What is the surface area of the right rectangular prism with square bases
pictured below with measurements a = 5 cm, b = 8 cm?
Answer:
210 cm²
Step-by-step explanation:
SA = Ph + 2B
where SA = surface area
P = perimeter of the base
h = height of the prism
B = area of the base
SA = [(8 + 8 + 8 + 8)(5) + 2(5²) ]cm²
SA = 210 cm²
Answer:
288 cm^2
Step-by-step explanation:
Is this a function? Need halo on how to solve it
Answer:
Yes it is because it is a straight line.
(I hope it helps, because i'm just learning about this meself so...)
Katelyn needs to cover her sofa cushions. If each cushion is a 10 in. by 11 in. by 4 in. rectangular prism, and there are 3 cushions that make up her sofa, determine how many square inches of fabric she needs to cover ALL the cushions on the sofa.
Answer:
1,164 in²
Step-by-step explanation:
the area of 1 sofa cushion =
2× ( 10×11 + 10×4 + 11×4)
= 2 × (110+40+44)
= 2×(194)
= 388 in²
the fabrics she needs to cover 3 sofa cushions =
3 × 388 = 1,164 in²
What are the angles of a 5 12 13 triangle?
The angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
The angles of a triangle are determined by the triangle's side lengths. This is known as the Law of Cosines. To determine the angles of a 5-12-13 triangle, we can use the Law of Cosines formula:
Cos(A) = (b² + c² - a²) / 2bc
In this equation, A is the angle opposite side a, b is the angle opposite side b, and c is the angle opposite side c. In a 5-12-13 triangle, a = 5, b = 12, and c = 13.
Using the Law of Cosines formula, we can calculate the angle A:
Cos(A) = (12² + 13² - 5²) / 2(12)(13)
Cos(A) = (144 + 169 - 25) / 156
Cos(A) = 278 / 156
Cos(A) ≈ 1.78
Using a calculator, we can calculate the angle A:
A = cos-1 (1.78)
A ≈ 81.19°
Using the same Law of Cosines formula, we can calculate the other two angles of the triangle:
Cos(B) = (a² + c² - b²) / 2ac
Cos(B) = (5² + 13² - 12²) / 2(5)(13)
Cos(B) = (25 + 169 - 144) / 65
Cos(B) = 50 / 65
Cos(B) ≈ 0.77
Using a calculator, we can calculate the angle B:
B = cos-1 (0.77)
B ≈ 48.76°
We can also calculate the angle C:
Cos(C) = (a² + b² - c²) / 2ab
Cos(C) = (5² + 12² - 13²) / 2(5)(12)
Cos(C) = (25 + 144 - 169) / 60
Cos(C) = 10 / 60
Cos(C) ≈ 0.17
Using a calculator, we can calculate the angle C:
C = cos-1 (0.17)
C ≈ 9.98°
Therefore, the angles of a 5-12-13 triangle are A = 81.19°, B = 48.76°, and C = 9.98°.
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if f(x) =mx + c , find f(1)=5 and (-2) =1
Answer:
f(4) = 11 → mx + c = 11 → 4m + c = 11.
f(5) = 13 → mx + c = 13 → 5m + c = 13.
Subtract #1 from #2, giving m = 2.
Then, for x=4, mx + c = 11 → 2(4) + c = 11 → c = 3.
Finally, for x=2, mx + c = 2(2) + 3 = 7.
Answer:
sorry
Step-by-step explanation:
PLEASE HELP. I'LL DO ANYTHING THAT'LL BENEFIT YOU.
If you double the amount of fluid ounces, the amount of cups also double
There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.
The cost of renting equipment is sometimes proportional; because, it depends on whether the equipment has a rental fee and charge per hour or just a charge per hour. Option A.The cost of mailing a letter is proportional to the weight. The cost of mailing a 6-ounce letter is $2.82. Option BThe donation is proportional to the dinner bill
The donation for a dinner bill of $50 is $9
How to determine proportional relationship?If there are 8 fluid ounces in one cup
8 : 1 = 16 : x
8/1 = 16/x
8 × x = 16 × 1
8x = 16
x = 16/8
x = 2
The difference between weight = 1
The difference between cost = $0.68 - $0.47
= $0.21
$0.89 - $0.68
= $0.21
$1.10 - $0.89
= $0.21
Cost of mailing 6-ounce letter
1 : 0.47 = 6 : x
1/0.47 = 6/x
1 × x = 6 × 0.47
x = $2.82
The donation for a dinner bill $50 is
Dinner bill : donation
25 : 4.50 = 50 : x
25/4.50 = 50/x
25 × x = 50 × 4.50
25x = 225
x = 225/25
x =$ 9
Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.
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A retail store sold a case of candles for $17.85 that had been marked up 110%. What was the original price of the table
The original price of the case of candles before markup was $8.50.
Markup price is the price that comes after setting up additional layer of pricing on the original price of a good. In this case also markup price is there. To find the original price of the case of candles before markup, we can use the following formula:
Original price = Marked up price / (1 + markup percentage)
In this case, the original price would be:
$17.85 / (1 + 110%) = $17.85 / 2.10 = $8.50
So the original price of the case of candles before markup was $8.50.
Thus, Original price is $8.5
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3.5 x 4 + 11 x 2.2 = 115.5
i know what the answer is i used a calculator i just need to explain how i got the answer its the last question then im done it i might give the brain thing if i can
Answer:
3.5. 2.2.
x 4. x 1 1
------ -----------
14.0. 22
220
24.2
Step-by-step explanation:
answer for me is 38.2
are you sure ur math is right?
What type of lines will be presented by the system of equations 2x 3y 6 and 4x 6y 11?
The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.
The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.
Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.
The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.
Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .
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6,000mL=............L
Step-by-step explanation:
1L=1000mLso 6000mL÷1000mL*1L=6LI hope it helps have a great weekend!!How can you determine if the length of the 3 sides would make a triangle?
we can use the Triangle inequality Theorem a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side
How to Determine if Three Side Lengths Are a Triangle?It's simpler than it seems to determine whether a triangle has three side lengths. The Triangle Inequality Theorem, which asserts that the sum of a triangle's two side lengths is always greater than the third side, will suffice. You will have a triangle if this holds true for each of the three possibilities of increased side lengths.
1 . Triangle Inequality Theorem
smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.
In this case, a, b, and c are each equal to seven.
2. Check to see if the sum of the first two sides is greater than the third
Check to see if the sum of the first two sides is greater than the third adding the sides a and b yields 17, which is larger than 5, or 7 plus 10. It can alternatively be considered as 17 > 5.
3. Check to see if the sum of the next combination of two sides is greater than the remaining side
just see if the sum of sides a and c are greater than the side b.[4] This means you should see if 7 + 5, or 12, is greater than 10. 12 > 10,
4. Check to see if the sum of the last combination of two sides is greater than the remaining side.
Check to see if side b and side c added together are greater than side a. To accomplish this, you must determine whether 10 Plus 5 is greater than 7. The triangle is complete on all sides since 10 + 5 = 15 and 15 > 7.
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PLS HELP ASAP!!! In the following diagram DE | FG and KL | FG what is the measure of angle X
Answer:
<x=28 degrees
Step-by-step explanation:
Since we know line KL and FG are perpendicular, and DE and FG are parallel, then KL and DE must also be perpendicular.
Angles GCA, JCB, IAE, and CAD are all the same angle. Angles IAD, EAC, GCJ, and ACB are all the same angle. Since DE and KL are perpendicular, then angles KAD, KAE, EAL, and DAL all are 90 degrees, or right angles.
Because we know all this, we can take the angle of KAD, 90 degrees, and subtract 62 from it to find the angle of IAD. This is 28 degrees. Since angle IAD is equal to angle GCJ, which is also angle x, angle x is 28 degrees.
Hope this helps! Please mark me Brainliest!
The following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. The mean of the population is 64.97 inches, and the standard deviation is 2.66 inches.
One woman from the population will be selected at random.
Question 3
(c) The histogram displays a discrete probability model for height. However, height is often considered a continuous variable that follows a normal model. Consider a normal model that uses the mean and standard deviation of the population of women as its parameters.
(i) Use the normal model and the relationship between area and relative frequency to find the probability that the randomly selected woman will have a height of at least 67 inches. Show your work.
(ii) Does your answer in part (c-i) match your answer in part (a) ? If not, give a reason for why the answers might be different.
Question 4
(d) Let the random variable H represent the height of a woman in the population. P(H<60) represents the probability of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model or the normal model.
(i) Give an example of a probability of H that can be found using the discrete model but not the normal model. Explain why.
(ii) Give an example of a probability of H that can be found using the normal model but not the discrete model. Explain why.
Answer:
The following histogram shows the relative frequencies of the height recorded to the nearest inch of population of women the mean of the population is 64.97 inches and the standard deviation is 2.66 inches
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
Answer:
0.22268
Step-by-step explanation:
z-score is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
(a) Based on the histogram, what is the probability that the selected woman will have a height of at least 67 inches? Show your work
At least means equal to or greater than 67 inches
z = 67 - 64.97/2.66
z = 0.76316
P-value from Z-Table:
P(x<67) = 0.77732
P(x>67) = 1 - P(x<67) = 0.22268
The probability that the selected woman will have a height of at least 67 inches is 0.22268
Step-by-step explanation:
A variable that can have any value between two given value is known as continuous variable, while a variable have only integer values is a discrete variable
The correct values are;
(c) (i) The probability of a height of at least 67 is 0.2263
(ii) The answers do not match due to the difference between the discrete and normal probability models
(d) (i) A probability that can be found using the discrete model but not the normal model is P (H = 60)
The probability of an exact value using the normal distribution is zero
(ii) A probability that can be found using the normal model but not the discrete model is P(H = 56)
The value is for height of 56 inches is not given on the histogram and therefore
The reason the above selections are correct is follows:
(c) (i) Using the normal probability model, we have;
The mean = 64.27 inches, the standard deviation = 2.66 inches
The z-score for the height of 67 inches is given as follows;
[tex]z = \mathbf{\dfrac{x - \mu}{\sigma}}[/tex]
Therefore, we have;
[tex]z = \dfrac{67 -64.97}{2.66} \approx 0.7632[/tex]
From the z-score table, the probability P(x < 67) = 0.7737
P(x > 67) = 1 - P(x < 67) = 1 - 0.7737 = 0.2263
The probability of a height of at least 67, by the normal model = 0.2263
(ii) Based on the histogram, we have;
The probability of at least 67 = The area of the bars equal to and larger than 67 = (0.11 + 0.07 + 0.05 + 0.02 + 0.01 + 0.01) × 1 = 0.27
The probability of a height of at least 67 = 0.27
The answer in part (c-i) and the answer in part (a) using the histogram do not match
The reason they do not match is that the normal model used in part c is
based on normal probability, which focuses on future events, using the
normal model which is a continuous probability model, while the value of
probability calculated using the histogram is based on the relative
frequency, which focuses on historical values, based on the discrete model
(d) (i) An example of a probability that can be found using the discrete model but not the normal model is the probability that the height of a woman is a discreet single value such as 65 inches
Therefore, using the discreet model, we have;
P(H = 65) = 0.18
Using the continuous model, we have;
P(H = 65) = 0
This is so because the continuous model is given by the area under the curve, which for a single value is infinitesimally small
(ii) An example of a probability that can be found using the normal model but not the discrete model is the probability of the height of a woman selected is 56 inches, P(H = 56) is not given in the histogram
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Manuel is ordering an ice cream dessert. He must order a size, a flavor of Ice cream, and a topping. There are 6 sizes, 2 flavors, and 1 topping to choose from.
How many different ice cream desserts could he order?
How to convert log2 to log10?
To convert the log2 to log10, we can use the convert of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) / logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)/log10(2) = log(x)/log (2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is presented as “log e e”.
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A bookstore had 90 copies of a magazine. Yesterday, it sold 2/5 of them. Today, it sold 2/3 of what remained. How many copies does the bookstore have left?
Answer:
24 magazines
Step-by-step explanation:
Okay, I hope this is right...
So I did
90 * 2/5= 36
and then,
36 * 2/3= 24
A right triangle has the height of 20 cenimeters and a base of 10 cenimeters what is the area of the triangle
Answer:
100
Step-by-step explanation:
Area of a triangle is b*h/2
So it's 10*20/2 which is 100
answer fast need in 10 min
10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .
What is the probability of spinner?12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.
If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.
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Plsss hurry i need help brainliest involed
Suppoe that the tatitical power of a tudy deign i 80% to detect a treatment effect of 0. 5 tandard deviation, and that take-up of the program i 100%. Other thing equal, do we have more, le, or the ame amount of power to detect an effect ize of 0. 4 SD?
The correct option is option C which states that , less than 80% power to detect the standard deviation is 0.4.
We know that the power is less and the effect size is small therefore we can say that all other things given as equal, it's harder to detect than the larger effect. As a result power is reduced.
Statistical power is a measure of research efficiency that is estimated before the study begins . This is done so as to predict the likelihood of discovering an actual effect rather than receiving a false negative result or, in the worst case scenario, overestimating the effect by identifying noise in the data.
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a garden has an area of 32 square feet what is the smallest possible perimeter
Answer:
24 feet
Step-by-step explanation:
factors that produce an area of 32:
1x32 Would give a perimeter of 66
2x16 Would give a perimeter of 36
4x8 Would give a perimeter of 24
He observes that the cells triple every 3 hours. If he starts with 15 cells, how many will he have in 24 hours?
Answer:
98,415
Step-by-step explanation:
24/3=8
15 x 3x3x3x3x3x3x3x3 =98,415
Use the drop-down menus to complete each equation so the statement about its
solution is true.
Answer:
Step-by-step explanation:
What is the discriminant? What is the type and number of solutions?
-8x² +4x-1=0
Answer:
x= 1/4 - 1/4 x= 1/4 + 1/4
Step-by-step explanation:
Answer:
Type: (+ ve)
Number of solutions: 2
Step-by-step explanation:
Discriminant:The discriminant of the quadratic formula is the section under the radical. It tells us whether there are two solutions, one solution, or no solutions.D = b² - 4acWe are given an equation (-8x² + 4x - 1 = 0)
Now, change the sign
-8x² + 4x - 1 = 0
8x² - 4x + 1 = 0
Here,
a = 8b = (-4)c = 1Now, discriminant
D = b² - 4ac
D = (8)² - (4)(8)(1)
D = 64 - 32
D = 32 > 0
Here, 32 is greater than 0 so, it has two solutions.
Extra Information:b² - 4ac > 0 ↬ (+ ve), 2 solutionsb² - 4ac = 0 ↬ (= 0), 1 solutionb² - 4ac < 0 ↬ (- ve), No solutionHelpppp pleaseeeeeeeee
Answer:
Step-by-step explanation:
Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00
Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it
According to our question-
x is the quantity of oranges.
y is the quantity of apples.
Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.
Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.
0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).
x + y = 15
0.5x + 0.65y = 9.00
As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).
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Write an equation using the explicit formula to represent each graph or scenario then rewrite the formula in function form
The exponential function's y-intercept is 3, while the linear function's y-intercept is 20. The y-intercept for each is obtained by substituting 0 for x in each case.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The first function is linear, with a y-intercept of 20, and a slope of 4:
S(x)=4x+20
The second function is exponential and has a multiplier of 2 and an initial value of 3:
J(x)=3(2)x
The game number for each function is represented by x, while the score for each game is represented by y. Each has a domain of 0, 1, 2, 3, 4, 5, 6, 7 and 8.
The exponential function's y-intercept is 3, while the linear function's y-intercept is 20. The y-intercept for each is obtained by substituting 0 for x in each case.
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A class is learning about proportions and ratios, so the teacher decides to use the data about students in the local high school. There are 500-600 students and 29 - 32% of the student body participates in athletics. Which of the following is the most reasonable estimate of the number of students who are considered athletes
Using the provided data, We should consider the mid-value for the number of students and take the average of percentage to find the estimate number, The answer is 168.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It is used to make decisions, predictions and gain knowledge from data. It involves using statistical methods to collect, summarize, and draw conclusions from data. It is used in various fields such as business, economics, social science, engineering, and medicine. It helps to make sense of complex data and make informed decisions.
What do you mean by estimate?In statistics, an estimate is a value that is calculated from a sample of data in order to approximate a population parameter. The most common examples of estimates are sample mean, sample proportion, sample standard deviation, and sample variance. These estimates are used to infer information about the population from which the sample was drawn. For example, an estimate of the population mean is calculated by taking the average of a sample of data and using that value to infer the value of the population mean.
mid-value of 500-600 = 550
average % = 30.5%
Athletes number = 30.5% of 550
=168
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The logo on a recycling bin resembles an equilateral triangle with side lengths of 6 centimeters. Approximate the area of the logo.
Answer:
9[tex]\sqrt{3}[/tex] cm² or approximately 15.59 cm²
Step-by-step explanation:
Use the formula for the area of an equilateral triangle, A = [tex]\frac{\sqrt{3} }{4}[/tex]a²
Plug in the side length, 6 cm, as a in the formula:
A = [tex]\frac{\sqrt{3} }{4}[/tex](6²)
A = [tex]\frac{\sqrt{3} }{4}[/tex](36)
A = 9[tex]\sqrt{3}[/tex]
So, the area of the logo is 9[tex]\sqrt{3}[/tex] cm² or approximately 15.59 cm²
Is 2x3 is a polynomial?
In 2x^3, 3 is the greatest degree of the exponent. 2x^3 is a cubic polynomial as a result.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An example of a polynomial of a single indeterminate x is x² − 4x + 7.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
Sums of terms of the form kxn, where k is any number and n is a positive integer, make up polynomials.
For instance, the polynomial 3x+2x-5.
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
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