There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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What does it mean when the discriminant is greater than 0?
We are interested in values that make the quadratic expression negative if the quadratic expression is less than, equal to, or greater than 0. We are interested in numbers that make our quadratic expression positive if the quadratic expression is more than, greater than, or equal to 0.
An discriminant value definition ?
The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not. The quadratic function has one repeating real root if b2 - 4ac = 0.
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What are the 7 types of triangles?
The 7 names of triangles:
Scalene, Isosceles, Equilateral, Equiangular triangle, Acute triangle,
Right triangle, Obtuse triangle
What are triangles?
Three vertices make up a triangle, a three-sided polygon. The triangle's angles are formed by a point where the three sides are joined end to end. The triangle's three angles add up to a total of 180 degrees.
Equiangular triangle: All angles are equal.
Acute triangle . . . all three angles are less than 90°
Right triangle . . . one angle is 90°
Obtuse triangle . . . one angle is greater than 90°
Equilateral triangle . . . all three sides are the same length
Isosceles triangle . . . two sides are the same length
Scalene triangle . . . all three sides are different lengths
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If m<1 = 128, then m<8=
Answer:
m<8=1024
Step-by-step explanation:
Since they are asking for m<8, we do 128*8=1024.
André planted a cedar hedge 15 years ago (currently it's the start of the 16th year). The
hedge is now 3 metres high. The cedars grew an average of 12 cm per year. How tall were
the cedars when he planted them?
The height of the cedars when they were planted by André, found using the formulas for arithmetic progression is 1.32 meters
What is an arithmetic progression?An arithmetic progression is a number sequence that consists of numbers that have a constant or common difference between consecutive term of the sequence.
The year André planted the cedar hedge tree = 15 years ago
The present height of the hedge = 3 meters = 300 cm
The average rate at which the cedars grew = 12 cm per year
The height of the cedar hedge when André initially planted the them can be found by representing the situation using an arithmetic progression formula or as follows;
The nth term of an arithmetic progression, aₙ, can be found using the formula; aₙ = a₁ + (n - 1)·d
Where;
a₁ = The initial height of the tree
d = The amount the tree grows each year = 12 cm
n = The number of years ago, the tree was planted
When n = 15, we get;
a₁₅ = 3 meters = 300 cm
Therefore;
300 = a₁ + (15 - 1) × 12
a₁ = 300 - (15 - 1) × 12 = 132
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I need help on this Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answer:
{3, 4, 6, 7, 8}
Step-by-step explanation:
For sets U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 5, 6}, and C = {1, 2, 3, 4, 5}, you want the set {A∩C}'.
A∩CThe set A∩C contains the elements that are common to both sets. Those are {1, 2, 5}.
{A∩C}'The set of interest contains the elements of U that are not in A∩C. Those are ...
{3, 4, 6, 7, 8}
__
Additional comment
DeMorgan's theorem tells us the desired set is equivalent to A'∪C', or {3, 4, 7, 8}∪{6, 7, 8}. That, too, is ...
(3, 4, 6, 7, 8}
if I can vaccinate 10 people in 2 hours. how many people will I get vaccinated in 5 hours?
y=the number of people being vaccinated
x= the number of hours
Answer:
25 people
Step-by-step explanation:
10 people will be vaccinated for 2hrs
10 = 2
y people will be vaccinated for 5hrs
y = 5
(To find y we need to cross multiply)
10 = 2
y = 5
2y= 50
y=50/2
y=25
:- 25 people will be vaccinated in 5hrs.
Lets check if our answer is correct let us make 5 hrs our unknown x
10 = 2
25 = x
(cross multiply)
25×2=10x
50=10x
x=5hrs
so our answer is correct.
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What is the point of a triangle called?
The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
A triangle is a three-sided polygon.
The triangle's three points are known as vertices.
Several triangle-related points:
A triangle's centroid is the point where three medians cut each other. A median is the line that connects a vertex to the opposite side's midpoint.At the circumcenter, the three perpendicular bisectors of a triangle's sides meet. The circumcenter is also the center of the circle formed by passing through the three vertices of the triangle. The orthocenter is the point at which the triangle's altitudes, or the perpendicular lines between each vertex and the opposite side, intersect.The incenter of a triangle is the point at which the three bisectors of the triangle's interior angles intersect. This is also the center of the inscribed circle, also known as the triangle's incircle.A triangle's Euler line is the line that connects the orthocenter, circumcenter, and centroid. It also contains the Nine Point Circle's center.Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.
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help me i dont get this at all
Answer: 18
D
Step-by-step explanation:
The constant of proportionality is y/x, not x/y, which is what your friend found.
X= 1
y=18
18/1=18
please I need help on question 6
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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Rewrite sin(x-7pi/4) in terms of sin(x) and cos(x)
The expression written in terms of sinx and cosx is
sinx· cos7π/4 - cosx ·sin7π/4
What is an algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is sin(x - 7π/4).
Use the formula for sin(A-B) to rewrite the expression:
sin(x - 7π/4)
= sinx· cos7π/4 - cosx ·sin7π/4
Hence, the expression written in terms of sinx and cosx is sinx· cos7π/4 - cosx ·sin7π/4
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Represent the following statement on a number line: I have anywhere from $5 to $8 in my pocket.
The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Translating the statement, we have the following inequality:
Let the variable x represent the amount of money in pocket.
From $5 to $8 in my pocket = 5 ≤ x ≤ 8.
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Sheelu bought a scooter for Rs. 55000. While selling the value of the scooter decreased to Rs. 50600. Find the percentage of decrease in the value of the scooter.
Answer:
8%
Step-by-step explanation:
1. Subtract:
55000 - 50600 = 4400
2. Divide:
4400/55000 = 0.08
The followings are the sys. BP in mmHg of 12 patents
under certain therapy of hypertension
183
144
152
178
157
114
178
152
194
163
118
158
Can we conclude on basis of these data that sample
mean is less than pop mean 165 mmHg
Let a = 0.05
There is no sufficient evidence to support that the population mean is less than 165.
What is mean ?
The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.
From the given data
183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158
Mean = 157.5833
Standard deviation s = 24.39
n = 12
Null hypothesis [tex]H_{0}[/tex] : μ = 165
Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165
Level of significance ∝ = 0.05
degree of freedom (df) = n - 1
(df) = 12 - 1
(df) = 11
critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)
Test - statistics (t) = ( mean - μ ) / ( s / √n)
(t) = -1.053
p - value = 0.1574
p - value > Significance level (∝)
0.1574 > 0.05
We fail to reject the null hypothesis
Critical value [tex]t_{0.05 , 11}[/tex] = -1.796
|[tex]t_{0.05 , 11}[/tex]| = 1.796
|test - statistics| < |critical value|
1.053 < 1.796
We fail to reject the null hypothesis
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5. Julia is playing a computer game. To enter a new quest she has
to pay a "tax" of 2.5 points, but she expects to gain 75 points.
For each quest, how many points can she gain overall?
The number of points gained overall by Julia playing the game is 30 point
How to determine the number of points gained overall?From the question, we have the following parameters that can be used in our computation:
Tax paid for a new quest = 2.5 points
Total points gained playing the game = 75 points
The above parameters can be represented as
The number of points gained overall = Total points gained playing the game/Tax paid for a new quest
Substitute the known values in the above equation, so, we have the following representation
The number of points gained overall = 75/2.5
Express as a correct fraction
So, we have the following representation
The number of points gained overall = 750/25
Evaluate the quotients
So, we have the following representation
The number of points gained overall = 30
Hence, the number of points gained overall =is30
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How do you find the equidistant point of a triangle?
The equidistant point of the triangle is point O , which is shown below.
In the question ,
we have to find the equidistant point in the triangle ,
We know that the equidistant point from the vertices of the triangle is the circumcenter ,
let the circumcenter be point O .
The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .
We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .
So ,we draw OA ,OB and OC .
we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.
that means , OA = OC and OC = OB .
which means OA = OB .
we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.
So, we can say that point O is on the perpendicular bisector of AB .
and
Since OA = OB = OC , the point O is equidistant from A , B and C .
Therefore , the equidistant point of the triangle is the circumcenter (point O) .
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A rectangle is placed around a semicircle as shown below. The width of the rectangle is 4 yd. Find the area of the shaded region.
Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the shaded region is calculated as: 6.88 yd²
How to Find the Area of a Shaded Region?The area of the shaded region in the diagram = area of rectangle - area of semicircle.
Given the following:
Width of rectangle = 4 ydRadius of the semicircle (r) = 4 ydLength of the rectangle = 2(4) = 8 ydArea of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²
Area of the rectangle = length × width = 8 × 4 = 32 yd²
The area of the shaded region = 32 - 25.12 = 6.88 yd²
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You read 6 chapters. Each chapter has 8 pages. Your brother reads the same number of pages. His chapters have 12 pages. How many chapters does your brother read?
The sixth chapter's Brother 0.66 pages were read.
How to calculated the chapters in 12 pages?According to the order of operations, you should perform multiplication and division first, going from left to right, before adding and subtracting.
Add and subtract from left to right while continuing to multiply and divide. the next step is to add and subtract from left to right.
Assumed the question is how many pages are in each chapter.
Let it be x:
6x + 8 = 12
6x = 4
x = 4 /6
x = 0.66.
The sixth chapter's Brother 0.66 pages were read.
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help!! i’ve been stuck on this problem!
Answer:
x less than or equal to -2
Step-by-step explanation:
I believe that's the answer
Answer:
x < -2
Step-by-step explanation:
You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.
DomainThe domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.
ApplicationThe open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...
x < -2
The domain of the relation is x < -2.
The graph shows the amount of book sales
over several days. Determine if the
relationship is proportional. Find and
interpret the slope. Then find the unit rate
and compare it to the slope.
The two quantities have proportional relationship and it's slope is 333.33
ProportionsProportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
In this case, we have to determine is there's a uniform increase or decrease of the quantity.
The formula of proportionality is often given as
y = kx
k = constant of proportionalityLet's take two points and check if they share the same constant of proportionality
2000 = k(6)
k = 333.33
1000 = k(3)
k = 333.33
The relationship between sales and day is proportional.
The slope of the graph is given as
m = y₂ - y₁ / x₂ - x₁
m = 2000 - 1000 / 6 - 3
m = 333.33
NB: The slope and constant of proportionality in this case are the same quantity.
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Question 3: Multiply: 0.33.10⁵
330
330000
33000
3300
Answer:
33,000
Step-by-step explanation:
0.33 x 10^5 is 33,000
please help me answer this question
Answer:
this 1
Step-by-step explanation:
same doubt pease any help
The graph of F is shown below evaluate each integral by interpreting it in terms of area
The answer to this question is after solving definite integration 0,1,-4,-10
What is Definite integration?
It is just basically Simple Integration with limits. In other words it is completely same as area under curve
Solution:
We will proceed by finding area under curve
Here we have to consider the area above x axis as positive and area under x axis as negative area
In First part +ve area and -ve area cancels each other hence answer is 0
In second part after cancellation only 1 square block above x axis remains whose area is 1 hence answer is 1
remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative
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20 is ______times as much as 2
Is the exponential function 5 x?
It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.
What is exponential decay function?
A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
[tex]y=5^x[/tex]
It is a function called "Exponential function". The base determines the growth or decay of the function.
If base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.
Here, the base is positive and it's not 1 or 0.
If we have
[tex]y=5^{-x}[/tex]
this function can be rewritten in this way:
[tex]y=(1/5)^x[/tex]
Here, base between 0 and 1, the function decays
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The sum of two numbers is 66. Two times the lesser number is 15 more than the greater number. What are the numbers
If x is a lesser number, the equation is
Answer:
See below!
Step-by-step explanation:
Let the two numbers be x and y
Condition # 1:x + y = 66 ----------------(1)
Condition # 2:2x = y + 15
2x - y = 15 ---------------(2)
Add both equations
x + y + 2x - y = 66 + 15
x + 2x = 66 + 15
3x = 81
Divide both sides by 3
x = 27Put x = 27 in Eq. 1
27 + y = 66
Subtract 27 to both sides
y = 66 - 27
y = 39[tex]\rule[225]{225}{2}[/tex]
The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city.
Use the box-and-whisker plots to answer the questions.
Comparing the box-and-whisker plots for both data of each city, we have:
a. City B had more noon temperatures above 76°F
b. Both had the same interquartile range.
c. City B had a larger median noon temperature
d. City A had the largest noon temperature.
How to Analyze a Box-and-whisker Plot?The box-and-whisker plot has the following values it displays about a data distribution:
Minimum value: This is the value at the beginning of the left whisker.Lower quartile (Q1): This is indicated by the beginning of the edge of the box, 25% of the data are below this point.Median value: the line that divides the box is the median value which is 50% of the data.Upper quartile (Q3): This is indicated by the end of the edge of the box, 75% of the data are below this point.Maximum value: This is the largest data point and is located at the end of the right whisker.Interquartile range = Q3 - Q1
Analyzing the box-and-whisker plots given above, we have the following to conclude:
a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.
b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7
Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7
Both had the same interquartile range.
c. Median for City A = 70
Median for City B = 78
City B had a larger median noon temperature
d. City A had the largest noon temperature of 85.
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If −2≤f(x)≤5 on [−1,3] then find upper and lower bounds for ∫−13f(x)dx
Answer:
Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...
Step-by-step explanation:
The upper bound of the given function is 20 while the lower bound of the given function is -8.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
As per the given function,
-2 ≤ f(x) ≤ 5
At the upper bond, f(x) = 5
[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]
⇒ 5(3 + 1) = 20
At the lower bond f(x) = -2
[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]
⇒ -2(3 + 1) = -8
Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".
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Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
problem A: What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
Problem B: What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
problem C: What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green?
problem D: Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.
The probability for each event are
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have Chelsey who puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
[A] -
{3/12} x {3/11} x {4/10} =
36/1320
[B] -
{3/12} x {4/11} x {3/10}
36/1320
{C} -
{4/12} x {3/11} x {3/10}
36/1320
D) The probability doesn’t change in any order.
Therefore, the probability for each event are -
[A] - 36/1320
[B] - 36/1320
[C] - 36/1320
[D] - The probability doesn’t change in any order.
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After a 20% discount, you purchase a television for $240. What was the television's
price before the reduction? (Define a variable, create an equation, solve using algebra,
and answer in a sentence.)
===========================================
Work Shown:
x = price of the TV before the discount
20% of x = 0.20x = discount, aka amount saved
x - 0.20x = 0.80x = price after discount
0.80x = 240
x = 240/0.80
x = 300
The TV was $300 before the discount.
-------------
Check:
20% of 300 = 0.20*300 = 60 dollars is the amount saved
300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.
The ratio of flour to sugar is 2 cups to 3 cups. If there are 5 cups of flour, how many cups of sugar are there?
The number of sugar cups will be equal to 7.5 cups.
What are ratios and proportions?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.
Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.
The number of sugar cups will be calculated as,
F / S = 2 / 3
5 / S = 2 / 3
S = ( 5 x 3 ) / 2
S = 7.5 cups
Therefore, the number of sugar cups will be equal to 7.5 cups.
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