The true about the volumes of the triangular prism and the triangular pyramid is D; triangular pyramid has a volume one-third the volume of the triangular prism.
What is a triangular prism?Suppose a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.
Usually, about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.
In order for us to know the volume of the triangular pyramid, first we need to know the ratio of the volume of triangular prism and the volume of the triangular pyramid.
Take a traingle as a base then take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.
Volume of the pyramid = 1/3 volume of the prism.
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The triangular pyramid has a volume one-third the volume of the triangular prism .
Correct option is D.
What is volume?Volume is the measure of the capacity that an object holds. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space enclosed/occupied by any 3-dimensional object or solid shape.
Given,
A triangular prism and a triangular pyramid have the same base and height.
Let the height be h unit and area of base be x square unit
Volume of triangular prism
= base area × height
= Ah cubic unit
Volume of triangular pyramid
= (1/3)× base area × height
= (1/3)Ah
= (1/3) volume of triangular prism
Hence, volume of triangular pyramid is one-third of volume of triangular prism.
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A fair coin is tossed 100 times. Using normal approximation to binomial probabilities, find the probability that the number of heads would take a value within one standard deviation from the mean. a. 0.7698 b. 0.7286 C. 0.6826 d. 0.6318
The answer is C
The probability that the number of heads would take a value within one standard deviation from the mean is 0.6826. This can be found by using the normal approximation to binomial probabilities.
First, we need to find the mean and standard deviation of the binomial distribution. The mean of a binomial distribution is given by np, where n is the number of trials and p is the probability of success. In this case, n = 100 and p = 0.5 (since it is a fair coin), so the mean is 100 * 0.5 = 50.
The standard deviation of a binomial distribution is given by √(np(1-p)). In this case, the standard deviation is √(100 * 0.5 * (1-0.5)) = √(25) = 5.
Now, we can use the normal approximation to find the probability that the number of heads is within one standard deviation from the mean. This is equivalent to finding the probability that the number of heads is between 45 and 55 (since the mean is 50 and the standard deviation is 5).
Using the normal approximation, we can find the z-scores for 45 and 55:
z = (x - μ) / σ
z1 = (45 - 50) / 5 = -1
z2 = (55 - 50) / 5 = 1
Now, we can use a z-table to find the probability that the number of heads is between 45 and 55. The probability that the number of heads is less than 55 is 0.8413, and the probability that the number of heads is less than 45 is 0.1587. So, the probability that the number of heads is between 45 and 55 is 0.8413 - 0.1587 = 0.6826.
Therefore, the answer is C. 0.6826.
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Knowledge Check Divide. (x+6)/(3x+9)-:(7)/(9x)+42 Simplify your answer as much as possible.
(3x²+18x)/(7x+21) is the simplified answer of (x+6)/(3x+9)-:(7)/(9x)+42.
To divide the given expressions, we need to first simplify the expressions as much as possible and then use the rule for dividing fractions. The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction.
Simplifying the expressions:
(x+6)/(3x+9) = (x+6)/(3(x+3)) = (x+6)/3(x+3)
(7)/(9x) = 7/9x
Now, using the rule for dividing fractions:
((x+6)/3(x+3)) ÷ (7/9x) = ((x+6)/3(x+3)) * (9x/7)
= (9x(x+6))/(3(x+3)*7)
= (3x(x+6))/(x+3)*7
= (3x²+18x)/(7x+21)
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336 fewer the the product of u and 258 is 168
Answer:
335.6511628
Step-by-step explanation:
Ux258-336=168
U-336=0.6511628
U=336.6511628
Q1. Let \( A=\left[\begin{array}{lll}a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a\end{array}\right] \), where \( a \in \mathbb{F} \). Prove that \[ A^{n}=\left[\begin{array}{ccc} a^{n} & n a^{n-1} & \frac{n(n-
To prove that \[ A^{n}=\left[\begin{array}{ccc} a^{n} & n a^{n-1} & \frac{n(n-1)}{2}a^{n-2} \end{array}\right], we will use mathematical induction.
Base case: For \( n=1 \), \( A^{1}=A \). This is true since
\[ A=\left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]
which matches the left side of our equation.
Inductive step: Assume that the statement is true for some \( n=k \), i.e.
\[ A^{k}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right] \]
We will now show that it is true for \( n=k+1 \).
\[ A^{k+1}=A^{k}\cdot A \]
We substitute the induction hypothesis into this equation and get:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right]\cdot \left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]
Calculating the matrix product yields:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k+1} & (k+1)a^{k} & \frac{(k+1)k}{2}a^{k-1} \end{array}\right] \]
which matches the left side of our equation, completing the proof.
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What statement describes the decimal equivalent of 5 ? 16 Responses A It is a decimal that terminates after 4 decimal places. It is a decimal that terminates after 4 decimal places. B It is a decimal with a repeating digit of 5. It is a decimal with a repeating digit of 5. C It is a decimal that terminates after 3 decimal places. It is a decimal that terminates after 3 decimal places. D It is a decimal with repeating digits of 6
The statement which describes the decimal equivalent of 5/16 is option(a), It is a decimal that terminates after 4 decimal places.
To convert a fraction to a decimal, we need to divide the numerator by the denominator.
In this case, we want to find the decimal equivalent of the fraction 5/16,
⇒ 5 ÷ 16 = 0.3125
So, the decimal equivalent of 5/16 is 0.3125.
The option(a) states that, It is a decimal that terminates after 4 decimal places.
This statement is correct, because the decimal equivalent of 5/16 terminates after 4 decimal places.
Therefore, the correct statement is option is (a).
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The given question is incomplete, the complete question is
What statement describes the decimal equivalent of 5/16?
(a) It is a decimal that terminates after 4 decimal places.
(b) It is a decimal with a repeating digit of 5.
(c) It is a decimal that terminates after 3 decimal places.
(d) It is a decimal with repeating digits of 6.
Convert the Cartesian coordinates (1,−5) to polar coordinates
with r>0 and 0≤θ<2π. give theta answer in radiants
The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.
To convert the Cartesian coordinates (1, -5) to polar coordinates with r>0 and 0≤θ<2π, we need to use the following formulas:
r = √(x^2 + y^2)
θ = tan^-1(y/x)
First, let's find the value of r:
r = √(1^2 + (-5)^2)
r = √(1 + 25)
r = √26
Now, let's find the value of θ:
θ = tan^-1((-5)/1)
θ = tan^-1(-5)
θ = -1.373400766945016
Since we need the angle to be between 0 and 2π, we can add 2π to the negative angle to get the positive equivalent:
θ = -1.373400766945016 + 2π
θ = 4.910188838655984
Therefore, the polar coordinates of the Cartesian coordinates (1, -5) are (r, θ) = (√26, 4.910188838655984).
So the answer is:
r = √26
θ = 4.910188838655984
The Cartesian coordinates (1, -5) are equivalent to the polar coordinates (√26, 4.910188838655984) with r > 0 and 0 ≤ θ < 2π.
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Martin buys 2(5)/(6) pounds of peanuts and 4(3)/(4) pounds of almonds. How many pounds of nuts does Martin buy?
Martin buys a total of 2(5)/(6) + 4(3)/(4) = 10/6 + 19/4 = 40/24 + 57/24 = 97/24 pounds of nuts.
To find the total amount of nuts Martin buys, we need to add the amount of peanuts and the amount of almonds he buys.
First, we need to convert the mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator. For 2(5)/(6), we multiply 2 by 6 and add 5 to get 10/6. For 4(3)/(4), we multiply 4 by 4 and add 3 to get 19/4.
Next, we need to find a common denominator in order to add the two fractions. The least common denominator for 6 and 4 is 24, so we multiply the numerator and denominator of 10/6 by 4 to get 40/24 and the numerator and denominator of 19/4 by 6 to get 57/24.
Finally, we add the two fractions by adding the numerators and keeping the same denominator: 40/24 + 57/24 = 97/24.
Therefore, Martin buys a total of 97/24 pounds of nuts.
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vv^(1) 2 4 Solve by using the quadratic formula. Express the solution set in exact simplest form. x^(2)-5x-5=0 The solution set is
To solve the equation x^(2)-5x-5=0 using the quadratic formula, we can use the formula x = (-b ± √(b^(2)-4ac))/(2a), where a, b, and c are the coefficients of the equation. In this case, a=1, b=-5, and c=-5.
Plugging in the values into the formula, we get:
x = (-(-5) ± √((-5)^(2)-4(1)(-5)))/(2(1))
Simplifying the equation, we get:
x = (5 ± √(25+20))/2
x = (5 ± √45)/2
x = (5 ± 3√5)/2
Therefore, the solution set in exact simplest form is x = (5 ± 3√5)/2.
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A quadratic function models the graph of a parabola. The quadratic functions, y=x and y=x² +3, are modeled in the
graphs of the parabolas shown below.
-10-9-8-76
y M
10
-2-1
0
8
40
6
-7
-8
9
-10-
y=x²+3
y=x²
。
Determine which situations best represent the scenario shown in the graph of the quadratic functions, y=x² and y=x²
+3. Select all that apply.
The situations that best represent the scenario shown in the graph of the quadratic functions, y = x² and y = x² + 3 include the following:
B. "From x = -2 to x = 0, the average rate of change for both functions is negative."
C. "For the quadratic function, y = x² + 3, the coordinate (2, 7) is a solution to the equation of the function."
D. "The quadratic function, y = x², has an x-intercept at the origin."
What is the x-intercept?In Mathematics, the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).
In this context, we can logically deduce that the x-intercepts of the graph of the given equation y = x² is at the origin:
x = (0, 0)
For the the coordinate (2, 7), we would evaluate the quadratic function, y = x² + 3 as follows;
7 = 2² + 3
7 = 4 + 3
7 = 7 (True).
By critically observing the graph of both functions, we can logically deduce that their average rate of change is negative from x = -2 to x = 0.
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In 1 hour 32 cars pass through a particular intersection. At the same rate, how long would it take for 96 cars to pass through the intersection?
It wοuId take 3 hοurs fοr 96 cars tο pass thrοugh the intersectiοn at the same rate as 32 cars in 1 hοur.
We can use the cοncept οf prοpοrtiοnaIity tο sοIve this prοbIem. The number οf cars passing thrοugh the intersectiοn is directIy prοpοrtiοnaI tο the amοunt οf time taken. This means that if we dοubIe the number οf cars passing thrοugh, we wiII aIsο dοubIe the amοunt οf time taken.
Let x be the amοunt οf time it takes fοr 96 cars tο pass thrοugh the intersectiοn. Then, we can set up the fοIIοwing prοpοrtiοn:
32 cars / 1 hοur = 96 cars / x hοurs
Tο sοIve fοr x, we can crοss-muItipIy and simpIify:
32x = 96
x = 3
Therefοre, it wοuId take 3 hοurs fοr 96 cars tο pass thrοugh the intersectiοn at the same rate as 32 cars in 1 hοur.
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Three equivalent fractions for 30/48
1) 5/8
2) 15/24
3) 300/480
Answer: 5/8
10/16
15/24
Step-by-step explanation:
A $900 item is on sale for 20% off.
What is the final price with 7% sales tax?
Money off:
Amt, of tax:
Money paid:
Final price:
AW
IN. I need help I’m stuck
A $900 item on the sale of 20% discount the
Money off: $180
Amt. of tax: $50.40
Money paid: $770.40
Final price: $770.40
what is discount ?
A discount is a reduction in the price of an item or service, often offered as a promotion or incentive to encourage customers to make a purchase. The discount is usually expressed as a percentage of the original price and represents the amount of money that the customer can save on the purchase.
For example:
Percentage discount: a certain percentage of the original price is deducted from the selling price. For example, a 20% discount on a $100 item would reduce the price to $80.
According to the question:
To calculate the final price of the item with sales tax, we can follow these steps:
Calculate the amount of money off by multiplying the original price by the discount percentage:
Money off = 0.20 x $900 = $180.
Calculate the price after the discount by subtracting the money off from the original price:
Price after discount = $900 - $180 = $720.
Calculate the amount of sales tax by multiplying the price after discount by the tax rate:
Amount of tax = 0.07 x $720 = $50.40.
Calculate the money paid by adding the price after discount and the amount of tax:
Money paid = $720 + $50.40 = $770.40.
Therefore, the final price with 7% sales tax is $770.40.
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Five different stores sell a bag of flour for one of the following prices: $1.45, $1.55, $1.90, $1.95, $1.45. What are the mean, median, and mode of the data?
The mean, median and mode of the prices that the bags of flour are sold at are:
Mean - $ 1.66Median - $ 1. 55Mode - None How to find the mean, mode and median ?To find the mean, we add up all the prices and divide by the total number of prices:
Mean:
= (1.45 + 1.55 + 1.90 + 1.95 + 1.45) / 5
= 1.66
To find the median, we need to arrange the prices in order from lowest to highest:
1.45, 1.45, 1.55, 1.90, 1.95
There are five prices, so the median is the middle value, which is 1.55.
To find the mode, we need to look for the price that appears most frequently in the data set. In this case, there are two prices that appear twice, 1.45 and 1.55. So there is no unique mode for this data set.
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
g(7) = -1
g(-13)= 20
g(-4)= - 11
g(0) = 2
The statement that could be true for g is g(-4) = -11.
What is a function?
A function is a mathematical relationship between a set of inputs (called the domain) and a set of outputs (called the range), where each input has a unique output. In other words, for every value of x in the domain, there is exactly one corresponding value of g(x) in the range.
For the given function g, the domain is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.
To determine which statement could be true for g, we can check each option against the given domain and range, as well as the known values of g(0) and g(-9):
g(7) = -1: This statement is not necessarily true, as g(7) may fall outside the given range of -5 ≤ g(x) ≤ 45.
g(-13) = 20: This statement is not necessarily true, as g(-13) may fall outside the given domain of -20 ≤ x ≤ 5.
g(-4) = -11: This statement could be true, as -20 ≤ -4 ≤ 5 and -5 ≤ -11 ≤ 45. However, we cannot confirm this without additional information.
g(0) = 2: This statement is not true, as g(0) is known to be -2.
Therefore, the statement that could be true for g is g(-4) = -11.
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What are the x-intercepts of the quadratic function?
f(x)=x^2+6x−27
enter your answer in the boxes
blank and blank
Step-by-step explanation:
To find the x-intercepts of the quadratic function f(x) = x^2 + 6x - 27, we need to set f(x) equal to zero and solve for x.
So we have:
f(x) = 0
x^2 + 6x - 27 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 6, and c = -27.
Substituting these values into the quadratic formula, we get:
x = (-6 ± sqrt(6^2 - 4(1)(-27))) / 2(1)
x = (-6 ± sqrt(180)) / 2
x = (-6 ± 6sqrt(5)) / 2
x = -3 ± 3sqrt(5)
So the x-intercepts of the quadratic function are approximately -10.16 and 4.16.
Letf(x)=x−5xandg(x)=x3. Find the following functions. Simplify your answers.f(g(x))=g(f(x))=
The f(g(x))=−4x3and g(f(x))=x3−15x2+25x−125x3.
To find f(g(x)), we need to substitute the function g(x) into the function f(x). This means that wherever we see an "x" in f(x), we replace it with the function g(x). So, f(g(x))=g(x)−5g(x)=x3−5x3=−4x3. Similarly, to find g(f(x)), we substitute the function f(x) into the function g(x). So, g(f(x))=f(x)3=(x−5x)3=x3−15x2+25x−125x3.
Therefore, f(g(x))=−4x3and g(f(x))=x3−15x2+25x−125x3.
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Use the pair of functions to find f(g(x)) and g(f(x)). Simplify your answers.
f(x) = x²+1, g(x) = √x+5
f(g(x)) =
g(f(x)) =
The solutions of the given functions are:
f(g(x)) = x+10√x+26 and g(f(x)) = √(x²+6)
f(x) = x²+1, g(x) = √x+5 are given.
To find f(g(x)), we need to substitute g(x) into the function f(x):
f(g(x)) = f(√x+5) = (√x+5)²+1 = x+10√x+26
To find g(f(x)), we need to substitute f(x) into the function g(x):
g(f(x)) = g(x²+1) = √(x²+1+5) = √(x²+6)
Therefore, the simplified answers are:
f(g(x)) = x+10√x+26
g(f(x)) = √(x²+6)
Note: It is important to include the parentheses when substituting one function into another to ensure the correct order of operations.
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The number of coins in a person's collection changes based on buying, selling, and trading coins. A function defined as f(t) = t³ - 6t² + 9t
is modeled by the table, which represents the number of coins in the coin collection t years since the person began collecting coins.
(Picture has the rest of the problem)
The statements that are true are
The relative minimum function is (3, 0)
When t > 3 the function will increase
Finding the maximum and minimum function:To find the maximum and minimum of a function, find the points where the function's derivative is equal to zero or undefined. These points are called critical points.
We then evaluate the function at these critical points and at the endpoints of the interval to determine the maximum and minimum values. To find the critical points of the function find the derivatives of the given function
Here we have a graph
The graph shows the number of coins in a person's collection
The function is defined as f(t) = t³ - 6t² + 9t
To find the maximum and minimum of the function
Find the critical points where the derivative is equal to zero or undefined.
Differentiate f(t) with respect to t
=> f'(t) = 3t² - 12t + 9
Now, set the derivative equal to zero and solve for t
=> 3t² - 12t + 9 = 0
=> t² - 4t + 3 = 0 divide by 3
On Factoring the quadratic equation, we get:
=> (t - 3)(t - 1) = 0
=> t = 3 and t = 1
Therefore,
The critical points of the graph are t = 1 and t = 3.
Now differentiate f'(t) with respect to t
=> f''(t) = 6t - 12
At t = 1, f''(1) = 6 - 12 = - 6, which is less than zero.
Hence, f(t) has a local maximum at t = 1.
At t = 3, f''(3) = 18 - 12 = 6, which is greater than zero.
Hence, f(t) has a local minimum at t = 3.
At t = 4, f''(4) = 24 - 12 = 12
At t = 5, f''(5) = 30 - 12 = 18
Hence, f(t) will increase when t > 3
Therefore,
The statements that are true are
The relative minimum function is (3, 0)
When t > 3 the function will increase
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find the slope of the line that contains each pair of points (2,6) and (0,1)
5/2 is the slope of line .
What is slope, exactly?
Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2).
The letter "m" is frequently used to signify slope. A line's steepness can be determined by its slope. In mathematics, slope is calculated as "rise over run" (change in y divided by change in x).
points (2,6) and (0,1)
Slope = 1 - 6/0 - 2
= -5/-2
= 5/2
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what even number is not a composite number 6,4,2,8
Answer: 2
Step-by-step explanation:
Answer and Explanation: The only even number that is not a composite number is 2. All even numbers are defined as numbers that are divisible by, or have a divisor of, 2.
Answer:
The answer to your question is, 2
Step-by-step explanation:
The reason why that is our answer is because, 2 can either be multiplied and divided but 2 NUMBERS.
Such as the following:
2 / 1 = 2.
1 x 2 = 2.
What is a composite number?
A composite number are numbers that have more than two factors like the number 2:
2 / 1 = 2.
1 x 2 = 2.
Thus the answer to your problem is, 2
isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft
The area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft
Isosceles trapezoid, also known as isosceles trapezium, is defined as a convex quadrilateral, which mainly consists of a line of symmetry that bisects one pair of the opposite side, it is also know that the base angles are of equal measure. It has parallel bases with the legs also being of the equal measure, on the other hand the opposite angles of the isosceles trapezoid are supplementary, which makes it a cyclic quadrilateral.
Area of an Isosceles Trapezoid = [(a+b)h]/2 square units,
when we put these values in the formula, we get:
Area = [(2+5)2.5]/2
Area = (7 × 2.5)/2
Area = 17.5/2
Area = 8.75ft²
therefore, we know that the area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft
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A puppy weighed 28 ounces on Monday. It gained 7 ounces in one week. What is the percent increase of the puppy's weight rounded to the nearest percent?
The percent increase of the puppy's weight is 25%
How to calculate the percentage increase of the puppy's weight?A puppy weighed 28 ounces on Monday
It gained 7 ounces in one week
Total weight is = 28 + 7
= 35
The percent increase can be calculated as follows
= 35/28
= 1.25
= 1.25-1
= 0.25 × 100
= 25%
Hence the percent increase of the puppy's weight is 25%
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Triangle ABC is enlarged with a scale factor of -2 and the origin of the centre to give triangle ABC . WORK OUT THE COORDINATES OF A and B
The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).
What is a dilation?Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.
here, we have,
From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).
Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.
Now, A(1, 3) → -2(1, 3)→A'(-2, -6)
B(7, 1) → -2(7, 1) → B'(-14, -2)
C(1, 1) → -2(1, 1) → C'(-2, -2)
Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).
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Can somebody PLEASE help me ASAP? I really need help. It’s due today!! Please show work!! I will give brainliest.
Answer:
1. c
2. b
3. a
Step-by-step explanation:
Surface Area of a cylinder = 2πrh + 2πr²
1. 2(3.14)(5)(11) + 2(3.14)(5)² = 502.4
2. 2(3.14)(6)(10) + 2(3.14)(6)² = 602.88
3. 2(3.14)(2)(12) + 2(3.14)(2)² = 175.84
The diagonals of a rhombus measure 8cm and 6cm .what is the length of a side of the rhombud
All sides of the given rhombus measure 5 cm respectively.
What is a rhombus?A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry.
The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Quadrilaterals having four congruent sides are called squares.
Squares are rhombuses by definition since they are quadrilaterals with four congruent sides.
So, consider the following values: AC = 8 cm, BD = 6 cm, OD = OB = 3 cm, and OA = OC = 4 cm.
Now,
OB² + OC² = BC²
3²+ 4² = BC²
9 + 16 = BC²
25 = BC²
5 = BC
A rhombus has an equal number of sides.
Therefore, all sides of the given rhombus measure 5 cm respectively.
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If the simple interest on $7000 for 7 years is $3430, then what is the interest rate?
The interest rate will be 7%
What is simple interest?A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount.
Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,
The formula for simple interest is:
S = p*t*r/100
the simple interest on $7000 for 7 years is $3430
r = S*100/(p*t)
r = (3430*100)/(7000*7)
r = 7%
Hence the interest rate will be 7%
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that the denominators are different. Simplify the result, if possible. (2)/(y-5)+(7)/(y+7)
The simplified expression is (3y-7)/(y^2-35)/3.
To simplify the given expression, we need to find the least common denominator (LCD) of the two fractions. The LCD of (y-5) and (y+7) is (y-5)(y+7).
Next, we need to multiply each fraction by the LCD in order to get the same denominator for both fractions.
(2)/(y-5) * (y+7)/(y+7) + (7)/(y+7) * (y-5)/(y-5)
= (2y+14)/(y^2-35) + (7y-35)/(y^2-35)
Now, we can combine the two fractions since they have the same denominator.
(2y+14+7y-35)/(y^2-35)
= (9y-21)/(y^2-35)
Finally, we can simplify the fraction by factoring out a 3 from the numerator.
= (3)(3y-7)/(y^2-35)
= (3y-7)/(y^2-35)/3
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Order the numbers from least to greatest
pls edit yours and i will give an answer
Step-by-step explanation:
Answer:
I can't order the numbers without knowing the numbers sorry
PLEASE HELP I NEED HELP PLEASE
Answer:
Step-by-step explanation:
You take 528- divided by 2000- and then you get your answer.
Expressio
5. The teacher of Class 705 gave out permission
slips for students to go to MoMath, the math
museum in NYC.
On the first day, 12 students returned their
permission slips.
On the second day, 15% of the remaining
students returned their slips.
A total of three permission slips were
returned on the second day.
What is the total number of students in Class 705
The total number of students in Class 705 is 32.
How to calculated the total number of students in Class 705
Let's start by using algebra to solve the problem. Let's assume that the total number of students in Class 705 is "x". We know that 12 students returned their permission slips on the first day, so the number of students who have not returned their slips is (x-12).
On the second day, 15% of the remaining students returned their slips, which means that 0.15(x-12) students returned their slips. We also know that a total of three permission slips were returned on the second day, so we can write an equation:
0.15(x-12) = 3
Simplifying this equation:
0.15x - 1.8 = 3
0.15x = 4.8
x = 32
Therefore, the total number of students in Class 705 is 32.
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