, you get this:

4x=x+27

3x=27

x=9

Hope this helps!! :)

To solve for x, we can use cross-multiplication.

First, we will simplify the right side of the equation by reducing the fraction:

12/20 = 3/5

Now, we have:

x/5 = 3/5

To isolate x, we will multiply both sides by 5:

x/5 * 5 = 3/5 * 5

x = 15/5

Simplifying the fraction on the right side, we get:

x = 3

Therefore, x is equal to 3.

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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Answer:

\(\sf y =\dfrac{2}{5}x+4\)

Step-by-step explanation:

 \(\sf y = \dfrac{-5}{2}x-3\\\\\\m_1=\dfrac{-5}{2}\)

\(\sf \text{Slope of the perpendicular line = $\dfrac{-1}{m_1}$}\)

                                                 \(\sf m =\dfrac{-1}{\dfrac{-5}{2}}\\\\\\= -1*\dfrac{-2}{5}\\\\= \dfrac{2}{5}\)

\(\sf slope = m = \dfrac{2}{5}\)  

Line passes thorugh ( -5 , 2)

Equation of line:  y = mx + b

         \(\sf y = \dfrac{2}{5}x + b\)

Substitute the point(-5,2) in the above equation and find the value of 'b'.

          \(\sf 2 =\dfrac{2}{5}*(-5)+b\\\\\\ 2 = -2 + b\\\)

     2+ 2 = b

           b = 4

  Equation of the line :

              \(\sf \boxed{y =\dfrac{2}{5}x+4}\)

Vertical angulation refers to the angle at which the x-ray beam is directed when taking dental radiographs. It is an important factor in obtaining clear and accurate images.

In both the paralleling and bisecting techniques, the group of answer choices remains the same. However, the vertical angulation is generally greater for images taken with the paralleling technique compared to the bisecting technique.

This is because the paralleling technique requires the x-ray beam to be directed more vertically in order to capture the entire tooth structure on the film. On the other hand, the bisecting technique involves angling the x-ray beam downward to intersect the imaginary bisector between the long axis of the tooth and the film.

Therefore, the vertical angulation differs depending on which technique is being used.

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Step-by-step explanation:

t2 - t1 = t3- t2

or , 2 - X = 4.5 -2

or , X =4.5 -2 -2

:. X = 0.5

In a certain isoceles triangle, the sum of the measures of the base angles is 88 degrees less than the measure of the remaining angle. Then the measure of each angle is 44° and 92°.

Determine the measure of each angle

These are the specified parameters:

The sum of the measures of the base angles is 88° less than the measure of the remaining angle.

Large pedestal angle

a + a = 88

2a = 88

 a = 88/2

 a = 44°

Peak angle

a + a + b = 180

88 + b = 180

       b = 180 - 88

       b = 92°

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Answer:

Yes it can

Step-by-step explanation:

u=10x

Divide both sides by 10

u/10=x

Step-by-step explanation:

X = u/ 10

That's the answer

Step-by-step explanation:

4

\(7x + 5 = 4 x + 10 \\ 7x - 4x = 10 - 5 \\ 3x = 5(divide by three \: both \: sides) \\ x = \frac{5}{3} \)