the high school mathematics teacher handed out grades for his opening statistics test. the scores were as follows. 62, 66, 71, 80, 84, 88 (a) identify the lower and upper quartiles. Q1 =
Q2 =
(b) Calculate the interquartile range, Entram wat marker.

Answer:

2/3

Step-by-step explanation:

slope = rise/run

Start at point (0, -3).

Go up 2. That is a rise of 2.

Go right 3. That is a run of 3.

slope = rise/run = 2/3

Answer:

"The solution(s) of a system of linear equations give points of intersection of specific lines or planes. The solution(s) of a system of linear inequalities give areas of intersection wherein any specific pair of points or lines are solutions. PROCESS-WISE there are little differences between solving systems."

Step-by-step explanation:

www.algebra.com

The answer would be aas

Answer:

The answer to this question would be AAS (Angle-Angle-Side)

Step-by-step explanation:

The triangles both have the same side and another same angle as shown in the image, but to make this AAS, there must be another angle, which is the center point of both triangles... these are the same because they are vertical angles.

Answer: 4 inches

Step-by-step explanation:

Caterpillars are small, so it wouldnt be 4feet

Brainliest plz ◉‿◉

An object that is in motion as a projectile follows a path or trajectory of a parabola

The function and values are;

Reason:

a) Known parameters are;

Let f(x) = a·x² + b·x + c represent the equation of the parabola modelling the path of the ball, we have;

Points on the path of the parabola = (0, 0), (35, 1.5), 37, 0)

Plugging the values gives;

0 = a·0² + b·0 + c

Therefore, c = 0

1.5 = 35²·a + 35·b

0 = 37²·a + 37·b

Solving gives;

a = -3/140, b = 111/140

The equation of the quadratic function is therefore;

b) The maximum height is given by the vertex of the parabola

The x-coordinate at the vertex is the point \(-\dfrac{b}{2 \cdot a}\)

Which gives;

\(x-coordinate = \dfrac{\frac{111}{140} }{2 \times \dfrac{3}{140} } = 17.5\)

The maximum height is therefore;

\(f(x)_{max} = \dfrac{111}{140} \times 17.5 - \dfrac{3}{140} \cdot 17.5^2 \approx 7.334\)

The maximum height of the ball is approximately 7.334 m

c) The distance the ball has travelled to horizontally is given by half of the range, R as follows;

The range of the motion, R = 37 meters

\(Horizontal \ distance \ to \ maximum \ height = \dfrac{R}{2}\)

Therefore;

\(Horizontal \ distance \ to \ maximum \ height = \dfrac{37}{2} = 18.5\)

The distance the ball has travelled horizontally to reach the maximum height horizontally 18.5 meters

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Answer: 12

Step-by-step explanation:

Answer:

6 teaspoons

Step-by-step explanation:

If there are 12 tanks of 20 quarters each, that is 240 quarts of water in total. A quarter is only 1/4 of gallon, so you divide 240/4 to give you 60 Gallons. If it is 1 tsp per 10 gallons, that is 6 tsps for 60 gallons

Answer:

B

Step-by-step explanation:

\(3\sqrt{5}\)

The area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

To find the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9), we can follow these steps:

1. Calculate the vectors PQ and PR by subtracting the coordinates of P from Q and R, respectively.

2. Find the cross product of PQ and PR.

3. Calculate the magnitude of the cross product.

4. Divide the magnitude by 2 to find the area of the triangle.

Step 1: Calculate PQ and PR

PQ = Q - P = (-4 - 1, -3 - 1, -6 - 1) = (-5, -4, -7)

PR = R - P = (6 - 1, 10 - 1, -9 - 1) = (5, 9, -10)

Step 2: Find the cross product of PQ and PR

PQ x PR = ( (-4 * -10) - (-7 * 9), (-7 * 5) - (-10 * -5), (-5 * 9) - (-4 * 5) ) = ( 36 + 63, 35 - 50, -45 + 20 ) = (99, -15, -25)

Step 3: Calculate the magnitude of the cross product

|PQ x PR| = √( (99)² + (-15)² + (-25)² ) = √( 9801 + 225 + 625 ) = √(10651)

Step 4: Divide the magnitude by 2 to find the area of the triangle

Area = 0.5 * |PQ x PR| = 0.5 * √(10651) ≈ 51.61

So, the area of the triangle determined by the points P(1, 1, 1), Q(-4, -3, -6), and R(6, 10, -9) is approximately 51.61 square units.

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Complete question is below

Find the area of the triangle determined by the points p(1, 1, 1), q(-4, -3, -6), and r(6, 10, -9)

Answer:

130

Step-by-step explanation:

Hello There!

An included angle is equal to half the measure of its included arc

So more specifically for this circle

∠mABC = \(\frac{1}{2}\) arc(mAB)

So in order to find the value of x we are going to want an equation

Because angle ABC is equal to 1/2 of arc AB we are going to want to multiply angle ABC's expression by two

So 2(3x+32) = 10x+20

now we solve for x

step 1 distribute the 2

2 * 3x = 6x

2 * 32 = 64

now we have

6x + 64 = 10x + 20

step 2 subtract 20 from each side

64 - 20 = 44

20 - 20 cancels out

now we have 6x + 44 = 10x

step 3 subtract 6 x from each side

10x - 6x = 4x

6x - 6x cancels out

now we have 44 = 4x

step 4 divide each side by 4x

44/4=11

4x/4=x

we're left with x = 11

finally we want to plug in 11 to x for (10x+20)

10(11)+20

10*11=110

110+20=130

so arc ab = 130

Answer:

AB = 130

Step-by-step explanation:

So, according to a certain theorem to do with arcs and their angles, If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

In this case, the ARC is AB, and the angle is CBA.

CBA = 3x+32

AB = 10x+20

And,

\(CBA = \frac{1}{2} AB\)

Now,

\(3x+32=\frac{1}{2} (10x+20)\)

\(3x+32=5x+10\\32=2x+10\\22=2x\\11=x\)

Now we can substitute x into the equation that equals AB

\(10(11)+20 \\=110+20\\=130\)

So, the answer is 130, sorry I took a while, the explanation takes a long time to do lol.

Have a nice day fam. Spread The Love.

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

Two intersecting chords is the correct answer

thank you

Answer:

intersecting chords theorem

Answer: 15x + 150 = 950

Step-by-step explanation:

Let x equal the number of weeks.

He saves $15 per week, so 15 times the number of weeks, 15x.

He has already saved $150, so the money saved up over the weeks gets added to 150, 15x + 150.

all of the money he saves up has to equal 950, so 15x + 150 = 950.

I hope this helps!

Answer:

15x + 150 = 950

Step-by-step explanation:

I did dont paper I dont knwo how to upload it

#Everything4Zalo

The three numbers are: 23, 25, 27, The boy is 140 cm tall, the father is 140 + 30 = 170 cm, and the sister is 70 cm tall.

In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions.

The terms 3x + 5 and 14 are separated by the word "equal" in the equation 3x + 5 = 14. The three main formats for linear equations are the slope-intercept form, standard form, and point-slope form.

Two expressions are combined with an equal sign to form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. It is possible to solve this equation, and the answer reveals that the value of the variable x is 7.

Let the the first number is : x

So, the other two numbers are :x+2, x+4

a) x+(x+2)+(x+4)=75

3x+6=75

3x=69

X=23

The three numbers are: 23, 25, 27

b)The sister's height is denoted as x. Two times, since the boy is twice as tall. His height is 2x + 30 because the father is 30 centimeters taller than the boy. The total height is 3.8 meters, or 380 centimeters. You can now create an equation.

x + 2x + 2x + 30 = 380

assemble similar terms

5x = 350

x = 70

The boy is 140 cm tall,

the father is 140 + 30 = 170 cm,

and the sister is 70 cm tall.

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Answer:

please screen shot it so we cna help you

Answer:

Step-by-step explanation:

Points given

Slope of line AB

Slope of line CD

The slopes are neither equal nor opposite reciprocal

Hi there! :)

\(\large\boxed{d = \sqrt{73}}\)

Use the distance formula to solve for the distance between P and Q:

\(d = \sqrt {\left( {x_2 - x_1 } \right)^2 + \left( {y_2 - y_1 } \right)^2 }\)

The coordinates of point P are (-3, 2) and the coordinates of point Q are (5, -1). Plug these values into the equation above:

\(d = \sqrt {\left( {5- (-3) } \right)^2 + \left( {-1 - 2 } \right)^2 }\)

Simplify:

\(d = \sqrt {\left( 8 } \right)^2 + \left( {-4} \right)^2 }\)

\(d = \sqrt {64 + 9 }\)

\(d = \sqrt{73}\)

Answer:

no

Step-by-step explanation:

adding random numbers and variables to any equation changes the equation. No, the answer would not be equal.

Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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Answer:

5/8

Step-by-step explanation:

slope: (y₂ - y₁) / (x₂ - x₁)

(3 - 8) / (1 - 9) = -5/-8 = 5/8

Answer:

m= 5/8

Step-by-step explanation:

The slope of a line can be found using the following formula:

\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }\)

where (x₁, y₁) and (x₂, y₂) are the points the line passes through.

The points given are: (1,3) and (9,8). Therefore,

\(x_{1}=1 \\y_{1}=3 \\x_{2}=9 \\y_{2}=8\)

Substitute the values into the formula.

\(m=\frac{8-3}{9-1}\)

Perform the operation in the numerator. Subtract 3 from 8.

\(m=\frac{5}{9-1}\)

Perform the operation in the denominator. Subtract 1 from 9.

\(m= \frac{5}{8}\)

The slope of the line is 5/8

The probability of two events happening one after another is the product of both probabilities.

The probability of winning at the machine X is 12/100 and the probability of winning at the machine Y is 7/100. Then, the probability of winning at both playing once at each machine, is:

On the other hand, since the probability of winning at machine X is 12/100, then the probability of loosing is 88/100. Similarly, the probability of loosing at machine Y is 93/100. Then, the probability of loosing at both machines is:

Therefore, the probability of winning at both machines is 0.84% and the probability of loosing at both machines is 81.84%.

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \bold{ \sf{x = 2}}}}}}\)

Step-by-step explanation:

\( \sf{2x + 14 = - 6 + 12x}\)

Move 12x to left hand side and change it's sign

⇒\( \sf{2x - 12x + 14 = - 6}\)

Move 14 to left hand side and change it's sign

⇒\( \sf{2x - 12x = - 6 - 14}\)

Collect like terms

⇒\( \sf{ - 10x = - 6 - 14}\)

Calculate

⇒\( \sf{ - 10x = - 20}\)

Divide both sides of the equation by -10

⇒\( \sf{ \frac{ - 10x}{ - 10} = \frac{ - 20}{ - 10} }\)

Calculate

⇒\( \sf{x = 2}\)

Hope I helped!

Best regards!!

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

Answer:

i need this asap

Step-by-step explanation:

when you get it please let me know

The ratio of the amount of money alice has to the amount bob has 31:9.

Assume the following:

Alice's amount = P

Bob's amount = Q

Amount received = n

If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.

P + n = 4(Q - n)

P + n = 4Q - 4n

P = 4Q - 4n - n

P = 4Q - 5n - - - - (1)

If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob

P - n = 3(Q + n)

P - n = 3Q + 3n

P = 3Q + 3n + n

P = 3Q + 4n - - - - - - (2)

Equating both equations - (1) and (2)

4Q - 5n = 3Q + 4n

4Q - 3Q = 4n + 5n

Q = 9n

Express P in terms of n, use either equation (1) or (2)

From equation 2:

P = 3Q + 4n

Substituting Q = 9n

P = 3(9n) + 4n

P = 27 + 4n

P = 31n

Alice's amount = P, Bob's = Q

Ratio = P:Q

31 : 9

Hence, the ratio of the amount of money alice has to the amount bob has 31:9.

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The equation is 2x - 3 = 5x + 21. Solving for "x" gives the solution of x = -8.The equation for this issue is as follows:

2x - 3 = 5x + 21

where "x" stands for the unidentified number.

We can separate the variable term on one side of the equation and the constant terms on the other side in order to solve for "x".

To begin, we can take away 2x from both sides to obtain:

-3 = 3x + 21

Then, we can take 21 away from both sides to get at:

-24 = 3x

Finally, multiplying both sides by 3 gives us:

x = -8

Consequently, x = -8 is the answer to the equation.

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Answer:

12.12

Step-by-step explanation:

4% of 110 = 4.4

4.4 x 3 = 12.12

Answer:

x= 0

FO=20

OG=20

FG=40

Step-by-step explanation:

FG=FO+OG

3x+10=x+10+x+10

3x+10=2x+20

20=x+10

10=x