The individual-size box of cereal is a rectangular prism with a volume of 44.625 inches³.
What is the volume of a rectangular prism?The volume of rectangular prism of length l, width w and height h is given by:
V = lwh.
In this problem, the standard dimensions are:
l = 3(1/2) = 3 + 0.5 = 3.5 inches.w = 8(1/2) = 8 + 0.5 = 8.5 inches.h = 15 inches.The individual-size box has a 1/10 of the volume of the original box, hence:
V = 0.1 x 3.5 x 8.5 x 15 = 44.625 inches³.
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A six foot diameter circular table top has a area of about how many square feet
Answer:113.1 square feet
Step-by-step explanation:
D
7. Solve the system:
f(x)=(x-3)² +1
g(x)=-3x+10
Answer: (0,10) and (3,1)
Step-by-step explanation:
Before I solve the system, I am going to rewrite it to make it easier for me to understand it.
[tex]y=(x-3)^2+1\\y=-3x+10[/tex]
Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.
[tex](x-3)^2+1=-3x+10[/tex] [exponent]
[tex]x^2-6x+9+1=-3x+10[/tex] [add both sides by 3x]
[tex]x^2-3x+10=10[/tex] [subtract both sides by 10]
[tex]x^2-3x=0[/tex] [factor]
[tex]x(x-3)=0[/tex]
Notice that x=0 and x-3=0. This means the solutions are x=0 and x=3.
To find the actual full solution, we have to plug those points back into the original equations.
[tex]-3(0)+10=0+10=10\\-3(3)+10=-9+10=1[/tex]
Therefore, the solutions to this system are (0,10) and (3,1).
What are the slopes of the point o,2 1 , -1
The slope of the line that goes through the points (0, 2) and (1, -1) is -3.
What is the slope of the line?
The slope of a line is a number that describes the steepness of a line and the direction it is heading. It is also known as the "rise over run" or the "rate of change" of a line. The slope of a line is typically represented by the letter "m" and is found using the formula:
slope = (y2 - y1) / (x2 - x1)
To find the slope of a line, you need two points on the line (x1, y1) and (x2, y2) and substitute their coordinates into the slope formula.
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, we have two points: (0, 2) and (1, -1). To find the slope between these two points, we can substitute their coordinates into the slope formula:
slope = (-1 - 2) / (1 - 0)
slope = -3
Hence, the slope of the line that goes through the points (0, 2) and (1, -1) is -3.
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what is this expression simplified
Therefore , the solution of the given problem of expression comes out to be as a result, we can minimize the radical statement by doing the actions listed below.
Expression: What is it?the value of an object variable is represented by collections of numbers, signs, and procedures (like + and).Examples: The equation is 5+7. 3 x/2 is an alternative formula. An expression lacks the equals symbol.
Here,
To simplify a radical expression, use the Product Property.
1) Determine the radical's largest factor, which is also the index's precise power. Use that factor to rewrite the radicand as the intersection of two factors.
2) Apply the product rule to the radicals to rewrite them as the outcomes of two additional radicals.
3. Decompose the root of the ideal power.
Therefore, by taking the methods outlined above, we may simplify the radical expression.
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A breakfast stall at a market stays open for 4 hours 30 minutes every morning opens at 06 45 every morning, what time does it close? shift at 10.30
Answer:
10:15
Step-by-step explanation:
fsd
I NEED HELP ASAP RN!
Answer:
TQN
Step-by-step explanation:
7X+2Y=-14 FIND THE X INTRERCEPT AND THE Y INTERCEPT
Answer:
x-intercept = -2; y-intercept = -7
Step-by-step explanation:
A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled? Enter your answer, to the nearest tenth, in the box.
Answer:
Height = 557.1 to 1dp.
Step-by-step explanation:
Surface area of the given prism
= 2(12*3 + 12*10 + 10*3)
= 7272
The new prism must have surface are 2*7272 = 14544.
Let the new height be h, then:
2(3h + 10h + 30) = 14544
6h + 20h = 14544 - 60
26h = 14484
h = 14484/26
= 557.1 cm.
What is the solution to this system of equations?
-3x + 4y = 24
y = 3/4x+6
No solution
(-3,3)
(4,6)
Infinitely many
Equations now take the shape:
[1] 3x - 4y = 24
[2] 3x + 4y = 6
What number is infinitely many solutions?Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself. Combine like terms 2x and 2x.As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation infinitely many. (mathematics) Having a quantity or cardinality that is infinite or unbounded“No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.To learn more about infinitely many solutions refers to:
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Determine whether or not the equation is linear or exponential and explain how you know.
y= 4(5^x)
Please help me I’m stuck
Answer: B
Step-by-step explanation:
2/3 = 1/3 and 1/4 is already there
Hope this helps !
Answer:
Step-by-step explanati
Your answer would be A.
Write a system of linear inequalities represented by the graph.
Inequality 1:
Inequality 2:
A system of linear inequalities represented by the graph are;
Inequality 1: y ≤ 3x - 3
Inequality 2: y ≥ ¹/₂x - 3
How to interpret Inequality Graphs?Inequalities that use < or > symbols are usually plotted with a dashed line that shows us that the line is not included in the region. Meanwhile, Inequalities that use ≤ or ≥ symbols are normally plotted with a solid line that shows us that the line is included in the region.
The general formula of equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, the graph that rises to the right side in the first quadrant has;
Slope = (3 - 1)/(3 - 2)
Slope = 3
the y-intercept is at y = -3
Thus, equation is;
y ≤ 3x - 3
Thus, the graph that rises to the left side in the second quadrant has;
Slope = (1 - 0)/(2 - 0)
Slope = 1/2
the y-intercept is at y = 1
Thus, equation is;
y ≥ ¹/₂x - 3
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grapg the line 2/3 passing through (-4,1)
The equation of the line with a slope of 2/3 passing through (-4, 1) is y = (2/3)x + 11/3
What is an equation?An equation is an expression relating two or more numbers and variables.
The slope - intercept form of a linear equation is:
y = mx + b
Where m is the rate of change(slope) and b is the y intercept.
The equation of a line passing through (x₁, y₁) with a slope of m is given by:
y - y₁ = m(x - x₁)
The line has a slope of 2/3 and pass through point (-4, 1). Hence:
y - 1 = (2/3)(x - (-4))
y - 1 = (2/3)(x + 4)
y = (2/3)x + 11/3
The equation of the line is y = (2/3)x + 11/3
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5/6 × (-4 1/2) × (-2 1/5)
show your work
what are the coorindates of point A
Point A has coordinates (x1, y1). The x-coordinate, x1, is the horizontal distance from the origin, while the y-coordinate, y1, is the vertical distance from the origin.
What are coordinates?Coordinates in math refer to a pair of numbers that indicate the position of a point on a two-dimensional graph or in a three-dimensional space. The two numbers are usually referred to as the x-coordinate (or abscissa) and the y-coordinate (or ordinate). In three-dimensional space, the third number is referred to as the z-coordinate (or applicate). A point located at (3, 4) on a two-dimensional graph would be located 3 units along the x-axis and 4 units along the y-axis. Similarly, a point located at (3, 4, 5) in three-dimensional space would be located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis.
Both coordinates indicate the exact location of Point A in a coordinate system. For example, if Point A is located at (2, 4), it means that the x-coordinate of Point A is 2, which is 2 units away from the origin in a horizontal direction, and the y-coordinate of Point A is 4, which is 4 units away from the origin in a vertical direction. The origin is usually located at (0, 0) in a coordinate system.
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5. 5(x + 10) + x
A. 6x + 15
B.5x + 15
C.6x + 50
D.4x – 50
Answer: C
Step-by-step explanation:
a smothie recipe calls for 2 1/4 cups of frozen mango. If the recipe serves two. ow many cups of frozen mango is needed to serve one?
1.125 cups of frozen mango is needed to serve one
A smoothie recipe contains 2 1/4 cups of frozen mango
This recipe can serve a total number of two people
The first step is to change the mixed fraction to an improper fraction
2 1/4
9/4
The number of cups of frozen mango needed to serve one person is
9/4 ÷ 2
9/4 × 1/2
= 9/8
= 1.125
Hence the number of cups of frozen mango required to serve one person is 1.125
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please answer i need
Answer:A
Step-by-step explanation:
(Slope MC)
A linear relationship is given in the table.
x-2 -1 0 1 2
y -18 -12 -6 0 6
What is the slope of the relationship?
0-6
-1/6
1/6
6
The given linear relationship slope of the line is D) 6.
What is slope?
An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.
Here from given tables lets take any two points to find slope, then
[tex](x_1,y_1)=(0,-6) and (x_2,y_2)=(1,0)[/tex]
Now using slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] then
=> m = [tex]\frac{0-(-6)}{1-0}[/tex]
=> m =[tex]\frac{6}{1}[/tex]
=> m = 6.
Hence the slope of the given table is D)6.
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On a certain hot summer's day, 183
people used the public swimming pool. The daily prices are $1.75
for children and $2.50
for adults. The receipts for admission totaled $390.00.
How many children and how many adults swam at the public pool that day?
Using substitution method to solve the system of linear equation, the number of children is 90 and adults is 93.
What is System of Linear EquationIn mathematics, a system of linear equations is the collection of two or more linear equations that share the same variables. The maximum power of the variable in the linear equations in this situation is 1, making them first-order equations. A linear equation may have one, two, or three variables. We can therefore create linear equations with n variables.
To solve this problem, we have to define our variables and then write the equations.
Let;
x = childreny = adultx + y = 183 ...eq(i)
1.75x + 2.5y = 390 ...eq(ii)
solving both equations
From equation (i)
x + y = 183
x = 183 - y ...eq(iii)
Put equation (iii) into equation (ii)
1.75(183 - y) + 2.5y = 390
y = 93
Put y = 93 into equation (i)
x + 93 = 183
x = 90
The number of child is 90 and adult is 93
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this distance time graph shows the journey of a tortoise. how far did the tortoise travel in total. give answer in metres
The tortoise travelled the maximum distance of 9 m estimated from the time graph journey of a tortoise.
Define the term distance time graph?Distance-time graphs demonstrate how a moving object's distance travelled varies over time.
A distance-time graph shows how far a person travels in a given amount of time. An illustration of this would be a graph where a straight line represents uniform motion and a gradient represents rapid motion. Time is drawn along the X-axis, just like any other graph, and distance is displayed along the Y-axis.For the stated time graph of the journey of tortoise.
On x axis - time taken.
On y axis - distance covered by the tortoise.
Thus, the maximum distance is covered by the tortoise is 9 m at the time of 3 minutes.
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The diameter of a hat is 6.8 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
A. 2.17 inches
B. 10.68 inches
C. 21.35 inches
D. 36.29 inches
Answer:
C. 21.35 inches
Step-by-step explanation:
circumference = πd
circumference = 3.14 × 6.8 inches
circumference = 21.35 inches
Find GH in each trapezoid.
Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.
what is trapezium ?Having at least one pair of parallel sides, a trapezoid is a quadrilateral in American and Canadian English. In the UK and other nations that speak English, it is referred as as the Trapezium. A trapezoid is a convex quadrilateral according to Euclidean geometry. Its parallel sides make up the trapezoid's base. The trapezoid, a convex quadrilateral, is defined by an identical pair of opposite sides that are parallel to one another. On paper, the two-dimensional trapezoid shape seems like a table. The term "quadrilateral" in Euclidean geometry refers to a polygon with four sides and four vertices.
given
A trapezoid's midsegment runs parallel to each base and is half as long as all of the bases combined.
1/2 * 3x - 6 = 2x
3x - 6 = 4x
= -6 = 7x
x = 0.85
Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.
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4. In a class of 26 students, 18 of the students have a pet. Of
the pet owners, 12 prefer dogs to cats. Of the 8 non-pet
owners, 3 prefer dogs to cats. What is the probability of
selecting a student from the class who is a pet owner or
prefers cats to dogs?
The probability of selecting a student from the class who is a pet owner or prefers cats to dogs is; 0.4
What is the probability of selection?In probability, If events A and B are not mutually exclusive, then the probability of A or B is expressed as;
p(A or B) = p(A) * p(B).
Total number of students = 26
Total number of students that are pet owners = 18
Total number of students that prefers cats to dogs = 26 - (8 + 3) = 15
Thus;
P(pet owner) = 18/26
P(prefers cats to dogs) = 15/26
P(Pet owner or prefers cats to dogs) = (18/26) * (15/26)
= 0.4
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Last summer, the Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. This summer, they purchased a larger kiddie pool that holds 150 gallons of water.
If the Abrams fill the larger pool at the same rate, how long will it take to fill it?
The answer is 10 minutes
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: Abrams family had a 30-gallon baby pool that they could fill in just 2 minutes. Thus speed = 30/2
=15 gallons per day
Thus to fill 150 gallons the time required is 150/15=10 mins
Hence, The answer is 10 minutes
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Stephen deposits $5,000 in a bank account that
earns 4.25% interest compounded continuously.
Approximately, when will Stephen have $10,000 in
his bank account if he makes no deposits or
withdrawals?
could some one please answer this for me, thanks
Answer:
x = 2
Step-by-step explanation:
The triangle shown in the image is a right triangle.
The missing side, x, is the leg and its length is equal to other leg because this is also an isosceles triangle. So this triangle is special 45°-45°-90° and the side lengths are represented with a-a-a√2 respectively. The length of hypotenuse is equal to √8 so:a√2 = √8
Divide both sides by √2a = √4
Remember we said a represents legs, in the image x represents the legs so the answer is:
x = √4 and √4 = 2, therefore the answer is 2.
f(x)=x^2+3x-40 find the zero, thanks in advance
The zeroes of the equation x² + 3x - 40 is -8 or 5.
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0. with a ≠ 0 .
It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
Given:
F(x) = x² + 3x - 40
Now, solving the quadratic Equation
x² + 3x - 40 = 0
x² + 8x - 5x - 40 = 0
x(x + 8) - 5(x + 8)=0
(x+8) (x-5)= 0
So, x+8 = 0 or x-5=0
x=-8 or x= 5
Hence, the zeroes are -8 and 5.
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If the odometer is reading 20,000 miles, how many miles have you actually traveled?
Answer:
22,256
Step-by-step explanation:
If the speedometer reading is 60, your actual speed is miles. miles per hour. Since the value of k = 1.1128 for the two tires in comparison, 1.1128 (20,000) = 22,256 miles (actual) and 1.1128 (60) = 66.768 miles per hour (actual). The percent error is 11.28% for both readings.
please need help asap answer 23, 24, and 25!!!!!!!!!!!!! 30 points
Question 23
Using the alternate interior angles theorem, [tex]m\angle BCA=20^{\circ}[/tex].
Question 24
[tex]\overline{AD} \cong \overline{DC}[/tex] by the definition of a rhombus. This means that [tex]\triangle ADC[/tex] is isosceles. It follows that [tex]m\angle ACD=20^{\circ}[/tex]. Using the angle sum of a triangle, [tex]m\angle CDA=140^{\circ}[/tex].
Question 25
All rhombi are parallelograms, and diagonals of parallelograms bisect each other. This means that [tex]AC=2(4)=8[/tex].