The original cardboard measures 25 cm by 40 cm. By cutting out a 10 cm by 10 cm corner square, the new measurement of the cardboard will be 15 cm by 30 cm. The volume of the container will be 4500 cm^3.
The goal of this project is to build a container out of a rectangular piece of cardboard measuring 25 cm by 40 cm. To do this, a square must be cut out of each corner of the cardboard and the sides must then be bent up. In order to produce a container with the most internal volume, the corner square should be 10 cm by 10 cm. This will result in four equal sides and a larger internal volume. The larger internal volume will allow the container to hold more material, thus making it more efficient for the project.
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Your cousin plays point guard for her community basketball team. When she plays in a game, five out of seven baskets she scores for her team are lay-ups.
If your cousin scores fourteen baskets for her team at Saturday night's game, how many were lay-ups?
If, during the course of the season, your cousin scores one hundred forty baskets for her team, how many were lay-ups?
If, over the course of several games, your cousin makes twenty lay-ups, how many total baskets did she score for her team?
The total number of lay-ups in 14 baskets is 10
The total number of lay-ups in 140 baskets is 100The total number of baskets in 20 lay-ups is 28The total number of lay-upsIn fourteen baskets
From the question, we have the following parameters that can be used in our computation:
Lay-ups = 5 out of 7 baskets
This means that
Lay-ups = 5/7 baskets
When the number of baskets is 14, we have
Lay-ups = 5/7 * 14
Evaluate
Lay-ups = 10
In one hundred forty baskets
From the question, we have the following parameters that can be used in our computation:
Lay-ups = 5 out of 7 baskets
This means that
Lay-ups = 5/7 baskets
When the number of baskets is 140, we have
Lay-ups = 5/7 * 140
Evaluate
Lay-ups = 100
The total number of basketsHere, we have
Lay-ups = 20
Recall that
Lay-ups = 5/7 baskets
So, we have
Baskets = 7/5 lay-ups
This gives
Baskets = 7/5 * 20
Evaluate
Baskets = 28
Hence, the number of baskets is 28
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delivered.
a. What is the constant rate of change? What does it represent?
b. What is the initial value? What might that represent?
The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.
The given problem can be solved as follows,
(a) The graph given is a straight line that passes through (0, 40) and (10, 240).
The constant rate of change is equivalent to the the slope of the line given as,
⇒ (240 - 40)/(10 - 0) = 20
(b) The initial value of the graph is given as the y-intercept of the line.
Which is given as 40.
It might represent the fixed cost.
Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.
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The missing graph is attached here.
question and ente your response in the box provided. Use the
Factor the following expression: x² + x - 6
Answer:
-3
Step-by-step explanation:
x² + x = 3
3 - 6 = -3
FILL IN THE BLANK. a(n) ____________ difference is due to some systematic influence and not due to chance.
The correct option is (a) significant.
a(n) significant difference is due to some systematic influence and not due to chance.
Significant: Having or likely to have influence or effect : important. a significant piece of legislation also of a noticeably or measurably large amount. a significant number of layoffs.
Insignificant: small or unimportant
null: Lacking meaning or having no value
serendipitous: come upon or found by accident
As per the question the suitable answer is option (a).
Therefore, the correct answer is Significant
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A(n) significant difference is due to some systematic influence and not due to chance. Choose one answer.
a. significant b. insignificant c. null d. serendipitous
The sum of two numbers is 62, and their difference is
12. What are the numbers?
Answer:
25 and 37
Step-by-step explanation:
x+y=62
y-x=12
+x. +x
y=12+x
x+(12+x)=62
2x+12=62
-12. -12
2x=50
/2. /2
x=25
25 is one of the numbers
y-25=12
+25 +25
y=37
hopes this helps
What is 5 times 10000
Answer:
50000
Step-by-step explanation:
Mai is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Mai has been adding money. Suppose that x and y are related by the equation y= 550 + 40x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
The change per week in the amount of money in the account is 40
The starting amount of money in the account is 550.
How to illustrate the equation?The statement that exemplifies the provided variables is called an equation. In this instance, the scenario is described by taking into account two or more factors. The definition of an equation as a mathematical statement that consists of two expressions joined by an equal sign must be understood.
In this instance, x and y are connected by the formula y=550 + 40x. In light of this, the weekly change in the account's balance is 40 dollars, while the initial balance was 550.
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The printer at Seneca office can print out one A1 page every 5 seconds. In 4.3 hours time, how many pages can be printed out? Add any workings here
Answer: There are 4.3 hours * 60 minutes per hour = 4.360=258minutes in 4.3 hours.
There are 258 minutes * 60 seconds per minute = 25860=15480 seconds in 258 minutes.
Therefore, the printer at Seneca office can print out 15,480 pages / 5 seconds per page =15480/5=3096 pages in 4.3 hours. Answer: 3096
Step-by-step explanation:
In a game, the number of dominos in various rows forms an A.P. If the number of dominos
in the 3rd and 11th cell together is 68 and number of dominos in 11th cell is 24 more than of
3rd cell, then answer the following questions based on this data.
The number on the third term and the eleventh term will be 22 and 46, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
In a game, the number of dominos in different lines structures an A.P. Assuming that the quantity of dominos in the third and eleventh cell together is 68 and the quantity of dominos in the eleventh cell is 24 a bigger number than of the third cell.
Let 'x' be the third number and 'y' be the eleventh number. Then the equations are given below.
x + y = 68 ...1
y = x + 24 ...2
From equations 1 and 2, then we have
x + x + 24 = 68
2x = 44
x = 22
Then the value of the variable 'y' will be given as,
y = 22 + 24
y = 46
The number on the third term and the eleventh term will be 22 and 46, respectively.
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9x+7y=256 and 3x+5y=125
Answer:
y= 14.875
x= 16.875
Step-by-step explanation:
simultaneous equation
substitution method
question 4 while verifying cleaned data, a data analyst encounters a misspelled name. which function can they use to determine if the error is repeated throughout the dataset? 1 point case counta check count
To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.
Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.
What is a dataset, using an example?
A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.
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Line k has a slope of 1/3. Line j is perpendicular to line k and passes through the point (1,4). Create an equation for line j.
The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.
How does one point slope?
The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).One of the three forms we can use to express a straight line is the point slope form, also referred to as the point-gradient form.This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.Line k is perpendicular to line j
m(j) = - m(k)
m(j) = -(1/3)
One slope one point formula:
y - y₁ = m( x - x₁ )
y - 4 = -(1/3)(x - 1)
3y - 12 = -x + 1
x + 3y -13 = 0
Hence, The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.
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Establish the identity.
(csc0+ cot 0)(csc0- cot0) = 1
a. Multiply and write the left side expression as the difference of two squares: ?
b. The expression from the previous step is equivalent to 1 using what?
O A. Reciprocal Identity
O B. Quotient Identity
O C. Pythagorean Identity
O D. Cancellation Property
O E. Even-Odd Identity
pls help asap i can’t pass this class without passing this test
To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.
The left side of the given equation can be written as:
(csc0+ cot 0)(csc0- cot0)
We can then apply the difference of squares formula to this expression to get:
(csc0+ cot 0)(csc0- cot0) = (csc0+ cot 0)(csc0- cot0)
Now, we can see that this expression is equivalent to 1 using the Cancellation Property. This property states that if two numbers or expressions are equal, then their corresponding parts are also equal. In this case, since 1 = (csc0+ cot 0)(csc0- cot0), we can cancel out the corresponding parts on both sides of the equation to get 1 = 1.
Therefore, the correct answer is D. Cancellation Property.
2) Choose the equation of a line parallel to the given equation and passing through a point P.
-3x - y = - 4; P = (1, 4)
Equation of the line is y = -3x + 7.
What are parallel line ?Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines.
Suppose the line's equation is y=mx + c, where m and c are unknowns.
Since it is parallel to the equation y = -3x + 4 and -3x - y = -4, its slope is now -3. So m = -3.
Additionally, point (1,4). Therefore, this should be satisfied by our line's equation.
Consequently, 4 = -3(1) + c
therefore c = 7
The line's equation changes to y = -3x + 7.
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5x2 to the power of 5
find the exact length of the curve. x = et − t, y = 4et/2, 0 ≤ t ≤ 4
The exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].
Let the given equation is [tex]x=e^t-t, y=4 e^{\frac{t}{2}}, 0 \leq t \leq 5[/tex].
Length of Parametric Curve: A parametric curve is a function expressed in components form, such that x=f(t),y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral [tex]$L=\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$[/tex]
Let’s begin by getting the first derivative of the components of the function with respect to the variable t.
[tex]$$\begin{aligned}x & =e^t-t, y=4 e^{\frac{t}{2}} \\\frac{d x}{d t} & =\frac{d}{d t}\left(e^t-t\right)=\frac{d}{d t}\left(e^t\right)-\frac{d}{d t}(t)=e^t-1 \\\frac{d y}{d t} & =\frac{d}{d t}\left(4 e^{\frac{t}{2}}\right)=\left(4 e^{\frac{t}{2}}\right) \frac{d}{d t}\left(\frac{t}{2}\right)=\left(4 e^{\frac{t}{2}}\right)\left(\frac{1}{2}\right)=2 e^{\frac{t}{2}}\end{aligned}$$[/tex]
Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval [a,b]=[0,5].
[tex]$$\begin{aligned}L & =\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^t-1\right)^2+\left(2 e^{\frac{t}{2}}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}-2 e^t+1\right)+\left(4 e^t\right)} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}+2 e^t+1\right)} d t \\& =\int_0^5 \sqrt{\left(e^t+1\right)^2} d t \\& =\int_0^5\left(e^t+1\right) d t\end{aligned}$$[/tex]
We need to find the value of the definite integral to get the exact length of the curve.
Take out the limits of integration and evaluate the resulting indefinite integral to solve.
[tex]$$\begin{aligned}L & =\left.\left[\int\left(e^t+1\right) d t\right]\right|_0 ^5 \\& =\left.\left[\int e^t d t+\int 1 d t\right]\right|_0 ^5 \\& =\left.\left[e^t+t\right]\right|_0 ^5\end{aligned}$$[/tex]
Evaluate the solution at the limits of integration to get the length.
[tex]$$\begin{aligned}& L=\left[e^{(5)}+(5)\right]-\left[e^{(0)}+(0)\right] \\& L=\left(e^5+5\right)-\left(e^0+0\right) \\& L=e^5+5-(1+0) \\& L=e^5+5-1 \\& \mathbf{L}=\mathbf{e}^5+\mathbf{4}\end{aligned}$$[/tex]
Therefore, the exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].
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molly is playing a game that requires her to roll a fair die repeatedly until she first rolls a 1, at which point she must stop rolling the die. what is the probability that molly will roll the die less than four times before stopping?
The probability that molly will roll the die less than four times before stopping is 91/216
Probability is the calculation of an outcome or the chance of an event ever happening.
Probability determines the likelihood of an event occurring: P(A) = f / N.
Probability(Event) = Favorable Outcomes/Total Outcomes
She can do this in 1 roll, 2 rolls, or 3 rolls.
Probability of getting 1 in the first roll: 1/6
Probability of getting 1 on the second roll: 5/6∗1/6=5/36
Probability of 1 on the third roll: 5/6∗5/6∗1/6=25/216
As it can happen in 1, 2, or 3 rolls we add the probabilities: 1/6+5/36+2/52
⇒26/216+30/216+25/216
⇒91/216
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find the value of x in the figure?
Answer:
x = 11
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
80 + 60 + 3x + 7 = 180
147 + 3x = 180 ( subtract 147 from both sides )
3x = 33 ( divide both sides by 3 )
x = 11
Answer:
x = 11
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
60 + 80 + 3x+7 = 180
Combine like terms
3x+147=180
Subtract 147 from each side
3x+147-147=180-147
3x = 33
Divide each side by 3
3x/3 = 33/3
x = 11
What is the circumference of the following circle?
Use 3.14 for \piπpi and enter your answer as a decimal.
Answer:
9.42cm
Step-by-step explanation:
according to fig :
diameter (d) =3cm so ,
radius (r) = d/2 =3/2 = 1.5cm
solution:
as we know that ,
circumference of a circle = 2πr
=2×3.14×1.5
=9.42 cm
Answer:
21.98 cm
Step-by-step explanation:
The circumference formula is [tex]2\pi r[/tex] which can be expressed as [tex]\pi d[/tex], where r is radius and d is the diameter length.
Since we know the diameter is 3 cm, that means we can plug in that value for d and get [tex]7 \pi[/tex] as the circumference
However, the question tells us to use 3.14 for [tex]\pi[/tex], so we must find the value of [tex]7 * 3.14[/tex]. By doing mental math or by using a calculator we can find this value to be 21.98.
Thus, the circumference of the circle is 21.98 cm
The function S(d)= 86log d +112 relates the speed of wind, S, in miles per hour, near the centre of a tornado to the distance the tornado travels, d, in miles. Estimate the rate at which the speed of the wind at the centre of the tornado is changing the moment it has traveled its 50th mile.
The rate at which the speed of the wind changes at the 50th mile is 258.114 miles per hour
How to estimate the rate at which the speed of the windFrom the question, we have the following parameters that can be used in our computation:
Function: S(d) = 86log d + 112
Express the above function properly
So, we have the following representation
S(d) = 86log(d) + 112
From the question, we have:
Distance = 50th mile.
This means that
d = 50
Substitute the known values in the above equation, so, we have the following representation
S(50) = 86log(50) + 112
Evaluate the logarithm
So, we have the following representation
S(50) = 86 * 1.699 + 112
Evaluate the products
S(50) = 146.114 + 112
Lastly, we have
S(50) = 258.114
Hence, the speed is 258.114 miles per hour
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If angle D is 22 degrees, what is the measure of angle B?
Answer:
22 degrees
Step-by-step explanation:
D=B and C=A
x + 2y = 5; P = (2,-5)
Answer:
....................
Help please! I will mark brainliest.
Problem Walkthrough: Find the area of this figure.
Use 3.14 to approximate pi.
F
6
9
To solve for the area, split the figure into simple figures as
shown below. Solve for the area of each and combine.
6
Triangle
6
9
Rectangle
Half-circle
Enter the value
that belongs in
the green box.
Total Area
12
Answer:
86.13
Step-by-step explanation:
area of Triangle: ½ × height × base = ½ ×6×6= 18 cm
area of Rectangle: length × width= 6×9 = 54 cm
area of circle= π × (radius)² then...
area of Half-circle = [π×(radius)²] ÷2 = [3.14×(6/2)²] ÷2 = 14.13 cm
The Area of this figure= 18 + 54 + 14.13 = 86.13 cm
Answer:
[tex]A = 86.13[/tex]
Step-by-step explanation:
In order to find the area of the given figure
We need to divide the figure Into the following shapes
Firstly,
A triangle
Rectangle
Semi Circle
Area of a triangle + Area of a rectangle + Area of a semi circle = Area of the whole figure
So lets find the area of the figures
Area of Triangle = [tex]\frac{1}{2}[/tex]X[tex]6[/tex]X[tex]6[/tex]
= [tex]18[/tex]
Area of a rectangle = [tex]l[/tex]x[tex]b[/tex]
= [tex]9[/tex]x[tex]6[/tex]=[tex]54[/tex]
Area of a semi circle = [tex]\frac{1}{2}\pi r^{2}[/tex]
= [tex]\frac{1}{2} X \frac{22}{7} X(3)^{2}[/tex]
= [tex]14.13[/tex]
[tex]A = 18 + 54 + 14.13[/tex]
[tex]A = 86.13[/tex]
The total area of the geometry will be 86.13 square units.
Pls Mark me Brainliest
PLEASE HELP QUICK I WILL GIVE BRAINLIEST
Answer:
z > 1 1/3
Step-by-step explanation:
See picture
[very easy] [100 pt and brainliest]
The table shows the weights of apples at a grocery store. There is a proportional relationship between the number of apples and their weight. What is the weight of TWO apples?
TYPE ONLY THE NUMBER
Answer:
2 apples = 0.24 kg
12 apples = 1.44 kg
Step-by-step explanation:
Find the weight of one apple.
If 5 apples weigh 0.60 kg, then 1 apple weighs:
[tex]\implies \sf 1\;apple=\dfrac{0.60}{5}=0.12\; kg[/tex]
Therefore:
2 applies = 2 × 0.12 - 0.24 kg12 apples = 12 × 0.12 = 1.44 kgwhat is the power of the lens that has a focal length of 40 cm and a diameter of 5.0 cm?
The power of the lens is 2.5D
The focal length of 40 cm and a diameter of 5.0 cm.
Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f.
Power of lens = 1 / focal length (in meters)
For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot.
we have focal length 40cm (.4 m)
so
Converging lenses have positive optical power, while diverging lenses have negative power.
Power of lens = 1/0.4 m
=2.5 D [The unit of Power of lens is Dioptre]
Therefore, the power of the lens that has a focal length and a diameter of 5.0 cm is 2.5D
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A bakery old 26 vanilla cupcake in a day which wa 13 percent of the total number of cupcake old that day. How many total cupcake did the bakery ell that day
The bakery sold total 200 cupcake in that day.
What is percent value?The word percent means per hundred and percent value of a quantity refers to the hundred parts of that quantity. Percent value is expressed by sign %.
How to calculate percentage value?In order to determine a percent value of a quantity, we divide the quantity by the total quantity and finally the resultant value is multiplied by 100.
In the other hand, when we need to calculate total quantity from a percentage value, we multiply the specific quantity by 100 and finally the resultant is divided by the percentage value.
Given, Number of cupcakes sold at a specific time =26 which was 13 percent of total number of cupcakes sold in that day.
Therefore, number of total cupcakes sold in that day = 26× 100/13 =200
the total number is 200
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If the exponent of the leading term of the numerator is higher than the exponent of the leading term of the denominator, what can we conclude?.
If the degree on x in the denominator is larger than the degree on x a bigger leading exponent than the polynomial in the numerator.
After then the graph to the value found by dividing the leading coefficients of the two polynomials.
To find horizontal asymptotes:
1. If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
2. If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
3. Rational functions (a polynomial divided by a polynomial) and exponential functions have horizontal asymptotes.
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find an equation of the tangent line to the given curve at the specified point. y = e^x / x , (1, e)
y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)
Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.
The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).
thus , y' = [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]
y'(1) = 0 = m
Our slope is indicated by the horizontal line.
y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])
Our line will simply be our y-coordinate because our slope(m) is 0:
e
Therefore:
The tangent line's equation is y=e.
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20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
To calculate Keith's equivalent rate with simple compounding, we need to use the following formula:
r = (e^(i/n) - 1) * n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
In this case, we are given that i = 8.27% and we can assume that the number of compounding periods per year is 12, since many loans are compounded monthly. Plugging these values into the formula, we get:
r = (e^(0.0827/12) - 1) * 12
= (1.0082 - 1) * 12
= 0.0082 * 12
= 0.0984 or 9.84%
Therefore, Keith's equivalent rate with simple compounding is [B] 0.0998 or 9.98%.