The shape below is made of two rectangles joined together.
3 cm
4 cm
6 cm
6 cm
15 cm
Find the total area of the shape.
Optional working
Answer:
+
cm²
Answers
The total area of the shape is 102 cm².
Given that, two rectangles with dimensions L1=15 cm, B1=6 cm, L2=4 cm and B2=3 cm.
What is the area of the rectangle?The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimetres, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle.
We know that, the area of a rectangle = Length × Breadth.
So, the area of rectangle1 = 15 × 6 = 90 cm²
The area of rectangle2 = 4 × 3 = 12 cm²
Total area = 90+12 =102 cm²
Therefore, the total area of the shape is 102 cm².
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Related Questions
If Event A is "the card is black" and Event B is "the card is a king," demonstrate the equation holds true.
/ 52 = / 4 × / 52
Answers
The equation holds true because the probability of Event A happening, given that Event B has already happened, is equal to the probability of Event A happening and Event B happening at the same time.
The probability of Event A happening is 26/52, because there are 26 black cards in a standard deck of 52 cards. The probability of Event B happening is 4/52, because there are 4 kings in a standard deck of 52 cards. The probability of Event A happening and Event B happening at the same time is 2/52, because there are 2 black kings in a standard deck of 52 cards.
Given that Event B has already happened, there are only 4 cards left in the deck that could be drawn, and 2 of them are black kings. Therefore, the probability of Event A happening, given that Event B has already happened, is 2/4 = 1/2. This is equal to the probability of Event A happening and Event B happening at the same time.
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find the volume of the solid bounded by the paraboloids z=−9 2x2 2y2 and z=5−2x2−2y2
Answers
We are given two paraboloids as:z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)The volume of the solid enclosed between the two paraboloids is given byV = ∫∫R[(5 - 2(x^2 + y^2)) - (-9/2)(x^2 + y^2)] d\(z = (-9/2)(x^2 + y^2)andz = 5 - 2(x^2 + y^2)\)A
where R is the region in the xy-plane that is bounded by the circular region of radius a centered at the origin.We can rearrange the equation and simplify it as follows:V = ∫∫R (23/2)x^2 + (23/2)y^2 - 5 dAWe will use polar coordinates (r, θ) to evaluate the integral, and the limits of integration for the radius will be 0 and a, and the limits of integration for the angle will be 0 and 2π.
Hence, we can rewrite the integral as:V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθEvaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2\(V = ∫[0, 2π] ∫[0, a] (23/2)r^2 - 5r dr dθ Evaluating this integral:V = ∫[0, 2π] [23/6 * a^3 - 5/2 * a^2] dθV = 4π [23/6 * a^3 - 5/2 * a^2]V = (46/3)πa^3 - 10πa^2\) * a^2]V = (46/3)πa^3 - 10πa^2Hence, the volume of the solid enclosed between the two paraboloids is (46/3)πa^3 - 10πa^2.The explanation has a total of 152 words.
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You have just learned of survey results conducted by your university on the drinking behaviors of the college campus. Wondering about the results, you ask yourself the following questions: how were participants selected, were participants selected depending on if they lived on or off campus, were all the participants in a sorority or fraternity, were non–traditional age students included in the survey, and were men and women equally sampled? These types of questions indicate that you are concerned about what threat to internal validity?
Answers
To ensure internal validity, it is important to have a random and representative sample that accurately reflects the population of interest.
The types of questions you are asking indicate that you are concerned about the threat to internal validity known as selection bias.
Selection bias refers to the systematic differences between the characteristics of the selected participants and the characteristics of the population from which they are drawn. It occurs when the process of selecting participants introduces a non-random element that may impact the results of the study.
In this case, you are specifically interested in how participants were selected and whether certain subgroups, such as those living on or off-campus, sorority or fraternity members, non-traditional age students, and men and women, were included in the survey. These questions suggest that you are concerned about whether the selection process introduced any biases that could affect the internal validity of the survey results.
For example, if participants were only selected from a specific residence hall or from Greek organizations, it could introduce bias because those groups may have different drinking behaviors compared to the broader student population. Similarly, if non-traditional age students or men and women were underrepresented or overrepresented in the sample, it could affect the generalizability of the findings.
To ensure internal validity, it is important to have a random and representative sample that accurately reflects the population of interest. This helps minimize the potential for selection bias and increases the generalizability of the survey results to the larger college campus population.
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Determine the minimum sample size required when you want to be 95% confident that the sample mean is within two units of the population mean. assume a population standard deviation of 3.8 in a normally distributed population.
Answers
Minimum sample size (n) = 15
To determine the minimum sample size required, we can use the formula:
n = (Zα/2 * σ / E)^2
Where:
- n is the minimum sample size
- Zα/2 is the z-score at the 95% confidence level, which is 1.96
- σ is the population standard deviation, which is given as 3.8
- E is the maximum error we can tolerate, which is 2 units in this case
Substituting the values, we get:
n = (1.96 * 3.8 / 2)^2
n = 27.44
Rounding up to the nearest whole number, we get a minimum sample size of 28.
Therefore, we need to sample at least 28 individuals from the normally distributed population to be 95% confident that the sample mean is within two units of the population mean, assuming a population standard deviation of 3.8.
To determine the minimum sample size required for a 95% confidence level, we'll need to use the following formula:
n = (Z * σ / E)^2
where:
- n is the minimum sample size
- Z is the Z-score corresponding to the desired confidence level (1.96 for a 95% confidence level)
- σ is the population standard deviation (3.8 in this case)
- E is the margin of error (2 units in this case)
Step 1: Identify the values
Z = 1.96 (from the 95% confidence level)
σ = 3.8
E = 2
Step 2: Plug the values into the formula
n = (1.96 * 3.8 / 2)^2
Step 3: Calculate the result
n = (7.528 / 2)^2
n = (3.764)^2
n ≈ 14.15
Since the sample size must be a whole number, round up to the nearest whole number to ensure the desired level of confidence is achieved.
Minimum sample size (n) = 15
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How do I know which triangles are similar to ABC?
Answers
Answer:
I'm not sure if my answer is correct but anyways.
Step-by-step explanation:
If you drew a triangle and labeled it, that would be easier to determine your answer. So, 145-10=135 and then i guess 145-135=10???
If the applied force p = 2. 1 kip , determine the maximum normal stress in the bracket. assume the bracket is a rod having a diameter of 1. 75 in
Answers
The maximum normal stress in the bracket, assuming it is a rod with a diameter of 1.75 inches and an applied force of 2.1 kip, is approximately 9.41 ksi.
To determine the maximum normal stress in the bracket, we need to consider the applied force and the geometry of the rod.
Given:
Applied force (P) = 2.1 kip
Rod diameter (d) = 1.75 in
First, we need to calculate the cross-sectional area (A) of the rod using its diameter:
A = π * (d/2)^2
A = π * (1.75/2)^2
A ≈ 2.405 in^2
Next, we need to convert the applied force from kip to pounds (lb):
P = 2.1 kip * 1000 lb/kip
P = 2100 lb
The maximum normal stress (σ) can be calculated using the formula:
σ = P / A
Substituting the values, we have:
σ = 2100 lb / 2.405 in^2
σ ≈ 872.35 psi
Finally, we convert the stress from psi to ksi:
σ = 872.35 psi / 1000 psi/ksi
σ ≈ 0.87235 ksi
Therefore, the maximum normal stress in the bracket is approximately 0.87235 ksi or 872.35 psi.
The maximum normal stress in the bracket, assuming it is a rod with a diameter of 1.75 inches and an applied force of 2.1 kip, is approximately 9.41 ksi. This value is obtained by converting the force to pounds, calculating the cross-sectional area of the rod, and dividing the force by the area to obtain the stress. It is important to note that this calculation assumes the bracket is made of a homogeneous material and is subject to axial loading. Proper engineering analysis and consideration of factors like material properties, boundary conditions, and safety factors are essential for accurate stress analysis in practical applications.
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what is the measure of angles for x and y?
Answers
Bart drives a delivery van for a local florist. One afternoon, after his last delivery but before returning the van to the florist shop to pick up his personal vehicle, Bart stopped at Walmart to make a layaway payment on toys he is buying his children for Christmas. Because he expected to be away from the van for only a few minutes, he left the van running, but did set the emergency brake. While Bart was in the store, the brake slipped, and the van rolled across the parking lot, pinning a woman between her car and the van, resulting in severe injuries. The injured woman is suing the florist shop for negligence. What would be the result?
Answers
The result of the injured woman's lawsuit against the florist shop for negligence will depend on the specific circumstances and legal factors involved in the case and would depend on how these factors are argued and proven in court.
However, there are a few key considerations that may come into play:
1. Duty of care: The injured woman would need to establish that the florist shop owed her a duty of care. This would involve demonstrating that the shop had a responsibility to take reasonable precautions to prevent harm to others.
2. Breach of duty: The injured woman would need to show that the florist shop breached its duty of care. In this case, one argument could be that leaving the delivery van running and unattended with only the emergency brake set constituted a breach of duty.
3. Causation: The injured woman would need to establish a causal connection between the florist shop's alleged negligence and her injuries. This would involve demonstrating that the van rolling and pinning her was a direct result of the florist shop's actions or inaction.
4. Damages: Finally, the injured woman would need to prove that she suffered actual damages as a result of the incident. This could include medical expenses, pain and suffering, lost wages, and other relevant costs.
Ultimately, the result of the lawsuit would depend on how these factors are argued and proven in court. It's important to note that the specific laws and legal standards in the jurisdiction where the incident occurred would also play a significant role in determining the outcome.
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the sum of two sumbers is 3 more than four times the firsst number. their difference is 10 less than twice the second number. find each of the numbers
Answers
The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.
Let's call the two numbers x and y, where x is the first number and y is the second number.
The problem gives us two equations that relate the two numbers:
\(x + y = 3 + 4x\\y - x = 2y - 10\)
We can substitute the expression for y from equation 1 into equation 2:
\(y - x = 2(3 + 4x) - 10\)
Expanding the right side and simplifying, we get:
\(y - x = 6 + 8x - 10\\y - x = 8x - 4\)
Adding x to both sides:
\(y = 9x - 4\)
Substituting this expression for y into equation 1:
\(x + (9x - 4) = 3 + 4x\)
Expanding and simplifying the right side:
\(10x - 4 = 3 + 4x\)
Subtracting 4x from both sides:
\(6x - 4 = 3\)
Adding 4 to both sides:
\(6x = 7\)
Dividing both sides by 6:
\(x = 7/6\)
Substituting this value of x back into the expression for y:
\(y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5\)
So the two numbers are 7/6 and 5.
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what are the four conditions necessary for x to have a binomial distribution? mark all that apply.
Answers
Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process
a set number of trials, such as three rolls of the dice or five flips of the coin.Each trial can either be successful or unsuccessful. Note that the example with the die seems to have six possible outcomes. We must take into account options like "get a 6" (success) or "not obtain a 6." (failure).The likelihood of success must be constant (equal for every try). P(6) = 1/6 for each roll of the die in the example.The trials are separate. The likelihood of success in future trials is unaffected by the outcome of the first.Know more about binomial at:
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Which number set correctly represents the range of the given data? {(0, 0), (2, 0), (3, 0), (5, 0)} {0, 2, 3, 5} {0, 2, 3} {0, 2} {0}
Answers
{0}
Step-by-step explanation:The range of a function is the set of y-values within a function.
Finding the Range
As stated above, the range is all of the y-values. To find the y-values remember that in a coordinate pair the second point is the y-value. So, look at the second value of each pair. For all 4 points, the y-value is 0. This means that the range is 0.
Range Notation
Now that we know the range, we need to use the correct notation. When writing domain or range, make sure that the values are listed in order from least to greatest. Additionally, even if y-values repeat in the coordinate pairs, only state them once in the range. In this case, there is only 1 unique value, so the range should only have 1 value. Finally, the range is surrounded by braces. Therefore, the range should be written as {0}.
All the ratios that are equivalent to 6 : 2?
Answers
Answer:
here is three: 3:1, 12:4, 18,6
Step-by-step explanation:
Hunter picked three quarts of blueberries. some of the blueberries are ripe and some are not ripe. If he takes one blueberry from the basket without looking, what are the outcomes
Answers
Answer:
Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...
A spinner with four sections is spun 30 times.
I accidentally pushed an answer and answer as quickly as possible please I really need this answer now please and thank you
Answers
Answer:
Answer Choice A aka 1/5 (0.2)
Step-by-step explanation:
B = 6/7+8+6+9
= 1/5
The value root of 46 of lies between which two consecutive integers
Answers
Answer:
6 and 7
Step-by-step explanation:
What are the mean and median next 12 months pe ratios of the group? enter your answer as the mean multiple followed by the median multiple, comma separated with no spaces. For example: 25. 5x,15. 8x
Answers
The mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.
The mean and median next 12 months PE ratios of the group can be found by following these steps:
1. Gather next 12 months PE ratios for each company.
2. Calculate mean by summing the ratios and dividing by total number.
3. Arrange ratios in ascending order.
4. Find the middle value(s) to determine the median.
5. Write the mean multiple followed by the median multiple, comma-separated with no spaces.
Therefore, the mean and median next 12 months PE ratios of the group are the mean multiple followed by the median multiple, comma-separated with no spaces.
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A guidance counselor wants to determine if there is a relationship between a student’s number of absences, x, and their grade point average (gpa), y. the given data list the number of absences and gpas for 15 randomly selected students. using technology, what is the value of r2? a. –0.56
b. –0.32
c. 0. 32
d. 0.56
Answers
Linear regression is used to model the linear relationship between two variables and r2 measures the strength of this relationship. It is calculated by squaring the correlation coefficient, which is a measure of the strength and direction of the relationship.
To determine the value of r2, you can use technology to perform a linear regression analysis on the given data. Linear regression is a statistical method used to model the linear relationship between two variables, x and y. The value of r2, also known as the coefficient of determination, measures the strength of the relationship between x and y and indicates how well the model fits the data.
The value of r2 is calculated using the following formula:
r2 = (Correlation coefficient)2
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:
r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]
where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.
To determine the value of r2, you would first need to calculate the correlation coefficient using the given data. Once you have calculated the correlation coefficient, you can then square it to get the value of r2.
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You can use technology to do a linear regression analysis on the supplied data to find the value of r2. A statistical technique called linear regression is used to simulate the linear relationship between two variables, x and y. The strength of the link between x and y is measured by the coefficient of determination, or r2, which also serves as a measure of how well the model fits the data.
The value of r2 is calculated using the following formula:
r2 = (Correlation coefficient)2
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the relationship between two variables. It is calculated using the following formula:
r = ∑(x - x')(y - y') / √[∑(x - x')2 ∑(y - y')2]
where x' and y' are the means of the x and y variables, respectively, and ∑ indicates the sum of the values.
You must first compute the correlation coefficient using the provided data in order to obtain the value of r2. Once the correlation coefficient has been determined, you can square it to obtain the value of r2.
Help me with this question, please
Answers
Answer:
x = 3 oz of seeds
y = 7 oz of seeds
Step-by-step explanation:
1. x + y = 10 oz (total amount of snack mix in ounces; oz)
2. $1.50x + $2.50y = $22 (how much the seeds and dried fruit costs)
3. Solve the system of equations using algebra.
$1.50 x + $1.50y = $15
$1.50 x + $2.50y = $22
There are $1.50x's in both of the equations, so cancel them out.
Subtract $2.50y by $1.50y and $22 by $15. y = 7
4. Plug in the y value in one of the equations.
x + 7 = 10; x = 3
A rectangle has an area of 182 square feet and a base of 13 feet. What is the height?
Answers
Answer:
14 feet
Step-by-step explanation:
Area= base x height
Height=area/base
182/13=14
The asymmetric cryptography algorithm most commonly used is:
O GPG
O RSA
O ECC
O AES
Answers
Answer
Step-by-step explanation:
choices:
x=360-114
x=114-90
360=x +90+114
Answers
Answer:
see explanation
Step-by-step explanation:
The sum of the angles around D = 360° , then
x = 360 - (114 + 90) ← equation to find x
= 360 - 156
= 204
Given the figure below with the measures shown, is AEC similar to BDC?
Answers
Answer:
yes they're similar
Step-by-step explanation:
Answer:
Step-by-step explanation:
21
The value of R2 always ...
lies below 0
lies above 1
lies between 0 and 1
lies between -1 and +1
Answers
The value of R2 always lies between 0 and 1.The value of R2 represents the proportion of the variation in the dependent variable that can be explained by the independent variables, ranging from 0 to 1.
The value of R2, also known as the coefficient of determination, measures the goodness of fit of a regression model. It represents the proportion of the total variation in the dependent variable that is explained by the independent variables in the model.
R2 ranges between 0 and 1, where 0 indicates that the independent variables have no explanatory power and cannot predict the dependent variable's variation. On the other hand, an R2 value of 1 indicates that the independent variables perfectly explain all the variation in the dependent variable.
An R2 value greater than 1 or less than 0 is not possible because it would imply that the model explains more than 100% or less than 0% of the dependent variable's variation, which is not meaningful. Therefore, the value of R2 always lies between 0 and 1, providing a measure of the model's explanatory power.
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Train A runs back and forth on an east-west section of railroad track. Train A’s velocity, measured in meters per minute, is given by a differentiable function vA(t) where time t is measured in minutes. Selected values for vA(t) are given in the table below.t (Minutes) 0 2 5 8 12vA(t)(meters/minute) 0 100 40 -120 -150Find the average acceleration of train A over the interval 2 ≤ t ≤ 8.
Answers
The average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.
Explanation:
The average acceleration of a body over a given time interval is defined as the change in velocity divided by the time interval. In this case, we are given the velocity function vA(t) for Train A, and we want to find its average acceleration over the interval 2 ≤ t ≤ 8.
To find the change in velocity over this interval, we can subtract the velocity at t=2 from the velocity at t=8:
Δv = vA(8) - vA(2) = (-120) - 100 = -220 meters per minute
To find the time interval, we can subtract 2 from 8:
Δt = 8 - 2 = 6 minutes
Now we can use the formula for average acceleration:
a = Δv/Δt = (-220)/6 = -40 meters per minute squared
Therefore, the average acceleration of Train A over the interval 2 ≤ t ≤ 8 is -40 meters per minute squared.
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Factor the common factor out of each expression.
-21a + 35
Answers
Answer:
7 each
Step-by-step explanation:
-21a + 35
7(-3a) + 7(5)
Staples sells boxes of pens ($10) and rubber bands ($4). Leona ordered a total of 24 cartons for $210. How many boxes of each did Leona order
Answers
Answer:
19
Step-by-step explanation:
Answer:
Leona ordered 19 boxes of pens and 5 boxes of rubber bands
Step-by-step explanation:
150+3x-15=180 what’s is this answer in geometry
Answers
Answer:
x=15
Step-by-step explanation:
135+3x=180
-135 -135
___________
3x=45
÷3 ÷3
_______________
x=15
Hope it helps a bit :D
Fred's net worth is shown in the table below.
Assets are positive numbers and liabilities are negative
numbers If Fred's net worth is $74,000 how much
does he owe in credit card debt?
Item
House (current value)
Checking Account
Credit Card Debt
Vehicle (current value)
Student Loans
Personal Loans
Savings Account
Value
$105,900
$375
$13,500
-$32,000
-$800
$1,275
A) $6,725
B) $7,560
C) $9,750
D) $12,500
E) $14,250
F) $17,325
Answers
Fred owes $14,250 in credit card debt.
We must total up all of Fred's assets and liabilities, then subtract them to arrive at the amount he owes on his credit cards.
Let's figure it out:
Total Assets:
House (current value) = $105,900
Checking Account = $375
Vehicle (current value) = $13,500
Savings Account Value = $1,275
Total Liabilities:
Credit Card Debt = ?
Student Loans = $32,000
Personal Loans = $800
Total Assets - Total Liabilities = Net Worth
105,900 + 375 + 13,500 + 1,275 - (Credit Card Debt + 32,000 + 800) = 74,000
Solving for Credit card debt =
Credit Card Debt = 74,000 - 88,250
Credit Card Debt = -14,250 [The negative sign identifies it as a liability, as you can see.]
Therefore, Fred owes $14,250 in credit card debt.
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Find the zeros of the polynomial using the techniques specified by your text. State the multiplicity of each real zero.
P(x) = x^3 + 4x^2 − 15x − 18
x =
(smallest value)
with multiplicity
x = with multiplicity
x = (largest value) with multiplicity
Answers
The zeros of the polynomial P(x) = x^3 + 4x^2 − 15x − 18 are:
x = -3 (with multiplicity 2)
x = 2 (with multiplicity 1)
To find the zeros of the polynomial P(x) = x^3 + 4x^2 − 15x − 18, we can use the techniques specified by the text. These techniques involve factoring the polynomial and setting each factor equal to zero.
Step 1: Factor the polynomial P(x) = x^3 + 4x^2 − 15x − 18.
One possible factorization is (x + 3)(x − 2)(x + 3).
Step 2: Set each factor equal to zero and solve for x.
Setting x + 3 = 0, we get x = -3. This means that -3 is a zero of multiplicity 2, as it appears twice in the factorization.
Setting x − 2 = 0, we get x = 2. This means that 2 is a zero of multiplicity 1, as it appears once in the factorization.
So, the zeros of the polynomial P(x) = x^3 + 4x^2 − 15x − 18 are:
x = -3 (with multiplicity 2)
x = 2 (with multiplicity 1)
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HELPPP!! What is the slope of a line that is perpendicular to
y = - 3x + 10 ?
Answers
Answer:
the answer is 1/3. hope it help