Therefore, the length of each side of the original square is 5 cm.
What is area?Area is a measure of the size of a two-dimensional surface or region. It is the amount of space enclosed by a boundary in two dimensions. In simple terms, area is the size of a flat surface, such as the floor, a wall, or a piece of paper. It is usually measured in square units such as square meters (m²), square centimeters (cm²), square feet (ft²), or acres.
Here,
Let x be the length of each side of the original square.
When the length of each side is increased by 10 cm, the new length is x + 10, and the area of the new square is (x + 10)².
According to the problem, the increase in area is 200 cm², so we can set up the equation:
(x + 10)² - x² = 200
Expanding the left side of the equation, we get:
x² + 20x + 100 - x² = 200
Simplifying, we get:
20x + 100 = 200
Subtracting 100 from both sides, we get:
20x = 100
Dividing both sides by 20, we get:
x = 5
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For the last several weeks, Carol has been saving the coins from her waitressing tips so that she can buy her grandmother a music box for her birthday. If there are 70% more quarters than dimes in the money Carol has saved, and the combined value of her quarters and dimes is $31.50, how many dimes does she have
To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be: $31.50
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's start by using algebra to solve the problem.
Let x be the number of dimes that Carol has saved.
According to the problem, there are 70% more quarters than dimes. We can express the number of quarters in terms of x as 1.7x, since 1.7 times the number of dimes is equal to the number of quarters.
We also know that the combined value of her quarters and dimes is $31.50. We can express this as an equation:
0.10x + 0.25(1.7x) = 31.50
Simplifying and solving for x, we get:
0.10x + 0.425x = 31.50
0.525x = 31.50
x = 60
Therefore, Carol has 60 dimes.
Therefore, To check our answer, we can verify that the number of quarters is 1.7 times the number of dimes, which would be 102. And the total value of her dimes and quarters would be:
60 * $0.10 (dimes) + 102 * $0.25 (quarters) = $31.50
which matches the information given in the problem.
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A study found that 2/3 of the students surveyed are in a school sport or club. What must be true about the number of students in a school sport or club?
A It is equal to the number of students surveyed.
B It is twice as large as the number of students surveyed.
C It is less than the number of students surveyed.
D It is three times the number of students surveyed.
a passenger bus with a 45-person seating capacity travels at an average speed of 50 km per hour. what distance will it cover in 5 hours
a vending machine contains cans of grapefruit juice that cost 75 cents each, but it is not working properly. the probability that it accepts a coin is 10%. angela has a quarter and five dimes. determine the probability that she should try the coins at least 50 times before she gets a can of grapefruit juice.
It is assumed that the vending machine contains cans of grapefruit juice that cost 75 cents each, but the machine isn't functioning properly. The likelihood that the machine accepts a coin is 10 percent.Angela has a quarter and five dimes. We are expected to determine the probability that she would have to attempt the
coins at least 50 times before receiving a can of grapefruit juice.
Let p = 0.1 be the likelihood that the machine accepts a coin, and q = 0.9 be the likelihood that it doesn't.Let's consider X = number of trials required to acquire a can of grapefruit juice. We are looking for P(X ≥ 50).This is a geometric probability issue, and we may utilize the formula:
[tex]P(X ≥ k) = qk-1p[/tex], where k is the number of trials required.
The probability that it will take at least 50 attempts before obtaining a can of grapefruit juice is:
[tex]P(X ≥ 50) = (0.9)49(0.1)≈0.003 or 0.3[/tex] percent (rounded to one decimal place).
Therefore, the likelihood that Angela would have to attempt the coins at least 50 times before acquiring a can of grapefruit juice is 0.3 percent.
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there are 12 coins, such that 6 are real, weighing 10 grams each, and 6 are fake, weighing 9 grams each. you have a scale that shows the exact weight of the coins on it. how to find two coins of different weights in two weighings?
There are 12 coins, such that 6 are real, weighing 10 grams each, and 6 are fake, weighing 9 grams each. you have a scale that shows the exact weight of the coins on it. one of the two coins that were left out is heavier and the other is lighter.
Take 4 coins out of the pile and put them on one side of the balance scale. Take another 4 coins out of the pile and put them on the other side of the balance scale.
If both sides of the scale are equal, you know the remaining 4 coins contain the two coins of different weights you are looking for. In that case, take two coins out of the remaining 4 and weigh them on the balance scale. If they balance each other, the other two coins must be the ones of different weight. On the other hand, if the two coins on the balance scale don’t balance, you can be certain that one is real and the other is fake. In that case, you have already found the two coins you were looking for.
If the balance scale does not balance in the first weighing, you will know that the two coins of different weights must be contained in the group of 4 that is heavier or the group of 4 that is lighter. Remove two coins from the heavier pile, and place them on one side of the scale, and keep the other two on the other side. If the balance scale is still unbalanced, it means that the coin that is heavier is one of the two coins on the heavier side of the scale, and the coin that is lighter is one of the two coins on the lighter side. If the balance scale is now balanced, it means that one of the two coins that were left out is heavier and the other is lighter.
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Please help solve like now ASAP ASAP
an experiment requires a sequence of three steps. the first step can result in two possible outcomes, the second in six possible outcomes, and the third in five possible outcomes. what is the total number of outcomes possible?
There are 60 possible outcomes for this experiment.
The problem asks to determine the total number of outcomes for an experiment consisting of three steps with different numbers of possible outcomes at each step.
To solve this problem, we need to apply the multiplication principle, which states that the total number of outcomes for a sequence of events is equal to the product of the number of outcomes at each event.
In this case, there are two possible outcomes for the first step, six possible outcomes for the second step, and five possible outcomes for the third step.
Therefore, the total number of outcomes possible is:
2 * 6 * 5 = 60
Therefore, there are 60 possible sequences of events that can occur in this experiment.
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O
What is the image point of (-8, 2) after the transformation r y=x T -3,3?
Answer: The transformation r y=x reflects the point (x, y) across the line y = x, and the transformation T -3,3 translates the point (x, y) three units to the left and three units up. To find the image point of (-8, 2) after these transformations, we can follow these steps:
Apply the reflection r y=x to the point (-8, 2):
(-8, 2) reflects to (2, -8).
Apply the translation T -3,3 to the reflected point (2, -8):
(2, -8) translates to (-1, -5).
Therefore, the image point of (-8, 2) after the transformation r y=x T -3,3 is (-1, -5).
Step-by-step explanation:
help please!! :) the question is in the PNG
Answer: 63 degrees
Step-by-step explanation: On a triangle, all 3 of the angles add up to 180 degrees. I added the 2 angles we know, 92 degrees and 25 degrees. This gave me an answer of 117. Then I took 180-117, and got the answer of 63. That is why angle 3 is 63 degrees.
What additional information could be used to prove δabc ≅ δmqr using sas? select two options. m∠a = 64° and ab = mq = 31 cm cb = mq = 29 cm m∠q = 56° and cb ≅ rq m∠r = 60° and ab ≅ mq ab = qr = 31 cm
To prove ΔABC ≅ ΔMQR using the SAS criterion, the two options that provide the required information are AB = QR = 31 cm and m∠A = m∠M or CB ≅ RQ and m∠C = m∠Q.
To prove that ΔABC ≅ ΔMQR using the SAS (Side-Angle-Side) criterion, we need to show that two sides and the included angle of one triangle are congruent to the corresponding sides and angle of the other triangle. Therefore, we need to choose two options that provide us with the required information.
The two options that provide the required information are:
AB = QR = 31 cm and m∠A = m∠M: This option provides us with the congruent sides AB and QR and the included angle ∠A = ∠M, as both have a measure of 64°. This satisfies the SAS criterion.
CB ≅ RQ and m∠C = m∠Q: This option provides us with the congruent sides CB and RQ and the included angle ∠C = ∠Q, as both have a measure of 56°. This satisfies the SAS criterion.
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The given question is incomplete, the complete question is:
What additional information could be used to prove ΔABC ≅ ΔMQR using SAS? Select two options. m∠A = 64° and AB = MQ = 31 cm CB = MQ = 29 cm m∠Q = 56° and CB ≅ RQ m∠R = 60° and AB ≅ MQ AB = QR = 31 cm?
suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.44 . using the empirical rule, what percentage of the students have grade point averages that are between 1.28 and 3.92 ?
The percentage of students who have grade point averages between 1.28 and 3.92 is therefore 99.7%.
Suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.44.
Using the empirical rule, the percentage of the students who have grade point averages between 1.28 and 3.92 is 99.7%.
The empirical rule, which is often known as the three-sigma rule, states that in any normal distribution of data, the following percentage of data will be within one, two, or three standard deviations of the mean:-
68.27% of the data will lie within one standard deviation of the mean.- 95.45% of the data will lie within two standard deviations of the mean.- 99.73% of the data will lie within three standard deviations of the mean.
For this question, we want to know what percentage of students have grade point averages between 1.28 and 3.92, which is two standard deviations below and above the mean.
Using the empirical rule, we know that approximately 95% of the data will fall within two standard deviations of the mean, so 95% of the students will have grade point averages between (2.6 - 0.88) = 1.72 and (2.6 + 0.88) = 3.48. However, we want to know what percentage of students fall within the range of 1.28 to 3.92, which is slightly beyond two standard deviations from the mean. Since the empirical rule only provides estimates, we can assume that the additional percentage of students who fall beyond two standard deviations from the mean is roughly 2.5% on each side.
Therefore, the percentage of students who have grade point averages between 1.28 and 3.92 is approximately 95% + 2.5% + 2.5% = 99%.
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Juliana sells a house for $330,000. Her commission for the sale is $10,725. What percent commission did she earn? (Make sure to write your answer as a percent for example: 6.2%. Round your answer to the nearest hundredth of a percent.)
Answer:
3.25%
Step-by-step explanation:
To find the percentage commission Juliana earned, we need to divide her commission by the selling price of the house and then multiply by 100 to convert the decimal to a percentage.
Commission rate = (Commission / Selling price) x 100%
Commission rate = ($10,725 / $330,000) x 100%
Commission rate = 0.0325 x 100%
Commission rate = 3.25%
In a Wedding Ring quilt pattern, the design has intersecting circles, as shown
below. Each circle has a radius of 8 inches. To "quilt" the design, the
circumference of each circle must be stitched.
8
If there are 24 rings on the quilt, what is the total length, in inches, that
must be stitched?
Answer:384
Step-by-step explanation:
A parking lot space is in shape of a rectangle. If the space has a length of 23 feet and a width of 12 feet, what is the area of the parking space?A.128ft2B.266ft2C.276ft2D.138ft2
if 2400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
The largest possible volume of the box is 480 cm³.
Given that 2400 square centimeters of material is available to make a box with a square base and an open top.
To find the largest possible volume of the box, we need to maximize the volume. We can express the volume of the box in terms of its side length.
Let's say the side length of the square base is x cm. The area of the square base will be x² square cm. Since the box has no top, we can say that its height is also x cm. So, the volume of the box can be expressed as,
V(x) = x² × x = x³ cubic cm
We know that 2400 square cm of material is available to make the box. The material is used to create the sides of the box. The box has 5 sides - four walls and a base. The area of the four walls will be the same. So, the total area of the four walls can be expressed as, 4xh = 4x², where h is the height of the box.
Subtracting this area from the total available material, we get the area of the base, which is equal to the area of the remaining material, 2400 - 4x² = x²
Simplifying, 5x² = 2400x² = 480
Volume of the box, V(x) = x³cubic cm
Substituting x = 12 in the expression for V(x), we get the maximum volume of the box, 480 cm³. Therefore, there is a maximum volume of 480 cm³ for the box.
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Help with #7 I will mark you as brainliest I also need an explanation please
Answer:
Remark
Secants going through a circle form a ratio that's the same for all secants going through the circle and beginning at 1 point. See the diagram below for the ratio. Follow the Line designations carefully. This comes up many times.
General Ratio is (segment from the external point to the the first intersect point of the circumference divided by the distance from the external point to the second intercept point on the circumference).
General Ratio
Put in terms of the diagram the general ratio is (OA / OB)
Equation
OA/OB = OC/OD
Substitute and Solve
9/(9 + 11) = 10/(10 + x)
9/20 = 10/(10 + x) Notice that you can't combine the right side. Cross Multiply
9*(10 + x) = 10 * 20 Remove the brackets on the left. Combine the right factors.
90 + 9x = 200 Subtract 90 from both sides.
9x = 200 - 90
9x = 110 Divide by 9
110 / 9 = 12.22
An isosceles triangle has an angle that measures 70°. What measures are possible for the other two angles? Choose all that apply.
55 25 40 70
Jia is thinking of a number she gives three clues about the number the number is even, it's less then - 12 and the absolute value of the number is between 9 and 15 ,whats jia number, explain how you know
The number is -14 because it is even and less than -12. The absolute value of -14 is between 9 and 15. These conditions fulfill all the given clues.
Jia has given three clues about the number she's thinking of. The first clue is that the number is even, which means it is a multiple of 2. The second clue is that the number is less than -12. This means that the number is a negative number and it lies between -12 and -9 (because the absolute value of a number between -12 and -9 is between 9 and 12). The third clue is that the absolute value of the number is between 9 and 15. This condition is only satisfied by the number -14, which is even, negative, and has an absolute value between 9 and 15. Therefore, the answer is -14.
Based on the given clues, the number Jia is thinking of must be an even number that is less than -12 and whose absolute value is between 9 and 15. The only number that meets all three criteria is -14, which is an even number, less than -12, and has an absolute value of 14, which falls between 9 and 15. Therefore, we can conclude that Jia's number is -14.
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Write the equation of a line perpendicular to y = 2x + 5 and passing through the point (8,2).
1. y = -1/2 x + 2
2. y = -1/2 x + 6
3. y = -1/2 x - 2
4. y = 1/2 x - 2
Considering the definition of perpendicular line, the correct answer is option 2.: the equation of a line perpendicular to y = 2x + 5 and passing through the point (8,2) is y= -1/2x +6.
Definiton of linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Definition of perpendicular linePerpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 2x +5
where:
the slope is 2.the ordinate to the origin is 5.If you multiply the slopes of two perpendicular lines, you get –1. So:
2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ 2
slope perpendicular line= -1/2
The line passes through the point (8, 2). Replacing in the expression for perpendicular line:
2= -1/2× 8 + b
2= (-4) + b
2 +4 = b
6= b
Finally, the equation of the perpendicular line is y= -1/2x +6.
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Alisha spent 35 minutes completing her math homework. Jordana spent 1/5 less time than Alisha. How long did Jordana spend on her math homework?
Answer:
She spent 7 minutes on her math homework.
Step-by-step explanation:
Find an equation of the circle drawn below.
Answer:
x²+y²=58
Step-by-step explanation:
(x-x₁)²+(y-y₁)²=r²
(0,0)=(x₁,y₁) [centre of the circle)
x²+y²=r²
The point (3,7) belongs to the circle.
3²+7²=r²
r²=9+49
r²=58
x²+y²=58
pls answer
woth 51poits!!
1. 4
2.2
3.0,5
IT IS SAYING TO WORK OUT WHAT THAT LINE REPRESENTS
Answer: help me pleaz
Step-by-step explanation:
I’m stuck help please
Answer: .54 4 points away from 0.5, 0.62 2 points away from 0.6
Step-by-step explanation: nice prodigy
clayton and iris purchase admission to a carnival plus a number of game tickets. Clayton purchases 10 game tickets and spends $19.50. Iris purchases 15 game tickets and spends $23.25. Determine the cost per game ticket.
The cost per game ticket is 0.75. The solution has been obtained by using the linear equations.
What is a linear equation?
First order equations include linear equations. In the coordinate system, the linear equations are defined for lines. Several variables may be present in a linear equation. Linear equations in two variables, for example, are used when a linear equation contains two variables.
We are given that Clayton and Iris purchase admission to a carnival plus a number of game tickets.
Let the admission cost be 'x' and cost per game ticket be 'y'.
Since, Clayton purchases 10 game tickets and spends $19.50 so, we get an equation in two variables as:
x + 10y = 19.50
Similarly, Iris purchases 15 game tickets and spends $23.25 so, we get first order equation as:
x + 15y = 23.25
Now, on subtracting the first equation from the second, we get
⇒ 5y = 3.75
⇒ y = 0.75
Hence, the cost per game ticket is 0.75.
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Find the surface area of the figure. Round to the nearest hundredth when necessary (2 decimal places). SA = hp + 2B
The calculated surface area of the figure is 337 square meters
Calculating the surface area of the figurefrom the question, we have the following parameters that can be used in our computation:
SA = hp + 2B
From the figure, we have
B = 1/2 * 7 * 9 = 31.5
p = 7 + 9 + √(7² + 9²) = 27.40
h = 10
So, we have
SA = 10 * 27.40 + 2 * 31.5
Evaluate
SA = 337
Hence, teh surface area is 337 square meters
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Given f(x) = -3x² + 10x + 2, find ƒ(−6)
1A a cubes volume is 512 cubic units. what is the length of its edge?
b: if a sphere fits snugly inside this cube whats its volume
c:What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show you reasoning
Help me this is too hard
A. The length of its edge is 512 cubic units, B. The volume of the sphere is 268.08 cubic units and C. The fraction of the cube is 67 / 128 and the percentage is 52.34%.
A. We are given that the volume of the cube is 512 cubic units.
We are required to find the length of its edge. So, Let the length of an edge of a cube be a units.
Then, the volume of the cube = (length of edge)3
We have the volume of the cube = 512 cubic units.
So, (length of edge)3 = 512 cubic units
Now, we can find the length of the edge by finding the cube root of 512.
So,Length of edge = Cube root of 512 cubic units = 8 units
Now, we need to find the volume of the sphere which fits snugly inside the cube. When a sphere is inscribed in a cube, its diameter is equal to the edge of the cube.
Thus, the diameter of the sphere = 8 units.
Hence, the radius of the sphere = 8 / 2 = 4 units
B. volume of the sphere = (4 / 3)πr3
= (4 / 3) × π × 43
= 4/3 × 3.14 × 64= 268.08 cubic units
C. The fraction of the cube that is taken up by the,
sphere = volume of sphere/volume of cube
= 268.08 / 512= 67 / 128
So, the percentage of the cube taken up by the sphere is,
percentage of cube taken up by sphere = (67 / 128) × 100= 52.34% (approx)
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Factor completely. 4 − 12x + 9x^2 =
Answer:(3x-2)2
Step-by-step explanation: hope this helps
Answer: (3x-2)^2
Step-by-step explanation:
A randomly selected customer is asked if they like hot or iced coffee. Let H be the event that the customer likes hot coffee and let / be the event that the customer likes iced coffee. What is the probability that a randomly selected customer likes hot or iced coffee?
0 0.22
0 0.30
O 0.61
0 0.83
Answer:
83% or 0.83
Step-by-step explanation:
The probability that a randomly selected customer likes hot or iced coffee can be found using the formula:
P(H or I) = P(H) + P(I) - P(H and I)
where P(H) is the probability that the customer likes hot coffee, P(I) is the probability that the customer likes iced coffee, and P(H and I) is the probability that the customer likes both hot and iced coffee.
We are given that P(H) = 0.75, P(I) = 0.30, and P(H and I) = 0.22. Therefore:
P(H or I) = 0.75 + 0.30 - 0.22 = 0.83
So the probability that a randomly selected customer likes hot or iced coffee is 0.83, or 83%. This makes sense because some customers may like both hot and iced coffee, and so we cannot simply add the probabilities of liking each type of coffee. By subtracting the probability of liking both, we account for these customers and obtain the correct probability.
Solve for x :
2x = 100
[tex] \\ \\ \\ [/tex]
Thanks
Answer:
2x is equals to 100
x is equals to 100 / 2
x is equals to 50
therefore x=50