Desiree and Nick, the boy she was babysitting, were playing basketball together. Her score was 20 points, and his score was 10 points. Desiree wanted to make the game more fair, so she called a time-out and modified the rules a bit. Desiree explained that for the rest of the game she would get 3 points per basket, and Nick would get 4 points per basket. Then they played a bit longer. After a time-out, they both made the same number of baskets and ended with a tied score. How many baskets did each person make after the time-out?

The longest stick that can fit in the box is the diagonal line that goes from one corner of the box to the opposite corner.

A diagonal line is a straight line that slants or slopes in any direction. It is used to connect two points which are not on the same level, or to create a shape that would not be possible with a straight line. Diagonal lines are often used in art and design to add interest, movement, and texture.

This line is of length √A2 + B2 + C2.
This is because the diagonal line of a rectangular prism of side lengths A, B, and C is given by the Pythagorean theorem, √A2 + B2 + C2.

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The likelihood of randomly selecting a chocolate chip cookie is C. equally likely and unlikely.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

From the information, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 50%.

The likelihood of randomly selecting a chocolate chip cookie from the batch is 0.5. This implies that it is equally likely and unlikely.

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Answer: Its C

Step-by-step explanation:

360 degrees equals a circle. A circle can be divided into more manageable pieces. A circle's circumference is referred to as an arc, and an arc is given a name based on its angle.

Having no sides or edges, a circle is a figure with a round shape. A closed, two-dimensional curved form is what is meant by the term "circular" in geometry. The shape of a car tire, a wall clock that indicates the time, and a lollipops are a few objects that are circular in nature. The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.

The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the center at all angles. A curved line forms a circle, a two-dimensional shape. The curving line's tips are evenly spaced apart from the center since it is a sphere.

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If 537¹⁰²² were calculated the digit farthest to the right be 9.

If you started calculating 537¹⁰² it would not be possible , and your calculator doesn't display enough digits for you to be able to read off the ones digit for this very large number, so you have to figure out another way to "see" the ones digit. A good place to start might be to look at the ones digit for powers of 7 because 7 is the ones digit of 537. Maybe there will be a pattern:

7⁰ = 1 , 7² = 49, 7³ = 343, 7⁴ = 2401 , 7⁵ = 16807 , 7⁶ = 117649

7⁷ = 823543 and so on .

It looks like the pattern of the unit place digits is 1, 7, 9, 3, 1, 7, 9, 3 with the sequence of these 4 digits repeating over and over again. Now, if you can decide where in this pattern the unit place digit of  537¹⁰² falls, you'll have the problem solved.

So the number falling on the unit place digit is 9 when the power is in 2 so if 537¹⁰² is solves we would get 9 at the ones place according to the pattern we have seen earlier.

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Answer:

see attached.

Step-by-step explanation:

you can calculate tangent using your calculator.

The interpretation that the likelihood that the first question will be true is (a) Likely

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

From the question, we have the following parameters that can be used in our computation:

Probability value:-

The value of the probability and the notation are given as

P(true) = 0.8

As a general rule of probability, we have

Range of probability value = 0 to 1 (inclusive)

Unlikely = less than 0.5

Equally likely and unlikely = 0.5

Likely = greater than 0.5

Using the above as a guide, we have the following:

The value of P(true) = 0.8 is greater than 0.5

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The values of x and y are in option B. x = 10, y = 2

When two given equations are to be solve concurrently, then the equations are said to be simultaneous equations.

Thus to solve the given question, we have;

x + y = 12 ........... 1

x - 2y = 6 .......... 2

multiply equation 1 by 2, and equation 2 by 1 to have;

2x + 2y = 24 ........ 3

x - 2y = 6 ......... 4

Add equations 3 and 4,

3x = 30

x = 30/ 3

x = 10

Substitute the value of x in equation 1,

x + y = 12

10 + y = 12

y = 12 - 10

y = 2

Therefore, the values of x = 10 and y = 2. Option B.

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The distance traveled by car in one hour will be 56 miles.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a car goes 42 miles in 45 minutes (3/4 of an hour). the distance traveled by car in one hour will be calculated as,

45 minutes = 42 miles

1 minute = 42 / 45 miles

60 minutes = ( 42 / 45 ) x 60

60 minutes = 56 miles

Hence, the distance will be 56 miles.

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Investment B would have the greatest amount.

When we look at the compound interest, we know that the compound interest is compound not only on the principal but also on the interest that accrues to the investment.

We know that in the first case;

A = P(1 + r/n)^nt

A = amount

P = Principal

r = rate

n = Number of times compounded

t = time

Then;

A = 3000(1 + 0.08/2)^2 *7

= $5195

Again;

A = 5000(1 + 0.036/3)^3 * 4

A = $5769

The investment that would give a larger result is investment B.

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Answer:

45 degrees

Step-by-step explanation:

The equation of line is y = ( 1/3 )x - 2 and the slope is m = 1/3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -3 , -3 )

Let the second point be Q ( 0 , -2 )

Now , the slope of the line between the points is

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / ( 0 - ( -3 ) )

On simplifying the equation , we get

Slope m = 1 / 3

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = ( 1/3 ) ( x + 3 )

On simplifying the equation , we get

y + 3 = ( 1/3 )x + 1

Subtracting 3 on both sides of the equation , we get

y = ( 1/3 )x - 2

Hence , the equation of line is y = ( 1/3 )x - 2

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The volume of triangular pyramid is 26.4 cubic meters.

What is triangular pyramid?

A pyramid with a triangle base is referred to as a triangular pyramid. Vertices are essentially corners in geometry. Both regular and irregular triangular-based pyramids contain four vertices.

Pyramids with triangular bases have six edges, three of which run along the base and three of which rise above the base. The pyramid is referred to as a regular tetrahedron if all six edges are the same length and all the triangles are equilateral.

Volume of a triangular pyramid is given by:

V = ⅓* Base Area* Height

Base Area= Area of triangle

Area of triangle= Height*base*1/2

= 1/2*8*3

= 12 square meters

Height = 6.6m

V= 1/3*12*6.6

= 26.4 cubic meters

Hence, the volume of triangular pyramid is 26.4 cubic meters.

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Answer:

The coordinates of the image would be S(-8,8), U(-8,4) P(8,8).

Step-by-step explanation:

You would just multiply the pre-image by the scale factor.

Ex:

S(-2,2) *4

S(-8,8)

On solving the provided question, we can say that from the graph, area of the figure = 2*( 35+34.6+112+.3478 ) = 363.895sq units

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

From the graph,

area of the figure = 2*( 35+34.6+112+.3478 ) = 363.895sq units

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Answer: 1/2 If I'm understanding the question right.

Step-by-step explanation:

If one coin is heads on both sides and one is a regular coin, then there are two coins. 1 is 1/2 of 2 so there is a 1/2 chance that the coin you flipped is the heads on both sides coin.

The table shows the relationship describe the in the equation is B

In order to determine which table shows the relationship describe the in the equation, we need to find the slope of each table.

Slope is given by Slope = (y2-y1)/(x2-x1)

where (x1, y1) and (x2, y2) are any two corresponding values on the table

For A:

Slope = (16.98-7.99)/(2-1) = 8.99

y=  8.99x

For B:

Slope = (15.98-7.99)/(2-1) = 7.99

y = 7.99x

For C:

Slope = (32.96-7.99)/(4-1) = 8.32

y =  8.32x

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Answer: So, there is only a 72/22100 chance of being dealt a pair?

Step-by-step explanation:

If we put the blocks in a line, the possible arrangements are 12600 ways. The factorial of the total blocks is divided by the multiplication of the factorial of each color of the block.

We have

If we put the blocks in a line, determine the possible arrangements!

In that situation, the number of possible arrangements can be calculated by

[tex]Number \: of \: possible \: arrangements = \frac{Total \: blocks!}{Green! \: Red! \: White! \: Black!}[/tex]

So, the possible arrangements would be

[tex]= \frac{10!}{4! \: 3! \: 2! \: 1!}[/tex]

[tex]= \frac{5 \times 6 \times 7 \times 8 \times 9 \times 10}{3! 2!}[/tex]

[tex]= 5 \times 7 \times 8 \times 9 \times 5[/tex]

= 12600 arrangements

Hence, there 12600 possible arrangements to put the blocks in a line.

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Answer: -3/20

Step-by-step explanation:

Convert all numbers to fractions:

(-4/5 + 3/4)/(1/3)

=(-1/20)/(1/3)

=-1/20 * 3

= -3/20

Concurrent line segments are those that cross at least three other line segments at the same location.

Concurrent line segments are those that cross at least three other line segments at the same location. In geometry, if two lines intersect at a single point in a plane or higher-dimensional space, they are said to be concurrent. In contrast to parallel lines, they exist. Concurrent lines are those that cross more than one line at the same time through a single point in a plane. The point of concurrency is a location that each of those lines shares. Triangles provide another example where this concurrency characteristic can be observed.

Here,

Concurrent line segments are those where three or more line segments cross each other at the same location.

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Each table matched with Exponential or Linear based on the pattern shown:

Table A → exponential

Table B→ linear

Table C→ exponential

Table D→ linear

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

Given:

There are four tables.

If the first difference of the table's data is constant,

then the table shows the linear relationship.

And if the ratio is common, t

hen the table shows the exponential relationship.

Table A:

-6/-1 = 6

-36/-6 = 6

-216/-36 = 6

The common ratio is 6.

The table shows the exponential relationship.

Table B:

14 - 7 = 7

21-14 = 7

28 - 21 = 7

The first difference is constant.

The table shows the linear relationship.

Table C:

3/1 = 3

9/3 = 3

27/9 = 3

The common ratio is 3.

The table shows the exponential relationship.

Table D:

6 - 0 = 6

12 - 6 = 6

18 - 12 = 6

The first difference is constant.

The table shows the linear relationship.

Therefore, the relationship is given above.

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The value of x is 59°.

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

Given is a figure formed by three lines.

There is a triangle formed with one of the angle is x°, which has to be found.

The angles 108° and one of the interior angle of the triangle is supplementary.

One of the angles of the triangle = 180 - 108 = 72°

The third angle of the triangle is a vertically opposite angle of the pair 49° of the two lines.

Vertically opposite angles are formed by the intersection of two lines.

Third angle = 49°

Sum of the interior angles of triangle = 180°

x + 72 + 49 = 180

x = 180 - (72 + 49)

x = 59°

Hence the degree of angle of x is 59°.

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A. Georgia did not get a head start in the race as the y-intercept is 4

B. The y-intercept of the equation y = 3x + 4 is the point where the line crosses the y-axis. In this equation, the y-intercept is 4. This means that when x = 0 (at the start of the race), y = 4.

This is the point where Georgia started the race, and since x=0, the distance is 4 and she did not get any head start. Therefore, the y-intercept is not a head start.

The y-intercept value in the equation is the constant term (4) which is always added to the equation regardless of the value of x.

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a) The equation for a circle with centre (h, k) and radius r is: (x - h)^2 + (y - k)^2 = r^2

Since the centre of the circle is (0, 0), the equation for the circle with point B(5, -12) on its circumference is:

(x - 0)^2 + (y - 0)^2 = r^2

b) To determine whether point (8,10) lies inside or outside of the circle, we can substitute its coordinates into the equation for the circle.

If the equation is true, then the point lies on the circumference of the circle. If the equation is false, we can compare the left side of the equation to the right side to determine if the point is inside or outside of the circle.

For point (8,10), we can use the equation:

(x-0)^2 + (y-0)^2 = r^2

If we substitute (8,10) in the place of x and y, we get:

(8-0)^2 + (10-0)^2 = r^2

64 + 100 = r^2

164 = r^2

13 ≠ r

Since the left side of the equation is not equal to the right side, the point (8,10) lies outside of the circle.

Uday Tahlan

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Answer:

y=2

Step-by-step explanation:

Using the distributive law on  5(3x + 1 + 2)

she would get:                      5(3x) + 5(1) + 5(2)

Can you get this next step?                                Don't do anything but these multiplications!

Use the distributive law on each of these:

16(x + y)  =  16(x) + 16(y)  =                                <--- can you make this look a little simpler?

4(x + 3y)  =  4(x) + 4(3y)  =                                  <--- can you make this look a little simpler?

2(2x + 6y)  =  2(2x) + 2(6y)  =                               <--- can you make this look a little simpler?

(2x + 6y) + (2x + 6y)  

  =  2x + 6y + 2x + 6y

  =  2x + 2x + 6y + 6y                                  <--- can you make this look

   = 4x +12y

    =  4(x+ 3y)

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If the graph of function is V shaped, symmetric about y-axis or any line parallel to y-axis then the graph represents an absolute value function.

We know that an absolute value of any number describes the distance from zero of that a number is on the number line, without considering its sign (negative / positive number).

We know that the graph of the absolute value function is V shaped and symmetric about the y -axis or any line parallel to y-axis.

The graph makes a right angle at the origin.

The graph of absolute value consists of two pieces: one with a negative slope and the one with a positive slope.

Also, vertex is the point at which the graph of absolute value function changes its direction.

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Answer:

a) 3x^2-8x+14

b)x^2-8x-4

c)2x^4-8x+45

Step-by-step explanation:

Answer:

Step-by-step explanation:

b