Answer:
Step-by-step explanation:
To find out how many cuboids of dimension 5 cm x 5 cm x 3 cm are needed to form a cube, we need to calculate the volume of both the cuboid and the cube.
The volume of the cuboid is:
5 cm x 5 cm x 3 cm = 75 cubic cm
To form a perfect cube, the volume of the cube should be a multiple of the volume of the cuboid. The smallest cube that can be formed using a multiple of 75 cubic cm is a cube with a volume of 75 x 8 = 600 cubic cm.
To find the dimensions of this cube, we need to find the cube root of 600 cubic cm:
cube root of 600 = 8.66 cm
So, the dimensions of the cube are 8.66 cm x 8.66 cm x 8.66 cm.
To find how many cuboids are needed to form this cube, we need to divide the volume of the cube by the volume of the cuboid:
Volume of the cube = 8.66 cm x 8.66 cm x 8.66 cm = 658.39 cubic cm
Number of cuboids required = 658.39 cubic cm ÷ 75 cubic cm = 8.78
Since we can't use a fraction of a cuboid, Anuj will need 9 such cuboids to make a perfect cube.
for $3.98 you can get a salad, a main course, and a dessert at the cafeteria. If you have a choice of 3 different salads, 4 different main courses, and 6 different desserts. then how many meals can you get for $3.98
There are 72 different meals that you can get for $3.98
How many different meals can you get for $3.98?We know that for $3.98 you can get a salad, a main course, and a dessert at the cafeteria.
The total number of different meals that you can get, is equal to the product between the number of options for each one of the selections, such that the selections (and correspondent options) are:
Salad ---> 3 different options.Main course ---> 4 different options.Dessert ---> 6 different options.Then the total number of different meals is:
M = 3*4*6
M = 72
That is the number of different meals.
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Is the following shape a square? How do you know?
D.
2
PREVIOUS
"B
A. There is not enough information to determine
B. Yes, the opposite sides are parallel, and all sides are the same
length.
C. No, because the sides are not congruent
D. No, because opposite sides are not parallel
Answer:
B
Step-by-step explanation:
A square have 4 side that are all the same so its B
1) How many combinations of the letters A, B, C, D, and E taken 4 at at time?
5
720
20
9
Define theoretical probability.
possible outcomes times favorable outcomes
favorable outcomes times possible outcomes
favorable outcomes divided by possible outcomes
possible outcomes divided favorable outcomes
2) What is the theoretical probability you will roll a 2 on a die?
1/3
2/6
1/6
2
3) On a spinner with equal pie shapes of red, blue, green, yellow, and orange. What is the theoretical probability you will land on blue when you spin?
4/5
5
1
1/5
4) Susie has 12 cook books and 18 wine lists on her shelf. What is the ratio of wine lists to cook books in simplest form?
12/18
3/2
2/3
100
A bag contains 5 red, 6 blue, and 3 yellow marbles.
5) What is the probability of drawing a red or yellow marble from a bag?
5/14
14
8
8/14
6) For a game of bingo, balls are numbered 1-100, one ball is chosen. Find P(number greater than 10
10
9/10
1/100
100
7) Find the mean of this set of data. 10, 15, 25, 50
4
20
25
100
8) Find the median of this set of data: 6, 23, 46, 3, 17
46
95
19
17
9) What is the mode of this data set: 3, 7, 10, 18, 4, 5
6
0
no mode
9
10) What does the leaf represent in a stem-and-leaf plot??
the tens place of the numbers in the data set
the numbers in the data set
the ones place of the numbers in the data set
11) Finding quartiles are like finding what???
quarters
medians
money
means
12) In a sample of 1,000 coffee drinkers, 450 said they like the taste of the new coffee. Predict how many out of 10,000 will like the new coffee.
4500
450
100
45
Answer:
Step-by-step explanation:
1) The number of combinations of the letters A, B, C, D, and E taken 4 at a time is 5.
The formula for the number of combinations is n!/(r!(n-r)!), where n is the total number of items, and r is the number of items to be selected. In this case, n = 5 and r = 4. Therefore, the number of combinations is 5!/(4!(5-4)!) = 5.
Theoretical probability is the likelihood or chance of an event occurring based on the ratio of the number of favorable outcomes to the total number of possible outcomes.
2) The theoretical probability of rolling a 2 on a die is 1/6.
There are six possible outcomes when rolling a die, and only one of those outcomes is a 2. Therefore, the probability of rolling a 2 is 1/6.
3) The theoretical probability of landing on blue when spinning the spinner is 1/5.
There are five possible outcomes when spinning the spinner, and only one of those outcomes is blue. Therefore, the probability of landing on blue is 1/5.
4) The ratio of wine lists to cookbooks in simplest form is 3/2.
To simplify the ratio, divide both the numerator and denominator by their greatest common factor, which in this case is 6. 18/6 = 3, and 12/6 = 2, so the ratio of wine lists to cookbooks in simplest form is 3/2.
5) The probability of drawing a red or yellow marble from the bag is 8/14 or 4/7.
There are a total of 14 marbles in the bag, 5 of which are red and 3 of which are yellow. Therefore, the probability of drawing a red or yellow marble is (5+3)/14 = 8/14 or 4/7.
6) The probability of drawing a number greater than 10 from a ball numbered 1-100 is 9/10.
There are 90 numbers greater than 10 in the set of numbers from 1 to 100, and there are 100 total numbers. Therefore, the probability of drawing a number greater than 10 is 90/100, which simplifies to 9/10.
7) The mean of the set of data {10, 15, 25, 50} is 25.
To find the mean, add up all of the numbers in the set and divide by the total number of numbers. (10+15+25+50)/4 = 100/4 = 25.
8) The median of the set of data {6, 23, 46, 3, 17} is 17.
To find the median, first put the numbers in order from smallest to largest: 3, 6, 17, 23, 46. Since there are an odd number of numbers in the set, the median is the middle number, which is 17.
9) The mode of the set of data {3, 7, 10, 18, 4, 5} is no mode.
The mode is the value that appears most frequently in the data set. In this case, none of the values appear more than once, so there is no mode.
10) In a stem-and-leaf plot, the leaf represents the ones place of the numbers in the data set.
The stem-and-leaf plot is a way to organize numerical data by placing the tens digit in the stem and the ones digit in the leaf.
11) Finding quartiles is like finding medians.
Quartiles divide a data set into
Can yall help me with this pls
The measure of angle 1 in the given figure is 56 degrees.
What is the measure of angle 1?From the image of the angle:
Measure of angle ABD = 62 degrees
Measure of angle 2 = 6 degrees
Measure of angle 1 = ?
From the diagram, angle 1 and angle 2 makes up angle ABD.
To solve for the missing angle ( angle 1 ), sum up both angle 1 and 2 and equate to angle ABD.
Hence:
Angle 1 + Angle 2 = Angle ABD
Plug in the values and simplify:
m∠1 + 6 = 62
Subtract 6 from both sides
m∠1 + 6 - 6 = 62 - 6
m∠1 = 62 - 6
m∠1 = 56 degrees
Therefore, angle 1 measures 56 degrees.
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2. How are wealth and savings related?
Savings play a crucial role in wealth creation and financial security while savings alone may not determine an individual's overall wealth
Wealth and savings are closely related concepts and often go hand in hand.
Savings refer to the portion of income or resources that individuals or households set aside for future use or to meet financial goals.
It represents the act of not spending all of one's income and instead preserving a portion for later use.
Wealth, on the other hand, refers to the total accumulated assets, possessions, and financial resources that an individual or household possesses.
It encompasses not only the current income and savings but also the value of investments, properties, and other assets.
Savings contribute to the accumulation of wealth over time.
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PLEASE HELP-TIMED-40pts!!
Answer each question individually
___________________________
2. The list below shows the number of computer games a store sold each day for the
first 11 days it was open.
27, 28, 29, 35, 35, 36, 37, 42, 43, 46, 79
a) Find the five-number summary for the data. Show your work.
b) use your results from part A to display the data on a box plot
c)use your box plot from part b to find the interquartile range (IQR) of the data
The five-number summary of the data are:
Minimum: 27Q1: 32Median: 36Q3: 42.5Maximum: 79.The interquartile range (IQR) of the data is 10.5.
What are the five-number summary?We will arrange the data in ascending order first [tex]27, 28, 29, 35, 35, 36, 37, 42, 43, 46, 79[/tex]
Minimum: The smallest value is 27.
First Quartile (Q1):
We have an 11 odd number of data points (11), Q1 is the median of the first five numbers: 27, 28, 29, 35, 35.
The median of this subset is (29 + 35)/2 = 32.
Median (Q2): The middle value of the data set which is 36.
Third Quartile (Q3): The median of the upper half of the data. Q3 is the median of the last five numbers: 37, 42, 43, 46, 79. The median of this subset is (42 + 43)/2 = 42.5
Maximum: The largest value is 79.
The interquartile range (IQR) is calculated as Q3 minus Q1.
Using values from part a:
IQR = Q3 - Q1
IQR = 42.5 - 32
= 10.5.
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3 and 2/4 as a percent
3 and 2/4 converted as a percent is 3.50%.
What is a percentage?
Percent means 'out of 100'. Think of any measurement or object split into one hundred equal bits. Each bit is one percent of the whole thing.
Given the question above, we need to convert 3 and 2/4 as a percent.
So,
[tex]\sf \dfrac{2}{4} =0.50[/tex]
[tex]3+0.50[/tex]
[tex]=3.50\%[/tex]
Hence 3 and 2/4 converted as a percent is 3.50%.
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10. The game piece depicted below is composed of
two congruent right cones joined at their bases.
Calculate the surface area of this game piece if
the length is 20 inches and the height is 8 inches.
The total surface area of the figure is twice this amount, or 192π square inches.
How to solve for the surface areaGiven that the height of each individual cone is 8 inches, we can use the Pythagorean theorem (a² + b² = c² ) to calculate the radius. The hypotenuse of the right triangle formed by the cone is the slant height, which is 10 inches, and one side is the height, which is 8 inches. So:
10² - 8² = r²
100 - 64 = r²
r² = 36
r = √36 = 6 inches.
Substituting these values into the surface area formula, we get:
A = π * 6 * (6 + √(8² + 6² ))
= π * 6 * (6 + √(64 + 36))
= π * 6 * (6 + √100) = π * 6 * (6 + 10)
= π * 6 * 16 = 96π square inches.
Since we have two cones, the total surface area of the figure is twice this amount, or 192π square inches.
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please help i need this done as soon as possible will mark brainly!!!!!!!!
Answer: the function's y-intercept, 64°F
Step-by-step explanation:
Since "t" represents time, if we set t = 0 to find the initial temperature (0 minutes), we find the function's y-intercept.
To find the initial temperature, we will set t = 0. When we do this, we are finding the y-intercept which is the same as the constant value.
[tex]y=-\frac{1}{40}t^2+t+64[/tex]
[tex]y=-\frac{1}{40}(0)^2+(0)+64[/tex]
[tex]y=64[/tex]
64°F
What is the intermediate step in the form(x+a)^2=b as a result of completing the square for the following equation?
X^2-8x+32=12x-4
Answer:
To complete the square for the equation X^2-8x+32=12x-4, we first need to move all the constant terms to one side of the equation and all the variable terms to the other side.
X^2 - 8x - 12x + 32 = -4
Next, we can simplify the equation by combining like terms:
X^2 - 20x + 32 = -4
Then, we can add a constant term to both sides of the equation such that the left side becomes a perfect square trinomial:
X^2 - 20x + 100 = 64
Finally, we can write the left side of the equation in the form (x - a)^2, where a is a constant:
(X - 10)^2 = 64
Therefore, the intermediate step in the form (x + a)^2 = b as a result of completing the square for the equation X^2 - 8x + 32 = 12x - 4 is (X - 10)^2 = 64.
Joshua is 5 ft tall and casts an 8-ft shadow. he is standing next to Jason, who casts a 10 shadow. write a proportion that could be used ti determine Jason's height do not solve
The proportion that can be used to determine Jason's height based on the relationship between the lengths of their shadows is J/8 = H/10.
Given that Joshua is 5 ft tall and casts an 8-ft shadow.
He is standing next to Jason, who casts a 10 shadow.
We have to find a proportion that could be used to determine Jason's height
Let's denote Joshua's height as J and Jason's height as H.
We can set up the proportion by taking the height by shadow
J/8 = H/10
Hence, J/8 = H/10 is the proportion can be used to determine Jason's height based on the relationship between the lengths of their shadows.
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x^2-x-2=0 solve system of equation
If 3 and 4 are the legs of a right triangle, the hypotenuse is_____.
If 3 and 4 are the legs of a right triangle, the hypotenuse is 5.
What is the Pythagorean Theorem?In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
The theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, sometimes called the Pythagorean equation
[tex]\sf a^2+b^2=c^2[/tex]
Given the question above, we need to find the hypotenuse if 3 and 4 are the legs of a right triangle.
So,
[tex]\sf a^2+b^2=c^2[/tex]
[tex]=\sf 9+16=25[/tex]
[tex]\sf \sqrt{25}=5[/tex]
Hence, the hypotenuse is 5 if 3 and 4 are the legs of a right triangle.
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A lumber company is interested in seeing if the number of board feet per has decreased since moving to a new location of timber. In the past, the company has an average 93 board feet per tree. The company believes that the production has decreased changing locations, a random sample of 25 trees yields mean of 89 with standard deviation of 2.Assuming normality of the data, test the hypothesis at a 10 % level of significance.
There is sufficient evidence to suggest that the mean board feet per tree has decreased since moving to the new location of timber.
According to the information,
Set up the following hypothesis test:
Null hypothesis: The mean board feet per tree is still 93.
Alternative hypothesis: The mean board feet per tree is less than 93.
Here,
We can use a one-sample t-test to test this hypothesis.
The test statistic can be calculated as:
t = (sample mean - hypothesized mean)/(sample standard deviation/square root of sample size)
⇒ t = (89 - 93)/(2/sqrt(25))
⇒ t = -5.00
The degrees of freedom for this test are 24.
Using a t-distribution table,
we can find the critical t-value for a one-tailed test with 24 degrees of freedom and a 10% level of significance.
The critical t-value is -1.317.
Since our calculated t-value (-5.00) is less than the critical t-value (-1.317), we can reject the null hypothesis in favor of the alternative hypothesis.
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On a standardized exam , the scores are normally distributed with a mean of 195 and a standard deviation of 50. Find the z-score of a person who scored 330 on the exam
The relative position of a score and provide a standardized way to compare scores from different distributions with varying means and Standard deviations.
The z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where:
- z is the z-score,
- x is the value we want to find the z-score for (330 in this case),
- μ is the mean of the distribution (195 in this case),
- σ is the standard deviation of the distribution (50 in this case).
Substituting the values into the formula:
z = (330 - 195) / 50
Calculating this expression:
z = 135 / 50
Simplifying:
z = 2.7
Therefore, the z-score of a person who scored 330 on the exam is 2.7.
A z-score represents the number of standard deviations a particular value is from the mean of a normal distribution. In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean of 195. This means that their score is relatively high compared to the average performance on the exam.
Z-scores are useful for comparing and understanding individual scores within a distribution. They allow us to determine the relative position of a score and provide a standardized way to compare scores from different distributions with varying means and standard deviations.
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A tank in the shape of a hemisphere has a diameter of 10 feet. If the liquid that fills the tank has a density of 84.6 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
Answer:
22148 pounds
Step-by-step explanation:
radius = half of diameter = 5.
Volume of hemisphere = (2/3) X π X r ³
= (2/3) X π X (5) ³ = (250/3)π
density = mass/volume, mass = density X volume
= 84.6 X (250/3)π
= 7050π
= 22148 pounds (to nearest full pound)
Follow the guided instructions below to rotate the figure 270° counter-clockwise
about the origin.
Click and drag to draw a line through the yellow center and the vertex on
the circle.
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y
10
9
8
7
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5
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If you need assistance with rotating a figure or performing any specific task, please provide a detailed description or explain the steps involved, and I'll do my best to guide you through the process.
the area of a triangle is 16cm^2, if the base of the triangle is two less than its height. find the base and the height
Answer:
The base of the triangle is 4cm and the height is 6cm
I just need an explanation on how to solve the second one in the middle
Answer: C AND D
Step-by-step explanation:
Cross multiply C to get 59.82D=2512.44 and divide to get $42.
Cross multiply D to get the same thing as C.
If you cross multiply A or B you won’t get a correct conversion.
what are the roots of the equation
Answer:
Step-by-step explanation:
The roots (sometimes also called "zeros") of an equation are the values of for which the equation is satisfied.
in what time will a sum of rs2000 amounts to rs2240 at 4% pa simple interest
Answer: The time it takes for a sum of money to amount to a certain amount at a certain interest rate can be calculated using the following formula:
Time = (100 x (Amount - Principal)) / (Principal x Rate)
In this case, the principal is Rs. 2000, the amount is Rs. 2240, and the rate is 4%. Therefore, the time is:
Time = (100 x (2240 - 2000)) / (2000 x 4) = 3 years
Therefore, it will take 3 years for Rs. 2000 to amount to Rs. 2240 at 4% simple interest.
Step-by-step explanation:
Graph the line with slope
2/
passing through the point (1, -5).
Graphing a Line Using the Slope and Y-InterceptFind the y-intercept = b of the equation y = mx + b.Plot the y-intercept. The point will be (0, b).Find the slope=m of the equation y = mx + b.Make a single step, using the rise and run from the slope. ...Connect those two points with your line.
Determine which integer will make the inequality 4x + 6 < 2x + 12 false. S:{1} S:{-1} S:{4} S:{-4}
Answer:
S:{4}
Step-by-step explanation:
The inequality is
4x + 6 < 2x + 12
Subtract 2x from both sides:
4x - 2x + 6 < 2x - 2x + 12
2x + 6 < 12
Subtract 6 from both sides:
2x + 6 - 6 < 12 - 6
2x < 6
Divide both sides by 2
x < 3
So any value of x such that x ≥ 3 will make this statement false
In the answer choices, the only value that satisfies this conditionis the value 4
Two identical gardens are to be weeded, each by a two-person team. Team A includes one gardener who could weed the garden in 2 h and another who could weed the garden in 4 h. Team B includes two gardeners, either of whom could weed the garden in 3 h. Which team will finish first? Explain.
Step-by-step explanation:
Team A time is 1 garden / ( 1 garden/ 2 hr + 1 garden/4 hr) = 1 1/3 hr
Team B = 1 / ( 1/3 + 1/3) = 1 1/2 hr
Team A wins !
An automobile uses 18 gal of fuel to go 570 mi. How many gallons are required to travel 870 mi?
What is the square root of 598?
the square root of 598 is 24.4540385
Which is set of decimal numbers is correctly ordered from least to greatest from left to right? A. 328.463, 308.463, 330.693, 330.991 B. 308.463, 330.991, 330.693, 328.463 C. 308.463, 330.991, 328.463, 330.693 D. 308.463, 328.463, 330.693, 330.991
The set of decimal numbers that is correctly ordered from least to greatest from left to right is option C: 308.463, 330.991, 328.463, 330.693.
To order the decimal numbers from least to greatest, we compare the numbers digit by digit, starting from the left.
Let's compare the numbers in each option:
A. 328.463, 308.463, 330.693, 330.991
The numbers are not in the correct order because 308.463 should come before 328.463.
B. 308.463, 330.991, 330.693, 328.463
The numbers are not in the correct order because 328.463 should come after 330.693.
C. 308.463, 330.991, 328.463, 330.693
The numbers are in the correct order from least to greatest.
D. 308.463, 328.463, 330.693, 330.991
The numbers are not in the correct order because 330.693 should come before 328.463.
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1. in a deck of cards, what is the probability of
randomly selecting a Spade or a face card
given it's black?
(Please explain answer step by step)
The probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.
To calculate the probability of randomly selecting a Spade or a face card given that it's black, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
In a standard deck of cards, there are 52 cards. Since we're looking for a Spade or a face card, let's calculate the number of favorable outcomes separately for each category.
Number of Spades:
In a deck, there are 13 spades (Ace of Spades, 2-10 of Spades, Jack of Spades, Queen of Spades, and King of Spades).
Number of Face Cards:
In each suit (Spades, Hearts, Diamonds, and Clubs), there are three face cards: Jack, Queen, and King. Since we're only interested in black cards, we need to consider the face cards of Spades and Clubs, which are black. Therefore, there are 2 black face cards in each suit, giving a total of 8 black face cards in the deck.
So the total number of favorable outcomes is 13 (spades) + 8 (black face cards) = 21.
Step 2: Determine the total number of possible outcomes.
In a standard deck of 52 cards, half are black cards (26 cards) since there are 26 black cards and 26 red cards.
Step 3: Calculate the probability.
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 21 / 26
Simplifying the fraction, we get:
Probability = 0.8077 (rounded to four decimal places)
Therefore, the probability of randomly selecting a Spade or a face card given that it's black is approximately 0.8077 or 80.77%.
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Write an equation in slope-intercept form for the line with slope 3 and y-intercept - 9. Then graph the line.
Answer:
Slope intercept form is y=3x-9
Graphing:
Step-by-step explanation:
Find the missing coordinate in the ordered pair ( -1 , b )
if it is a solution to the equation 5x-3y=10
a -7
b-5
c-4
d 4
e o
.
Answer:
To find the missing coordinate in the ordered pair (-1, b), we can substitute the value of x into the equation 5x-3y=10. This gives us 5(-1)-3y=10. Solving for y, we get -5-3y=10, -3y=15, and y=-5. Therefore, the missing coordinate in the ordered pair (-1, b) is -5. The correct answer is b) -5.