A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours Total Number of Students
0 1
1 3
2 2
3 10
4 9
5 7
6 3


Determine the probability that a student studied for exactly 4 hours. Round to the nearest hundredth.
0.74
0.35
0.26
0.11

The area of the rectangle is given by the equation A = ( 9x² - 64 ) yards²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

Let the width of the rectangle be W = ( 3x - 8 ) yards

Let the length of the rectangle be L = ( 3x + 8 ) yards

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = ( 3x - 8 ) ( 3x + 8 )

On simplifying the equation , we get

Area of Rectangle = ( 3x )² - ( 8 )²

Area of rectangle A = ( 9x² - 64 ) yards²

Hence , the area of the rectangle is ( 9x² - 64 ) yards²

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The table is given as,

Z- Score     -0.299

Q₁                  36.47

Q₂                  38.45

Q₃                  41.2

IQR               4.25

Lower fourth   30.375

Upper fourth       47.375

An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

Given:

Sample Data = 31.5, 36.0, 37.8, 38.5, 40.1, 42.2, 34.2, 36.2, 38.1, 38.7, 40.6, 42.5, 34.7, 37.3, 38.2, 39.5, 41.4, 43.4, 35.6, 37.6, 38.4, 39.6, 41.7, 49.3

(a) The value of z-score is calculated as follows,

μ =[tex]\sum_{i=1}^n X_i[/tex]/ n = 933.1 /24 = 38.88

σ = 3.61

z = X - μ / σ  

  = 37.8 - 38.88/3.61

  = −  0.299

Therefore, the value of z-score is -0.299.

(b) Quartile:

Recalling the values: 31.5, 36, 37.8 ,38.5, 40.1 ,42.2, 34.2 ,36.2, 38.1, 38.7, 40.6 ,42.5, 34.7, 37.3 ,38.2, 39.5 ,41.4, 43.4, 35.6, 37.6 ,38.4 ,39.6 ,41.7, 49.3

Q₁ = ( n+1/4)th value

= (24+1/4)th value

= 6.25th value  

=  36.2 + 0.25 x ( 37.3 −  36.2 )  

= 36.47

and, M = ( n+1/2)th value

= (24+1/2)th value

= (24+1/4)th value

=  12.5 t h

= 38.4 + 38.5/2

= 38.45

Q₃ = 3( n+1/4)th value

= 3(24+1/4)th value

= 18.75 t h  v a l u e

= 40.6 + 0.75 x ( 41.4  −  40.6 )  

= 41.2

(c) Interquartile​ range =  Q ₃ −  Q ₁  

= 41.2  −  36.47  

= 4.25

Therefore, the IQR value is measure of spread of data, and here the value of IQR = 4.25.

(d) Lower fences =  Q₁− 1.5 ( I Q R )  

                            =  36.75 −  1.5  ( 4.25 )  

                            =   30.375  

Upper fences = Q ₃+1.5

                       =  41 + 1.5( 4.25 )  

                       = 47.375

Hence, there is outliers since observations are not less than 30.375 and greater than 47.375.

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Based on each given parallelogram, the correct answers are:

Let's try to solve each parallelogram problems

1. In paralellogram, each parallel sides have equal lengths; then:

x // 9; then x = 9

y // 15; then y = 15

2.  In paralellogram, each parallel sides have equal lengths; then:

m + 1 // 5; then m + 1 = 5

m = 4

n // 10; then n = 10

3.  In paralellogram, each parallel sides have equal lengths; then:

z - 8 // 20; then z - 8 = 20

z = 28

Opposite angles share the same size; then:

d - 21 = 105

d = 126

4. Uncomplete screenshot

5. In parallelogram, adjacent angles is supplementary to each other; then:

∠A + ∠B = 180°

51 + ∠B = 180°

∠B = 129°

6. In parallelogram, adjacent angles is supplementary to each other; then:

∠M + ∠N = 180°

95 + ∠N = 180°

∠N = 85°

In the given parallelogram LMNQ, the length of MP is 8.2 and PN is 7. Angle ∠MQN is 29° and ∠MLQ is 100°.

7. LM can be calculated by focusing on triangle MLQ. Under the Sinus Law, we can find that:

LM / sin LQM = MQ / sin MLQ

MQ is one of the parallelogram diagonal. MP is the mid point, then MQ is twice of MP.

MQ = 2(8.2) = 16.4

∠MLQ = 100°

∠LQN = 180° - 100°

∠LQN = 80°

∠LQN = ∠LQM + ∠MQN

80° = ∠LQM + 29°

∠LQM = 51°

LM / sin 51 = 16.4 / sin 100

LM / 0.78 = 16.4 / 0.98

LM = 12.9 = 13

8. LQ is parallel with MN; then they share the same length.

LQ = MN

MN can be calculated by focusing on triangle QMN. Under the Sinus Law:

MN / sin MQN = MQ / sin MNQ

∠MNQ is the opposite angle of ∠LMQ, then ∠MNQ = ∠LMQ = 100

MN / sin 29 = 16.4 / sin 100

MN = 8.07

9. LP = PN = 7

10. MQ = 2 x MP

MQ = 2(8.2)

MQ = 16.4

11. ∠LMN = ∠LQN = 80°

12. ∠NQL = 80°

13. ∠MNQ = ∠MLQ = 100°

14. ∠LMQ is the alternate interior angle of ∠MQN; then ∠LMQ = ∠MQN = 29°

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The inequality that represents the graph is option D: 13x - 3y - 14 < 0.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The x-intercept is a = 1.077

The y-intercept is b = -4.677

The equation of line having x-intercept a and y-intercept b is -

x/a + y/b = 1

The equation of line having x-intercept 1.077 and y-intercept -4.677 is -

x/1.077 + y/-4.677 = 1

y/-4.677 = 1 - x/1.077

y = (1 - x/1.077)-4.677

y = -4.677 + 4.677x/1.077

y = -4.677 + 4.342x

Multiply both sides by 3 -

3y = 3(-4.677 + 4.342x)

3y = -14.031 + 13.026x

Now, the line 3y = -14.031 + 13.026x divide the xy-plane in two regions and the region given in the graph is satisfied by the origin.

Also, the line 3y = 14.031 + 13.026x is dotted and not dark ,therefore, the points on the line are not included in the shaded region.

Therefore, the inequality that represents the shaded region is -

0 > - 3y - 14.031 + 13.026x ≈ 13x - 3y - 14 < 0

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Answer:

3x²+9x²-6x and add this

4x²+12x-8

Kindly, find the solution on the attachment.

The surface area of the pyramid that has these measures is given as 300 inches square

The surface area of a square pyramid is the sum of the area of the base and the areas of the lateral faces.

The area of the base of the square pyramid is given by the formula for the area of a square:

A = s^2, where s is the length of one side of the square.

In this case, each side of the base measures 10 inches, so the area of the base is:

A = 10^2 = 100 square inches.

The lateral faces of the pyramid are triangles, and the surface area of each lateral face can be found using the formula:

A = (1/2)bh, where b is the length of the base and h is the height.

In this case, the height of each lateral face is 10 inches, and the base is a side of the square base, which measures 10 inches.

So the surface area of each lateral face is:

A = (1/2)(10)(10) = 50 square inches.

Since there are 4 lateral faces on a square pyramid, the total surface area of the lateral faces is 4 * 50 = 200 square inches.

Finally, the surface area of the pyramid is the sum of the surface area of the base and the lateral faces:

A = 100 + 200 = 300 square inches.

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Answer:

180 hope this helps!

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation:

Answer:

14/70

Step-by-step explanation:

Answer:

581 divided by 8 should be 72 with a remainder of 5

Step-by-step explanation:

to check if i was correct i did 72 times 8 plus 5 and got 581

The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value.

Given here: Admission price=$10 and ride fee= $5

Now if Salma goes for 6 rides than we have

Total fee= 10+5×6

               =$40

And if Salma decides to go for r rides than we can express the total cost as some function of the number of rides r

T(r)=10+5r

Hence, The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r

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Answer: The space inside a figure -- Area

The sum of all sides in a figure -- Perimeter

The distance vertically in a triangle -- Height

The distance horizontally in a triangle -- Base

A coterminal angle is an angle that has the same initial point as another angle but has a different measure.

A coterminal angle is an angle that has a different measure in degrees from another angle but the same initial point and direction. It is an angle that is similar to another angle in orientation but may be different in size. Coterminal angles are significant in trigonometry and have numerous uses in physics, engineering, and mathematics.

Angles are frequently measured in degrees in mathematics, and they can have a value between 0 and 360. It's crucial to remember that different measures might be assigned to the same angle based on the starting and finishing points. For instance, a 90-degree angle is one that begins at the positive x-axis and ends at the positive y-axis. Additionally, the same angle can be expressed as 450 degrees, -90 degrees, and so forth. These angles are all regarded as coterminal angles.

According to question:

1. Find a coterminal angle between 0 and 360:

a) -330 degrees: 330 + 360 = 690, or -330 + 360 * 2 = 360

b) -4350 degrees: 4350 + 360 * 12 = 180

c) 640 degrees: 640

d) -4420 degrees: 4420 + 360 * 12 = 280

2. Find a coterminal angle between 0 and 27:

a) 35TC: 35TC modulo 27 = 35 % 27 = 8

b) 12 MARX: not a valid angle

c) 18 degrees: 18

d) 14 34: not a valid angle

e) 13 x 1ST: not a valid angle

3. Find a positive and a negative coterminal angle for each given angle:

a) 257 degrees: 257, -103

b) 15 74: 74, 15 + 360 = 375, -285

c) 36 degrees: 36, -324

d) 12 degrees: 12, -348

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The difference between the percentage of Americans who want to be rich and the percentage of Europeans who want to be rich, according to our 95% confidence level, is between (-0.078, -0.101).

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test.

In statistics, confidence is another word for probability. 

Given In a random sample of 80 Americans, 36 wished that they were rich. In a random sample of 90 Europeans, 49 wished that they were rich.

Let p₁ = probability of Americans wanting to rich

p₂ = probability of Europeans wanting to rich

p₁ = 36/80 = 0.45

p₂ = 49/90 = 0.54

so CI = (p₁ - p₂) ± z₁(p₁p₂/n₁ + p₁p₂/n₂)

CI = (0.45 - 0.54) ± 1.96(0.0236)(0.243)

CI  = -0.09 ± 0.0112

(-0.078, -0.101)

Hence the difference of the two proportions is between (-0.078, -0.101).

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Answer: Given the function f(x) = -3x^3 +3x^2+ 3x + 3, the following is true:

-It is not necessarily positive or negative as the value of f(x) depends on the value of x.

-It is a cubic function as it contains an x^3 term.

-The domain is all real numbers as there are no restrictions on the input x.

-It has at most 3 solutions as it is a cubic function and cubic functions can have at most 3 real roots.

-It is a polynomial function as it is a finite sum of terms involving non-negative integer powers of x.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

1. 2x + 6 = 8x

2. 8x + 8x = 16x

3. 16x - 11 = 5x

The value of variable m is 4.

Two or more expressions with an Equal sign is called as Equation.

We have to find value of m

As Y is between X and Z it is taken as the midpoint.

The values of XY, YZ and XZ are given as below.

XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .

We need to find the value of the variable m.

If we add xy and yx we get xz.

So by the equation xy+yz=xz we get the value m.

9m-3+6m+1=13m+6

Add the like terms

15m-2=13m+6

15m-13m=2+6

2m=8

Divide both sides by 2

m=4

Hence, the value of variable m is 4.

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The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).

What is polynomial?

The term "polynomial" in mathematics refers to a mathematical expression that consists of two or more algebraic terms that are added, subtracted, or multiplied (no division!). Constants and positive exponents are frequently used, along with at least one variable, in polynomial expressions. Polynomial definition: x2 = 4x + 7

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).

Therefore, the correct match is:

x² + 6x + 9 ------> (x + 3)(x + 3)

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The equations that represent each line are, respectively:

According to Euclidean geometry, we can generate any line from two distinct points on a plane. Herein we find two tables and two Cartesian representations of the lines, of which we must construct the corresponding line equations, whose definition is shown below:

y = m · x + b

Where:

The slope can be found by secant line formula:

m = Δy / Δx

Now we proceed to determine each equation of the line:

Case 1

Slope

m = [- 34 - (- 10)] / (13 - 5)

m = - 24 / 8

m = - 3

Intercept

b = y - m · x

b = - 10 - (- 3) · 5

b = - 10 + 15

b = 5

Equation of the line

y = - 3 · x + 5

Case 2

Slope

m = [- 3 - (- 11)] / [1 - (- 7)]

m = 8 / 8

m = 1

Intercept

b = y - m · x

b = 3 - 1 · 7

b = 3 - 7

b = - 4

Equation of the line

y = x - 4

Case 3

Slope

m = [0 - (- 1)] / (0.5 - 0)

m = 2

Intercept

b = y - m · x

b = - 1 - 2 · 0

b = - 1

Equation of the line

y = 2 · x - 1

Case 4

Slope

m = [0 - (- 4)] / (5 - 0)

m = 4 / 5

Intercept

b = y - m · x

b = - 4 - (4 / 5) · 0

b = - 4

Equation of the line

y = (4 / 5) · x - 4

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On solving the provided question, we can say that equation for Quinn  = > 625 + 12x and equation for Ryan =>  627 - 10x.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

Quinn has $625 in his retirement account, and Ryan has $627

Quinn is adding $12 per day

equation for Quinn  = > 625 + 12x, x is no. of days

Ryan is contributing $10 per day

equation for Ryan =>  627 - 10x, x is no. of days

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Answer:

24

Step-by-step explanation:

If there are 6 pitchers on the Sluggers and they make up 25% or 1/4th of the team, you can just add 6 (1/4th) to itself to 3 more times to gett 100% or 4/4ths.

6+6+6+6 (or 6×4) is 24.

According to Eltis, the Atlantic economy became more beneficial to slavery as a result of the rising demand for commodities that could be produced at a low cost by slaves, such as sugar, coffee, tobacco, and cotton textiles.

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Answer: The constant of proportionality and the unit rate represent the same value. A constant of proportionality can be any value, including fractions and decimals. The main difference between the constant of proportionality and a unit rate is how they are written.

The mean of the combined group can be calculated as follows:

   Calculate the total sum of test scores of both classes:

   Class 1: 36 students * 73.1 mean = 2631.6

   Class 2: 28 students * 67.4 mean = 1888.32

   Total: 2631.6 + 1888.32 = 4519.92

   Calculate the total number of students:

   Total students = 36 + 28 = 64

   Divide the total sum of test scores by the number of students to find the mean:

   Mean = 4519.92 / 64 = 70.9375.

Therefore, the mean of the combined group of 64 students is 70.9375.

If from the top of a 72 m high vertical cliff, a boat has an angle of depression of 32° then  the distance of boat from the base of the cliff is, 115 m.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

We can use trigonometry to solve for the distance of the boat from the base of the cliff.

Let's call the distance from the base of the cliff to the boat "d".

Then we have:

tan(32°) = 72 / d

Solving for d, we get:

d = 72 / tan(32°)

d = 115.22

Rounding to the nearest whole number, d = 115.

So the boat is 115 meters away from the base of the cliff.

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The number of digits which one would need to number all 178 buildings on a street is  426 numbers.

This is referred to as a single symbol used alone or in combinations, to represent numbers in a positional numeral system.

1-9 = 1 × 9 = 9

10-99 = 90 × 2 = 180

100-178 = 79 × 3 = 237

The total = 9 + 180 + 237 = 426 numbers.

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The first question is about algebra with two variables. To calculate the algebra, sum up all the same variable and count the value.

We have an mathematical expression: (5y + 2)(y - 3).

Find the equivalent value!

The equivalent value is

= (5y + 2)(y - 3)

= 5y² + (-15y) + 2y - 6

= 5y² - 13y - 6

The expression of (5y + 2)(y - 3) is equivalent to 5y² - 13y - 6.

The second question is about length in coordinate plane. The following is the formula for the length in coordinate plane.

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

A line segment with endpoints (-6, 2) and (3, 1).

Find the length!

From the endpoints, we have

The length is

d = √[(3 - (-6))² + (1 - 2)²]

d = √[9² + (-1)²]

d = √[81 + 1]

d = √82

Hence,

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Using matrix multiplication and addition, the total production cost for the items ordered by a customer is $2,692.

The total production cost consists of the costs of direct materials, direct labor, and overheads.

Overhead costs include indirect costs of materials, labor, and other production costs not traceable to each produced unit.

The total production cost is determined using matrix multiplication where the number of columns of the first matrix equal the number of rows of the second matrix.

                      Desks     Chairs     Tables    Cabinets

Materials         $5            $5           $10           $13

Labor               15              12             10             18

Overhead         5               5              3             20

              Number

Desks         10

Chairs        60

Tables       40

Cabinets     2

Production Costs for the Ordered Items:

                      Desks     Chairs     Tables    Cabinets              Total

Materials       $150         $300       $400      $26 ($13 x 2)     $876

Labor              150            720         400         36 ($18 x 2)     1,306

Overhead        50            300         120          40 (20 x 2)         510

Total costs  $350       $1,320      $920       $102               $2,692

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What is the total production cost of the ordered units?

Answer: 23

Step-by-step explanation:

first we put the values a=3,b=4 and d=-5. in a/b-d=2c/b equation which is given in the question. so,it gives us 3/4+5=2c/4,3+20=2c/4×4,3+20=c.so,the value of c is 23

Answer:

[tex]\huge\boxed{\sf c = -17/2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{a}{b} - d=\frac{2c}{b}[/tex]

Where, a = 3, b = 4, d = 5

[tex]\displaystyle \frac{3}{4} - 5 =\frac{2c}{4} \\\\Take \ LCM\\\\\frac{3-(5 \times 4)}{4} = \frac{c}{2} \\\\\frac{3-20}{4} = \frac{c}{2} \\\\\frac{-17}{4} = \frac{c}{2} \\\\Cross \ Multiply\\\\-17 \times 2 = 4 \times c\\\\-34 = 4c\\\\Divide \ both \ sides\ by \ 4\\\\-34/4 = c\\\\c = -17/2\\\\\rule[225]{225}{2}[/tex]