Answer:
11
Step-by-step explanation:
Evaluate the expression when m=8 and n=9.
4n+m
Answer:
44
Step-by-step explanation:
4(9) + 8
=36 + 8
=44
Two square based pyramids are joined, total volume is 2700mm, perpendicular height of top pyramid is 16mm, perpendicular height of bottom pyramid is 20mm, length and width of joint base area both x, find x. Please help me
Answer: 15 m
Step-by-step explanation:
Given
Total volume of the combined pyramid is \(V=2700\ mm^3\)
Height of top and bottom pyramid is
\(h_t=16\ mm\)
\(h_b=20\ mm\)
If the base has a side length of x, its area must be \(x^2\)
Volume of square prism is given by
\(\Rightarrow V=\dfrac{1}{3}Bh\quad [\text{B=base area}]\\\\\text{Total volume will be the sum of the two pyramids}\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times 16+\dfrac{1}{3}\times x^2\times 20\\\\\Rightarrow 2700=\dfrac{1}{3}\times x^2\times (16+20)\\\\\Rightarrow x^2=225\\\Rightarrow x=15\ mm\)
Thus, the value of \(x\) is 15 m.
One number is 6 times another number and their difference is 30 . find the numbers.
Step-by-step explanation:
7x6=42. 7+35=42. The numbers are 7 and 42.
Find the length of the third side. If necessary, write in simplest radical form.
Answer:
6
Step-by-step explanation:
This is a right triangle, and so the Pythagorean Theorem applies. The legs of this triangle are 3√3 and 3; squaring these gives us 9(3) = 27 and 9. Then, this Theorem gives us the length of the hypotenuse as
h^2 = 27 + 9, or h^2 = 36, so that h, the length of the hypotenuse, must be 6.
The measure of an angle is 97º. What is the measure of its supplementary angle?
\({ \color{teal}{ \huge{ \textsf{ \textbf{Answer}}}}}\)
We can calculate supplementary angles by subtracting the given one angle from 180 degrees. To find the other angle, use the following formula: ∠x = 180° – ∠y or ∠y = 180° – ∠x where ∠x or ∠y is the given angle.
The supplementary of 97° is (180°-97°)=83°
PLEASSSSEEEEEEEEE HELLLLLPPPPPPPPPPPPPPP
Q what is 2+2
A A.4 B. 1 C 2 D 3
The sum of five times a number and three is between -7 and 23.
The number of the given statement will be inequality -2 < x < 4.
We have been given the statement "the sum of five times a number and three is between -7 and 23".
Let the number would be x
As per the given statement, we can represent this algebraic form with inequality as:
⇒ -7 < 5x + 3 < 23
Subtract 3 on both sides of the above inequality
⇒ -7 - 3 < 5x < 23 - 3
⇒ -10 < 5x < 20
Divided by 5 into both sides of the above inequality
⇒ -2 < x < 4
Thus, the number of the given statement will be inequality -2 < x < 4.
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The question seems to be incomplete the correct question would be
Find the number if the sum of five times a number and three is between -7 and 23.
Can somebody tell me what 365 times 45 is??
Answer:
16,425
Step-by-step explanation:
For future references, I'd say use a calculator for multiplication or calculate on a piece of paper. :)
Step-by-step explanation:
please mark me as brainlest
Will give brainliest to the first person who answers
Answer:
z =86
Step-by-step explanation:
The exterior angle of a triangle is the sum of the opposite interior angles
z + z-39 = z+47
2z-39 = z+47
Subtract z from each side
z-39 = 47
Add 39 from each side
z = 47+39
z =86
The given information is,
To find the required value of z.
Property we use,
The exterior angle of a triangle is the sum of the opposite interior angles.
Now we can get the value of z,
→ z + z-39 = z + 47
→ 2z-39 = z + 47
→ 2z -z = 47 + 39
→ z = 47 + 39
→ [z = 86]
Thus, the required value of z is 86.
Both legs are 14, what is the hypotenuse?
Answer:
radical 392
or
19.79898987
Step-by-step explanation:
Take the first 4 digits of your student number as the first number and the last 3 digits as the second number. Write the matlab code to find the greatest common divisor of these numbers using the Euclidean algorithm.
The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.
To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:
% Replace '12345678' with your actual student number
studentNumber = '12345678';
% Extract the first 4 digits as the first number
firstNumber = str2double(studentNumber(1:4));
% Extract the last 3 digits as the second number
secondNumber = str2double(studentNumber(end-2:end));
% Find the GCD using the Euclidean algorithm
gcdValue = gcd(firstNumber, secondNumber);
% Display the result
disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);
Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.
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In a certain region the electric potential is given by the formula V(x, y, z)=2x2y+2y3z−4z4x. Find the components of electric field and the vector electric field at point (1,1,1) in this field.
The vector electric field at point (1,1,1) is:
E = E_xî + E_yĵ + E_zk = 0î - 8ĵ + 14k
To find the electric field components and vector at point (1,1,1), we need to take the negative gradient of the electric potential V(x, y, z) at that point.
The gradient of V is given by the vector:
∇V = (∂V/∂x)î + (∂V/∂y)ĵ + (∂V/∂z)k
where î, ĵ, and k are the unit vectors in the x, y, and z directions, respectively.
Taking partial derivatives of V with respect to x, y, and z, we get:
∂V/∂x = 4xy - 4z^4
∂V/∂y = 2x^2 + 6y^2z
∂V/∂z = 2y^3 - 16z^3x
Evaluating these partial derivatives at (1,1,1), we get:
∂V/∂x = 4(1)(1) - 4(1)^4 = 0
∂V/∂y = 2(1)^2 + 6(1)^2(1) = 8
∂V/∂z = 2(1)^3 - 16(1)^3(1) = -14
Therefore, the components of the electric field at point (1,1,1) are:
E_x = -∂V/∂x = 0
E_y = -∂V/∂y = -8
E_z = -∂V/∂z = 14
So the vector electric field at point (1,1,1) is:
E = E_xî + E_yĵ + E_zk = 0î - 8ĵ + 14k
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Helppppp 2 - 2x - 4= –2x + 5
Answer: Unless I am missing something, there are no solutions
(guessing you need to solve for x)
(given) 2 - 2x - 4= –2x + 5
(combine like terms) -2 -2x = -2x + 5
(add 2 to both sides) -2x = -2x + 5
Two ways to go from here:
(subtract 2x from both sides) 0 = 7 which I think means no solutions
Or you try to figure something out, but I am not sure what that would be currently, it's been a bit since I've done this, good luck!
1.1. How many m³ = are there in 3( mile )³
1.2. How many gal/min correspond to 5ft³ /s. 1.3. Convert the following: 9.50 cm to nm/sec² (5)
Using the conversion factors, we find that 3 cubic miles is approximately equal to 1.2504543 × 10^10 cubic meters. 5 cubic feet per second is equal to 2244.156 gallons per minute. 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.
1.1. One mile is equal to 1609.34 meters. Since we're dealing with cubic units, we cube the conversion factor.
1 mile = 1609.34 meters
1 mile³ = (1609.34 meters)³ = 4.168181 × 10^9 cubic meters
Therefore, 3 cubic miles is equal to 3 * 4.168181 × 10^9 cubic meters, which is approximately 1.2504543 × 10^10 cubic meters.
1.2. To convert from cubic feet per second (ft³/s) to gallons per minute (gal/min), we use the appropriate conversion factors.
Here are the conversion factors:
1 cubic foot = 7.48052 gallons
1 minute = 60 seconds
So, we set up the conversion as follows:
5 ft³/s * 7.48052 gal/ft³ * 60 s/min = 2244.156 gal/min
Therefore, 5 cubic feet per second is equal to 2244.156 gallons per minute.
1.3. To convert centimeters (cm) to nanometers per second squared (nm/sec²), we use the appropriate conversion factors. Here are the conversion factors:
1 centimeter = 10^7 nanometers
1 second = 1 second
So, we set up the conversion as follows:
9.50 cm * (10^7 nm/cm) / (1 sec)² = 9.50 * 10^7 nm/sec²
Therefore, 9.50 centimeters is equal to 9.50 * 10^7 nanometers per second squared.
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If b=24 and c=10 what is for the missing side a= ? by Use the Pythagorean Theorem to find
Answer:
a = 21.82 if and only if b=10 and c=24
if you meant b=24 c=10
there can't be such a triangle because the hypotenuse is the longest side
Step-by-step explanation:
\(a^2+b^2=c^2\\\\a=?\\\\b=24\\\\c=10\\\\\\a^2+(24)^2=(10)^2\\\\a^2=(10)^2-(24)^2\\\\a^2=(10-24)(10+24)\\\\a^2=-14(34)\)
which doesn't work because something squared can't be a negative
if you meant
c=24 and b=10
\(a^2+(10)^2=(24)^2\\\\a^2=(24)^2-(10)^2\\\\a^2=(24-10)(24+10)\\\\a^2=(14)(34)\\\\a\approx 21.82\)
9514 1404 393
Answer:
a = 26 or 21.82
Step-by-step explanation:
If 'a' is the hypotenuse, then ...
a² = b² +c²
a² = 24² +10² = 576 +100 = 676
a = √676 = 26 . . . if 'a' is the hypotenuse
__
If 'a' is the long side, then ...
b² = c² + a²
b² -c² = a² = 24² -10² = 576 -100 = 476
a = √476 ≈ 21.82 . . . if 'a' is the long leg
__
Comment on the question
The problem statement doesn't tell us what side of the triangle is labeled 'a'. There are two possibilities. An answer has been provided for each. Use the one that applies to the figure you are given.
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
You owe $561.54 on your credit card. The minimum payment is $45.00 and the interest rate on the credit card is
1.5% What is the interest charged?
The interest charged on your credit card is $0.65.
How to find the interest charged?To calculate the interest charged on your credit card, we first need to determine the balance after making the minimum payment.
After making the minimum payment of $45.00, the remaining balance on your credit card would be:
$561.54 - $45.00 = $516.54
Next, we need to calculate the monthly interest rate. The annual interest rate is 1.5%, so the monthly interest rate is:
1.5% / 12 = 0.125%
To calculate the interest charged, we can multiply the monthly interest rate by the remaining balance:
0.125% * $516.54 = $0.65
Therefore, the interest charged on your credit card is $0.65.
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2. A cylinder has a height of 4.5 cm and a diameter of 1.5 cm. What is the surface area of the cylinder in square centimeters? Use 3.14 for pi.
21.2
31.8
7.9
24.7
Answer:
\( SA = 24.73~cm^3 \)
Step-by-step explanation:
\( SA = 2\pi r^2 + 2\pi r h \)
r = d/2 = (1.5 cm)/2 = 0.75 cm
\( SA = 2(3.14)(0.75~cm)^2 + 2(3.14)(0.75~cm)(4.5~cm) \)
\( SA = 24.73~cm^3 \)
Answer:
24.7
Step-by-step explanation:
took this exam and got it right
if a is an nxn matrix that has n linearly independent eigenvectors, prove that also has n linearly independent eigenvectors.
To prove that a matrix A with n linearly independent eigenvectors also has n linearly independent eigenvectors, we need to use the fact that eigenvectors corresponding to distinct eigenvalues are linearly independent.
Let λ1, λ2, ..., λn be the n distinct eigenvalues of A with corresponding eigenvectors v1, v2, ..., vn, respectively. Since these eigenvectors are linearly independent, we know that any linear combination of them that equals the zero vector must have all coefficients equal to zero.
Suppose now that there exists a linear combination of these eigenvectors that equals the zero vector, say c1v1 + c2v2 + ... + cnvn = 0, where not all ci are zero. Without loss of generality, assume that c1 is nonzero. Multiplying both sides of this equation by A, we obtain
c1λ1v1 + c2λ2v2 + ... + cnλnvn = 0.
Since λ1, λ2, ..., λn are distinct, we know that λ1 cannot be equal to λ2, λ3, ..., λn. Therefore, we can divide both sides of the above equation by λ1 and obtain
c1v1 + (c2λ2/λ1)v2 + ... + (cnλn/λ1)vn = 0.
This equation shows that we have a nontrivial linear combination of the eigenvectors that equals the zero vector, contradicting the assumption that they are linearly independent. Therefore, our original assumption must be false, and we conclude that A has n linearly independent eigenvectors.
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a publisher reports that 52% 52 % of their readers own a laptop. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 190 190 found that 45% 45 % of the readers owned a laptop. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is -2.18.
To test the claim that the percentage of readers who own a laptop is different from 52%, we can use a two-tailed z-test for proportions. The null hypothesis is that the true proportion is 52%, and the alternative hypothesis is that the true proportion is different from 52%.
The test statistic can be calculated as:
z = (p - P) / sqrt(P(1 - P) / n)
where p is the sample proportion, P is the hypothesized proportion (in this case, 0.52), and n is the sample size.
Substituting the given values, we get:
z = (0.45 - 0.52) / sqrt(0.52(1 - 0.52) / 190)
z = -0.07 / 0.039
z = -1.79
The value of -1.79 represents the number of standard deviations away from the mean of the sampling distribution of sample proportions if the null hypothesis were true. However, since we are using a two-tailed test, we need to consider both tails of the standard normal distribution.
The critical value for a two-tailed test at the 0.05 level of significance is ±1.96. Since -1.79 is within the range of -1.96 to 1.96, we fail to reject the null hypothesis. Therefore, the correct answer is -2.18.
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Which system of measurement uses the minim as the basic unit of liquid measure?
The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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Find the volume of the right cone below.
Round your answer to the nearest tenth if necessary.
Answer:
261.8 units³
Step-by-step explanation:
Volume of Cone = \(\pi r^2\frac{h}{3}\)
We are given the radius as 5 and the height as 10.
\(\pi * (5)^2 (\frac{10}{3})\) \(\pi * 25 * \frac{10}{3}\) \(\frac{250}{3} * \pi\) 261.799 ≈ 261.8The volume of the right cone is 261.7 unit³.
What is volume?Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.
The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
We have,
Height of cone= 10
Radius= 5
So, Volume of cone
= 1/3 πr²h
=1 /3 (3.14)(5)² 10
= 1/3 x 3.14 x 250
= 261.66
= 261.7 unit³
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3xy - 15x + y ^ 2 - c In the polynomial above, c is a constant. If the polynomial is divisible by y - 5 , what is the value of c?
Answer:
25
Step-by-step explanation:
Synthetic division shows the remainder to be 25-c. In order for that remainder to be zero, the value of c must be 25.
Write three numbers that are divisible by 2, 4, 8, and 10
Answer:
40, 80, 120
Step-by-step explanation:
-they’re common multiples of 2, 4, 8, and 10
reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
How many kilometers is the race?
Enter your answer as a decimal in the box.
20 point 1 6
km
Total distance of the triathlon race is 23.34 kilometers.
Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
The total distance of the race is 23.34 kilometers.
Reg enters a triathlon race.
He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.
In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km
Total distance = 23.34 km.
The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.
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2. Jane, Susan and Mary walk to school every day.
Walking to school and back, Jane walks 1.12 miles, Susan
walks 0.97 miles and Mary walks 1.18 miles. How much
do Jane, Susan and Mary walk
Answer:
3.27 milesStep-by-step explanation:
GivenThe distance walked by three students:
Jane - 1.12 milesSusan - 0.97 milesMary - 1.18 milesFind the total distanceAdd up all three:
1.12 + 0.97 + 1.18 = 3.27 milesplease solve!!!!!!!!!!!!!!!!!!!!!!!
Solution:
We know that:
\(\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times \tex\text{Base} \times \tex\text{Height}\)
Let the base of the triangle be 11 yd. If we extend the base, it will allow us to find the height of the triangle, which is 8 yd.
Using the formula:
\(\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8\)
Now, let's simplify.
\(\bullet \ \ \tex\text{Area of triangle:} = \frac{1}{2} \times 11 \times 8\)
\(\bullet \ \ \tex\text{Area of triangle:} = 11 \times 4\)
\(\boxed{\bold{\tex\text{Area of triangle:} = 44 \ \tex\text{yd}^{2}}}\)
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
The value of the constant of variation include 8, 3.2, and 1.25
How to find the constant?From the information given, when x = -0.5, y = -4.0. The constant will be:
y = kx
-4 = -0.5k
k = -4.0/-0.5
k. = 8
When x = 2.5, y = 8
y = kx
8 = 2.5k
k = 8/2.5
k = 3.2
When x = 4, y = 5
y = kx
5 = 4k
k = 5/4
k = 1.25
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Where is the graph of f(x)=4[x-3]+2 discontinuos
Answer:
Below
Step-by-step explanation:
4 [x-3] + 2 = y is not discontinuous anywhere
However 4 / [x-3] + 2 DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!
I don’t get this math problem4/5 + 3/4
Answer:
AS a fraction: 1\(\frac{11}{20}\)
AS a decimal: 1.55
Step-by-step explanation:
4/5 + 3/4
least common multiple of 5 and 4 is 20. Conver \(\frac{4}{5}\) and \(\frac{3}{4}\) to fractions with denominator 20.
16/20 + 15/20
since \(\frac{16}{20} and \frac{15}{20}\) have the same denominator, add them by adding their numerators.
\(\frac{16 + 15}{20}\)
Add 16 and 15 to get 31.
\(\frac{31}{20}\)
\(\frac{31}{2^{2}x5 } = 1\frac{11}{20}\)
Hope that helps and have a great day! =) ~sunshine~