what is 2 1/2 + 1 1/8 + 1 1/4 - 1 1/2

In triangle QRS, ∠S=67⁰ if ∠R =∠S and ∠Q=46⁰

An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common endpoint, and are referred to as the sides of the angle. Two planes intersecting at an angle also produces an angle.

A measure of an angle or of a rotation is also referred to as an angle. The ratio of a circular arc's length to radius is known as this quantity. When it comes to a geometric angle, the arc's vertex serves as its center and its sides as its boundaries. When there is a rotation, the arc is defined by the rotation's image and any other point other than the rotation's center.

In triangle QRS,

And from the figure,

∠R=∠S

Therefore,

∠R+∠S+∠Q=180⁰

2∠S+46⁰=180⁰

2∠S=134⁰

∠S=67⁰

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The probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.

The total number of people in the 18-21 age bracket is 93. The number of people in this bracket who responded is 79. The number of people in this bracket who refuse to respond is 14. The total number of people in the 22-29 age bracket is 251. The number of people in this bracket who responded is 219. The number of people in this bracket who refuse to respond is 32.

A person is randomly selected from all the people surveyed. We need to find out the probability of getting someone in the 18-21 age bracket or someone who responds. Let the variables E1 and E2 represent the events.

E1 is the event of getting a person from the 18-21 age bracket.

E2 is the event of getting a person who responds.

P(E1∪E2) = P(E1) + P(E2) - P(E1∩E2)

P(E1∪E2) = (93/344) + [(79 + 219)/344] - (79/93)

P(E1∪E2) = 0.27035 + 0.86628 - 0.84946

P(E1∪E2) = 0.28717

Hence, the probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.

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Answer:

Step-by-step explanation:

-21 = -7x

-21 divided by -7 = -7 divided by -7

3=x

After solving the linear programming problem, we get the answer as 250.

What is linear programming?

When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

Solution explained:

[tex]\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.[/tex]            x=3, y=4    P(3,4)       Coordinates of the solution point

[tex]\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.[/tex]            x=4, y=3    Q(4,3)      

                                                           Coordinates of the simultaneous eqs.

[tex]\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.[/tex]            x=14/3, y=8/3

Putting the values of x and y in the equation P = 30x + 40y and calculating we get

P(P) = 250, P(Q) = 240, P(R) = 246.67

So, the answer is 250

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The solution is Option D.

Line plot , because a small number of scores are reported individually

What is a line plot?

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

Given data ,

Total number of athletes = 15

The score points of athletes = { 1 , 2 , 3 , 4 , 5 }

The number of athletes = { 1 , 2 , 3 , 4 , 5 }

The best option to plot the line plot because of the data set

The line plot , a data visualization chart that more accurately represents the small data set, is chosen.

And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation

Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps

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Answer:D

Step-by-step explanation:

Answer:

[tex]y=-\frac{5}{7}+5[/tex]

Step-by-step explanation:

the goal is to isolate y on one side

5x+7y=35

-5x.     -5x

7y=35-5x

/7. /7.  /7

y=-5/7x+5

Hopes this helps please mark brainliest

The eastbound airplane traveled 44 miles far.

Given:

Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.

Let x be the eastbound airplane traveled.

we know that,

north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.

According to pythagorean theorem:

[tex]33^2+x^2=55^2[/tex]

[tex]x^{2} =55^2-33^2[/tex]

= 3025 - 1089

x = [tex]\sqrt{1936}[/tex]

= 44 miles.

Therefore The eastbound airplane traveled 44 miles far.

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By using the distributive property, we will rewrite the expression as:

2n*(5m -1) = 10*n*m - 2n

The distributive property of the multiplication says that the product:

A*(B + C)

Can be rewritten as:

A*(B + C) = A*B + A*C

So we are "distributing" the product.

In this case, we have the expression:

2n*(5m - 1)

If we apply the distributive property, then we will get:

2n*(5m - 1) = (2n)*(5m) + (2n)*(-1)

Now we can simplify this expression to get:

(2n)*(5m) + (2n)*(-1) = 10*n*m - 2n

That is what we wanted to get.

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The value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

The equation is 3|x+3|−12=0

We need to rewite the equation above in standard form

The modulus function can be positive and negative

Considering it to be negative,

the equation is

3((-1)(x + 3) - 12

3(-x - 3) - 12

-3x - 9 - 12 = 0

3x + 21 = 0

3x = -21

x = -7

3(x + 3) - 12

3x + 9 - 12

3x - 3 = 0

3x = 3

x = 1

Therefore, the value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

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Answer:

x<1

Step-by-step explanation:

since the circle is not filled it will not be equal to one but either grater or equal to it

Since the arrow is pointing left than x is less than 1

x<1
hopes this helps please mark brainliest

Answer:

i think third answer is write

500

Step-by-step explanation:

research

The number of months after which she will be able to vault 11 feet is 30 months.

For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.

H(t) = 17 - 11e^(-0.02t)

We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.

11 = 17 - 11e^(-0.02t)

11e^(-0.02t) = 17 - 11

11e^(-0.02t) = 6

e^(-0.02t) = 6/11

Now, we will take the natural logarithm on both sides of the equation.

-0.02t = -0.606

t = 0.606/0.02

t = 30.3

Thus, she will be able to vault 11 feet in approximately 30 months.

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[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)

How can the answer is zero?

The first thing that we should do is simplify questions.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]

After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.

[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]

Next step is find the "a" by enter the "b" into the same question.

[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]

After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]

So, the answer is zero (0).

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Answer:

[tex] - 20a + 5b[/tex]

Step-by-step explanation:

[tex] - \frac{5}{2} (8a - 2b)[/tex]

[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]

[tex] - 20a + 5b[/tex]

Answer:

394, 396 and 398

Step-by-step explanation:

===============================================

Work Shown:

F = (9/5)*C + 32

F = (9/5)*27 + 32

F = 80.6

F = 81

Side note: 9/5 = 1.8

Answer:

81 degrees Fahrenheit.

Step-by-step explanation:

Using the standard Fahrenheit-Celsius conversion formula.

27 * 9/5 = 48.6.

48.6 + 32 = 80.6.

Rounded to 81.

Therefore 81 degrees Fahrenheit.

Answer:

Step-by-step explanation:

they are asking for probability

so they want to know,  what's the probability of getting a "heads"  on a coin toss.   What do you think it is?  You probably know this intuitively.

P(H) = ?

P(T) = ?  

They are asking for fractions,    so just say what  you already know to be how often you'll get a "heads"   in words, then just make that a fraction.  :)

Answer:should be 40 because WxL=area soooo try 40

Step-by-step explanation:

Answer:

Area = width x height

Area = 4cm x 10cm

Area = 40 cm²

The number of eraser Stefanie bought is 10.

Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.

Therefore, the number of eraser Stefanie bought can be calculated as follows;

let

x = number of eraser bought

Therefore,

4.25 = 1.75 + 0.25x

subtract 1,75 from both sides of the equation

4.25 - 1.75 = 1.75 - 1.75 + 0.25x

2.5 = 0.25x

divide both sides by 0.25

x = 2.5 / 0.25

x = 10

Therefore,

number of eraser = 10

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1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.

2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.

An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.

Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.

Drainage rate per hour = 1/(1 + t) gallons

t = 0

The capacity of the tank = 5 gallons

1/(1 + t) gallons

= 1/(1 + 0) gallons

= 1/1 gallons

= 1 gallon per hour

Since the tank is 5 gallons, it will take = 5 hours (5/1)

Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.

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The number of groups, using the combination formula, for each case, is given as follows:

a) Same number of students from each grade: 1,245,816,000

b) At least two grade nine students: 31,650,886,995.

c) James and Lucy are in it: 2,481,256,778.

The number of groups is obtained for the three cases using the combination formula, as the order in which the students are chosen is not important.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

For item a, the same number of students is taken from each class, hence 3 students are taken from each class, as 12 students are taken from 4 classes, hence 12/4 = 3.

Hence the number of groups, considering the number of students in each class, is of:

[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]

For item b, we use complementary events, first obtaining the total number of students that can be taken, and then removing the combinations that do not have at least two grade nine students.

The total number of groups is obtained as follows:

[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]

(as there are 10 + 11 + 12 + 13 = 46 students, and 12 are taken).

The number of groups with none students from grade 9 is:

[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]

(removing the 10 students from grade 9).

The number of groups with one student from grade 9 is:

[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]

(one from grade 10 and the remaining from the other classes).

This the number of groups with at least two grade 9 students is calculated as follows:

38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.

For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set containing the 44 remaining students, hence:

[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]

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Answer:

40%

Step-by-step explanation:

4.8 * 100 = 480

480 / 12 = 40

 = 40%

I hope this helps.

Answer: 8.7m

Step-by-step explanation:

We can use the Pythagorean theorem to solve this,

[tex]a^2+b^2 = c^2[/tex]

We have a (5m) and c (10m) so we're looking for b.

We can rearrange the equation to find b into,

[tex]b^2 = c^2-a^2[/tex]

[tex]b^2=10^2-5^2[/tex]

[tex]b^2 = 100-25[/tex]

[tex]b^2=75[/tex]

[tex]b=8.66025404[/tex]

Rounded to the nearest tenth is 8.7m.

The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm

A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.

How to find the lengths and height of a triangle?

from the statement,

A=1/2bh

A=1/2 xbx(8+b)

cross multiplying,

713 = 8b+b²

rearrange the function

b²+8b-713=0

Simplyfying the equation,

(b²+23b)-(31b-713)=0

b(b+23)-31(b+23)=0

b-31=0 or b+23 =0

b=31 or b=-23

length cannot be negative. therefore base = 31cm

Recall the h= b+8

this implies that h=8+31

h=39cm

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From the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞

From the given graph

The x axis represents the values of x, and the y axis represents the value of y

From the graph,

When the value of x moves from 0 to - ∞, then the value of f(x) is moves from 0 to - ∞

Similarly, when the value of x moves from 0 to ∞, the  the value of f(x) is increased to positive values and then decreased to - ∞.

Hence, from the given graph the correct statement is option (B) " As x approaches - ∞, f(x) approaches - ∞ and x approaches + ∞, f(x) approaches - ∞

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60 degrees is he angles which are made by bracket with the wall

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The shelf is perpendicular to the wall.

The shelf makes an angle of 90 degree to the wall because when the shelf is perpendicular then the wall and shelf should be ninety degrees.

From the shelf edge to wall there creates an angle x.

We need to find the angle x.

As it forms a right angle triangle one angle is 90 degrees and the other angles should be 60 degrees and 60 degrees.

Hence 60 degrees is the angles which are made by bracket with the wall

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Answer:

90% increase

Step-by-step explanation:

490-931=-441

931-490=441

931/490=1.9

therefore, 190% of 441=931

Answer:90% increase

Answer:140

Step-by-step explanation:

14 x 10=

The exponential function will be equal to y = 20ˣ.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Carter shared his post with 10 friends, who each share with only 2 people each day.

The exponential function will be written as,

y = abˣ

y = 10(2)ˣ

y = 20ˣ

Therefore, the exponential function will be equal to y = 20ˣ.

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Answer:

f(x) = 10(2)^x

Step-by-step explanation:

Rule for solving: The first number is the first part of the equation, and the second number is in parenthesis.