375 different combinations of pizza Grayson and his friends can create.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
They can pick thick, hand-tossed, or deep-dish crust.
Here, n=3 r=1
So, C(n, r) = 3!/1!(3-1)!
= 3
They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
Number of ways = 5×5×3×5
= 375
Hence, in 375 ways they can choose pizza.
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A 5-foot rope is cut into 2 pieces. Seven less than three times the length of the longer rope piece x is five times the length of the shorter piece, which is (5 − x) ft. Find the length of the longer rope piece x (in ft)
Let's call the length of the longer rope piece x and the length of the shorter rope piece y. We know that:
x + y = 5 (the total length of the rope is 5 feet)
And from the problem statement, we have:
3x - 7 = 5y
Now we can use the first equation to solve for y:
y = 5 - x
Substituting this expression for y into the second equation:
3x - 7 = 5(5 - x)
Expanding the right side:
3x - 7 = 25 - 5x
Adding 5x to both sides:
8x - 7 = 25
Adding 7 to both sides:
8x = 32
Dividing both sides by 8:
x = 4
So the length of the longer rope piece is 4 feet.
c) In the following figure, AE = 8 cm, BE =3 cm and CE = 4 cm. Find the length of DE .
Answer:
DE = 6 cm
Step-by-step explanation:
The concept behind this question is the Chord-Chord Power Theorem. This product states that "if two chords intersect in a circle, then the products of the lengths of the chords segments are equal". In this case:
CE × DE = AE × BE
4 × DE = 8 × 3
4 × DE = 24
DE = 6 cm
Hope this helps!
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In the figure, a || b and m1 = 34°.
What is the m5?
Enter your answer in the box.
Please give an explanation !!
Since in the figure, a || b and m∠1 = 34°, the magnitude of m∠5 is equal to 34°.
What are parallel lines?In Mathematics, parallel lines are two lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.
What are corresponding angles?In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.
By applying corresponding angles theorem to lines a and b, we have the following:
m∠1 ≅ m∠5
m∠5 = 34°.
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in a standard television set, the screen height is 0.75 times the screen width. if a television set measures 21 inches along the diagonal, what is the screen width?
The width of standard television set is 16.8 inches.
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Because to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
We can solve this by using the Pythagorean theorem which is below:
[tex]a^{2} +b^{2} =c^{2}[/tex]
Or we can say
[tex]w^{2} +h^{2} =d^{2}[/tex]
w = width
h = height
d = diagonal measure
With that said, we know the height is .75 times the width so .75w. We also know d = 21, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 21
[tex]w^{2} +h^{2} =d^{2}[/tex]
[tex]w^{2} +(0.75w)^{2} =21^{2}[/tex]
1.5625 w^2 = 441
w^2 = 441/1.5625
w ^2 = 282.24
w =16.8
The width of standard television set is 16.8 inches.
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A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 33 feet then another horizontal base below it of 19 feet. The longest side is to the right and is 37 feet. The top is 28 feet. There is a perpendicular from the vertex of the top to the first base of 33 that is labeled 14 feet. If the wax cost $1.67 a square foot, how much will the wax cost to cover the floor? $832.50 $1,300.10 $1,664.99 $2,600.19
If the wax was priced at $1.67 per square foot, it would cost $1,664.99 to wax the entire floor. The right answer is C.
How to calculate the area of the floor?The floor is made up of a trapezoid and a rectangle.
The area of a trapezoid can be calculated as:
A = (b₁ + b₂)/2 x h
Where b₁ and b₂ are the lengths of the bases and h is the height.
The trapezoid is 14 feet tall, and its bases are 33 feet long and (28 - 19) or 9 feet wide. Thus, its area is:
A = (33 + 9)/2 x 14
A = 294 square feet
The rectangle is 37 feet tall with a 19-foot base. Thus, its area is:
A = 19 x 37
A = 703 square feet
The area of the triangle and trapezoid together make up the overall area of the figure.
A = 294 + 703
A = 997 square feet
Finally, to find the cost of the wax, we multiply the area by the cost per square foot:
Cost = 997 * $1.67
Cost = $1664.99
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Complete the table using the given function Then plot the dots on the
graph Use the line tool to draw a line connecting the dots for each
line
Point of Solution:ixy)
Y = 3x
y
x
-1
03
1
Y = -2x + 5
X
y
-1
0
1
7
3456
The complete tables for the given equations is:-
For y = 3x
X Y
1 3
2 6
3 9
For y = -2x + 5
X Y
1 3
2 1
3 -1
What is an equation?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The given two equations are;-
y = 3x
y = -2x +5
The different points passing through the line y =3x are:-
X Y
1 3
2 6
3 9
The different points passing through the line y =-2x + 5 are:-
X Y
1 3
2 1
3 -1
The graph of the points and the line as is attached with the answer below.
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Write an equation in point-slope form for the line that passes through the point with the given slope.
(–2,–4); m=3
Answer:
x + y = -6
Step-by-step explanation:
Just put x and y and add the number on the RHS
Its really not that hard
But i hope it helped
can you answer the question in the picture and explain it please
Answer:
G descends about 8 ft per second
Step-by-step explanation:
You want to know the descent rate of an airplane whose altitude is shown on a graph as being 1500 ft at 0 seconds and 0 ft at 180 seconds.
Rate of changeThe airplane descended 1500 feet over a period of 180 seconds. That rate of change is ...
(-1500 ft)/(180 s) ≈ -8.333 ft/s
The plane descends about 8 feet per second.
__
Additional comment
The slope of the line segment is the change in y divided by the change in x. For computing these changes, it is useful to consider points whose coordinates are obvious. Here, the y-intercept (1500 ft) and the x-intercept (180 seconds) are good choices.
The change in y from 1500 to 0 is a change of -1500. The change in x from 0 to 180 is a change of +180. The ratio of these changes is the slope, which is often designated by the letter m:
m = -1500/+180 = -25/3 = -8 1/3 . . . . . . about -8
The units of the slope are the ratio of the y-axis units to the x-axis units: feet/second.
The slope of -8 feet/second tells you the plane is descending about 8 feet per second.
If you return an item that has an original price of $180, how much is the restocking fee if the stocking fee is 6%?
The restocking fee for an item with an original price of $180 and a restocking fee of 6% is $10.80.
A restocking fee is a fee that is charged when a customer returns an item, usually to cover the costs associated with processing the return and getting the item back in a sellable condition. The fee is typically calculated as a percentage of the original price of the item.
In this problem, we are given that the restocking fee is 6% and the original price of the item is $180. To find the restocking fee, we can use the formula:
Restocking fee = (Percentage fee / 100) x Original price
In this case, the percentage fee is 6% or 0.06 (since 6% is equivalent to 6/100). The original price is $180. Substituting these values into the formula gives:
Restocking fee = (0.06) x $180
Restocking fee = $10.80
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1) Simplify the following
a) 3√2+5√2
b) √3 x √2
c) 3√5x2√7
d) 8√10-2√2 x √5
The total cost of an order of personalized invitations from a company includes the cost of each invitation, plus a one-time design fee. The cost of each invitation is the same regardless of how many invitations are ordered.
The invitation company provides the following examples to customers in order to estimate the total cost of an order:
50 invitations $298.50
500 invitations $2049
The total cost of an order is $900 if 50 invitations cost is $298.50
To calculate the cost of an order of personalized invitations, you would need to know the cost of each invitation and the one-time design fee.
Let calculate the cost of each invitation and the one-time design fee as follows:
50 Invitations: $298.50 / 50 = $5.97 per invitation
500 Invitations: $2049 / 500 = $4.098 per invitation
Design Fee: ($2049 - ($5.97 × 50)) / 500
= $3.90 one-time design fee
If you wanted to order 150 personalized invitations, the cost would be:
150 Invitations x $5.97 per invitation = $896.50
Plus one-time design fee of $3.90 = $890.40
Total cost = $896.50 + $3.90 = $900.
Hence, the total cost of an order is $900 if 50 invitations cost $298.50
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Ethanedioic acid is a solid at room temperature. Calculate the mass of ethanedioic acid (H₂C2O4) needed to make 250 cm³ of a solution with concentration 0.0480 mol/dm³ Relative formula mass (M): H₂C2O4 = 90
Answer: 1.08g
Step-by-step explanation:
Concentration = Moles/ Volume
Moles = Concentration x Volume
Moles = 0.048 x 250/1000
Moles= 0.012
Moles= Mass / Relative Formula Mass
Mass = Moles x Relative Formula Mass
Mass = 0.012 x 90
= 1.08g
Gavin wraps a gift box in the shape of a triangular prism. The figure below shows a net for the gift box. How much wrapping paper did he use, in square meters?
The amount of wrapping paper used by Gavin to wrap a triangular prism box is 647.75 m².
What is a prism?
A prism is a polyhedron in geometry made up of an n-sided polygon basis, a second base that is a rigidly translated copy of the first base, and n additional faces that must all be parallelograms and connect the corresponding sides of the two bases.
The formula for area of rectangle is -
Area = length × breadth
The area of rectangle ABFG is -
Area = AB × BF
The value for line segment AB = 15 m
The value for line segment BF is -
BF = BC + CE + EF
BF = 14 + 7 + 15.65
BF = 36.65 m
So, the area of rectangle ABFG is -
Area = 15 × 36.65
Area = 549.75 m²
Now, the triangular prism has triangle part left.
The formula for area of triangle is -
Area = 1/2 × base × height
So, the area of triangle IJH is -
Area = 1/2 × IJ × JH
The value for line segment IJ = 14 m
The value for line segment JH = 7 m
So, the area of triangle IJH is -
Area = 1/2 × 14 × 7
Area = 49 m²
Since, there are two triangles (Δ IJH = Δ CDE ) so the area of total shape is -
Total area = Area of ABFG + 2(Area of Δ IJH)
Total area = 549.75 + 2(49)
Total area = 647.75 m²
Therefore, the area of triangular prism box is 647.75 m².
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3 added to 5 is the same as 3 more than 5. True or false
"3 added to 5 is the same as 3 more than 5", this statement is true. The statement "3 added to 5 is the same as 3 more than 5" means that the expression "3 added to 5" is equal to the expression "3 more than 5".
Another way to express the equality of two mathematical expressions is "3 added to 5 is the same as 3 more than 5".
"3 added to 5" is equivalent to the sum "3 + 5", which equals 8.
"3 more than 5" can be written as "5 + 3," which equals 8 as well.
Because both expressions have the same value of 8, the statement "3 plus 5 equals 3 more than 5" is correct.
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4. In the isosceles triangle shown, what is the value of b?
11. In the figure, the volume of the cube is 64. What is the distance from point A to point B?
4. The value of b is 180+2a (option C)
11. the distance between A and B is 4√2 (option A)
What is angle at a point?Angles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360 °.
The total angle at a point is 360°
therefore the third angle in the triangle = 180-(a+a) = 180-2a
therefore b = 360-( 180-2a)
b = 360-180+2a
b = 180+2a
If the volume of the cube is 64, then AB = √4²+4²
= √16+16 = √32
AB = √32
AB = √ 16×2
AB = 4√2
Therefore the distance between A and B is 4√2
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Which hotkey can be used to switch from Obiect Mode to Edit Mode and back in
Blender?
how many pattern block trapezoids would create 2 hexagons
The right response is, "5 hexagons are made up of 15 pattern block trapezoids."
Geometric shapes known as pattern block trapezoids are frequently utilized in arithmetic instruction. On a flat surface, they are one of a number of forms that can be used to make tessellations, or repeating patterns. Different colored plastic or foam pattern block trapezoids are available in a variety of sizes, with each color denoting a distinct size and form. Pattern block trapezoids are frequently used to teach geometry principles like area, perimeter, and angles in addition to their application in making tessellations. They can also aid in the development of kids' spatial reasoning and problem-solving skills.
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If cos A =0. 8945, find angle A to nearest tenth of a degree
The angle to the nearest tenth of a degree, we round the result to 50.7 degrees.
In trigonometry, cosine is a function that takes an angle as an input and produces a numeric value between -1 and 1 as an output. The cosine of an angle A is represented by cos A. In this problem, cos A is given to be 0.8945. To find the angle, we can use the inverse cosine function (or arccosine) which returns the angle in radians. To obtain the angle in degrees, we can multiply by 180/π (which is equal to 57.2958). The angle A is then equal to 50.6 degrees. To find the angle to the nearest tenth of a degree, we round the result to 50.7 degrees.
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Pls help thank you will mark the Brainliest
Answer:
y = 2ˣ
Step-by-step explanation:
Since, the question asked which function is best represented by the graph and the function given are:
y = 0.5ˣ
y = 2ˣ
y = 3ˣ
y = 2 * 0.25 ˣ
We can graph each of them to see which is the answer.
Base on the graph below we can see that;
the function that represents the graph is y = 2ˣ
RevyBreeze
Evaluate the following multiplication expression 7*38
To evaluate the multiplication expression 7*38, we simply multiply 7 and 38 together and the result after multiplication is 266.
Multiplication is a basic arithmetic operation that involves combining two or more numbers to obtain a product. In this case, we are given the expression 738, which involves multiplying the number 7 by the number 38 to obtain a product. To do this, we can use the multiplication operation, which involves adding 7 to itself 38 times.
This can be a time-consuming process when dealing with large numbers, but it is a fundamental skill in mathematics and is used in a wide range of applications, including engineering, science, finance, and computing. In this case, we have evaluated the expression 738 to be equal to 266, which is the product of 7 and 38.
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What value of x makes the equation true
3(2x-5+8x)=5(2x+5)
The value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2
How to evaluate for the value of x for the equationWe shall evaluate for the value of x to know what makes the algebraic equation true as follows;
3(2x - 5 + 8x) = 5(2x + 5)
3(10x - 5) = 5(2x + 5)
30x - 15 = 10x + 25 {expand bracket}
30x - 10x = 25 + 15 {collect like terms}
20x = 40
x = 40/20 {divide through by 20}
x = 2
Therefore, the value of x that makes the equation 3(2x - 5 + 8x) = 5(2x + 5) true is 2.
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Given:-1/2x>6.
Choose the solution set.
xix R, x>-12
xix
R, x>-3]
xIxER,x<-3)
R, x<-12
Solution of given inequality is x < -12.
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
Given inequality
- (1/2)x > 6
Multiplying with 2 on both sides
- (2/2)x > 6×2
- x > 12
Multiplying with -1 on both sides
x < -12
Hence, x < -12 is the solution of given inequality.
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Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs $4 per
bag. Shana bought / things from the concession, all either sodas or bags of popcorn.
Shana
spent a total o€$26. Write a system of equations involving the number of sodas, s, and the bags
of popcorn, b. Solve the system using elimination to
see how many
of each Shana bought.
In a case whereby Shana bought sodas and popcorn for the movies. Sodas cost $3 each and popcorn costs the system of equation involving the number of sodas, s, and the bags are: (3s + 4p )= $26 and s+p = 7 .Then Shana bought 5 sodas and 2popcorn.
How can the the system of equation be written?We know that :
Sodas cost =$3 each
popcorn costs= $4 per
total =$26
The system of equation can be written as :
(3s + 4p )= $26
We were also told that he bought things equal to the 7 things which can be expressed as:
s+p = 7
Then we can solve the equations as:
3s + 4p = 26 .............................................(1)
s+p = 7................................................................(2)
multiply equation by -3
-3s - 3p =-21 ..................................................................(3)
Then add (1) and 3
4p-3p = 26-21
p=5
Then substitute the value of p into equation 2 we have
s+5 = 7
s= 7-5
=2
s=2
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complete question:
Shana bought sodas and popcorn for the movies .Sodas cost $3 each and popcorn cost $4 per bag . Shana bought 7 things from the concession., all either sodas or bags of popcorn. Shana spent a total of $26 . Write a system of equations involving the number of sodas S ,and the bags of popcorn ,B .Solve the system to see how many of each shana bought
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The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)
what is graph of a quadratic and linear equationA graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:
y = ax^2 + bx + c,
where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.
A graph of a linear equation is a straight line. A general form of a linear equation is given by:
y = mx + b,
where m is the slope of the line and b is the y-intercept.
In this problem, the ordered-pairs will be the point in which they intersect with each other.
Looking carefully at the graph, the ordered pair will be at points
A = (-2, 7)
B = (2, -1)
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Please Answer (Iready)
The expression for the given model will be 3÷2/5.
What exactly are expressions?
Expressions in mathematics are mathematical assertions that comprise at least two phrases that contain numbers, variables, or both, and are connected by an operator in between. Addition, subtraction, multiplication, and division are examples of mathematical operators. For example, x + y is an expression in which x and y are terms separated by an addition operator. There are two sorts of expressions in mathematics: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is 6 more than half of another number, which is x. In a mathematical expression, this proposition is expressed as x/2 + 6. Complex riddles are solved using mathematical expressions.
Now,
as shown in figure the model is shaded uptil 3
and in 1 unit there are 5 total boxes which are divided in 2 parts
Therefore, it will be represented by 3÷2/5.
Hence,
The expression for the given model will be 3÷2/5.
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Until recently, Simon owned 1,510 acres of farmland. This year, he sold the old land and purchased a new plot that is 1,208 acres in size. What is the percent of decrease in the amount of land that Simon owns now?
The percentage of decrease in the amount of land that Simon owns is 20.1%.
1,510 - 1,208 = 302
302 / 1,510 = 0.201
0.201 x 100 = 20.1%
Simon recently sold his old farmland, which was 1,510 acres in size, and purchased a new plot of land that is 1,208 acres in size. To calculate the percent of decrease in the amount of land that Simon owns, we subtract the new land size from the old land size and divide the result by the old land size. This number is then multiplied by 100 to get the percent of decrease. In this case, we subtract 1,208 from 1,510 to get 302. We then divide 302 by 1,510 to get 0.201. When we multiply 0.201 by 100, we get 20.1%, which is the percent of decrease in the amount of land that Simon owns now.
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HELP POLSSSSSSSSSSSSSSSSS
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Answer: a^2 b^2 c^2
Step-by-step explanation:
because that is the pythageoran theorem the rule of it is a^2 + b^2 + c^2 so it's right
An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
Answer:
The total length of the two straight parts is 80 m x 2 = 160 m.
So, the length of the curved part of the track is 400 m - 160 m = 240 m.
Let the radius of the curved part of the track be "r".
Since there are two curves, each of length "l", in the track, the total length of both curves is 2l.
The length of one curved part can be given by the formula:
l = 2πr, where π is pi (approximately equal to 3.14).
So, 2l = 2 x 2πr = 4πr.
Therefore, 4πr = 240 m.
Dividing both sides by 4π, we get:
r = 240 m / (4π) = 240 / (4 x 3.14) = 15 m.
Hence, the radius of the curved part of the track on both sides is 15 m.
The first term of an A. P is 5 and the 10th term is 95 to find S10
The first term of an arithmetic progression is 5 and the 10th term is 95. The sum of the first 10 terms is 455.
The sum of the first 10 terms of an arithmetic progression (A.P.) can be found using the formula:
S_n = n/2 * (2a + (n-1)d)
where a is the first term, d is the common difference, and n is the number of terms.
Given that the first term is 5 and the 10th term is 95, we can find the common difference (d) using the formula:
a_n = a + (n-1)d
Plugging in n = 10 and a = 5, we get:
95 = 5 + (10 - 1)d
Solving for d, we get:
d = (95 - 5) / (10 - 1) = 9
Now that we know the common difference, we can find the sum of the first 10 terms:
S_10 = 10/2 * (2 * 5 + (10 - 1) * 9) = 10/2 * (10 + 81) = 10/2 * 91 = 455
So, the sum of the first 10 terms is 455.
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find the gcf 24x^3+36^2
The greatest common factor of the 24x³ + 36x² is 12x².
What is the greatest common factor?It is the greatest factor common to all the numbers given such that there are no greater factors common other than that.
Example:
4 is the gcd of 12, 8, 16.
We have,
24x³ + 36x²
Taking out the common factor.
= 12x² (2x + 3)
Thus,
GCF of the expression is 12x².
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