Answer:
The value of m is [tex]-\frac83[/tex].
Step-by-step explanation:
If two vectors [tex]\vec A[/tex] and [tex]\vec B[/tex] are perpendicular to each other then their dot product will be zero i.e [tex]\vec A.\vec B=0[/tex]
If two vectors [tex]\vec A[/tex] and [tex]\vec B[/tex] are parallel to each other then their cross product will be zero i.e [tex]\vec A\times\vec B=\vec 0[/tex]
Given vectors are a= (3,4) and b=(m,2)
The position vector of [tex]\vec a[/tex] is =[tex]3 \hat i+4\hat j[/tex]
The position vector of [tex]\vec b[/tex] is =[tex]m \hat i+2\hat j[/tex]
Since [tex]\vec a[/tex] and [tex]\vec b[/tex] are perpendicular.
Then,
[tex]\vec a. \vec b=0[/tex]
[tex]\Rightarrow (3\hat i+4\hat j).(m\hat i+2 \hat j)=0[/tex]
⇒3.m +4.2=0
⇒3m+8=0
⇒3m= -8
[tex]\Rightarrow m=-\frac 83[/tex]
The value of m is [tex]-\frac83[/tex].
A rice store estimates that if it sells each pack of rice forxdollars, then the projected number of packssold daily is 240−10x. What is the price per pack that maximizes its daily profit?
Answer:
Price per pack = 12
Step-by-step explanation:
The profit can be calculated as the product of the price by the quantity sold:
P = x * (240-10x)
P = -10x^2 + 240x
To find the maximum of this quadratic function, we can use the formula to find the vertix:
x_v = -b/2a
Where a and b are coefficients of the quadratic equation (a = -10 and b = 240)
x_v = -240/(-20) = 12
Now, we use this value to find the maximum profit:
P_max = -10*(12)^2 + 240*12 = 1440
can someone solve this for me?
Answer:
d 125
Step-by-step explanation:
Supplementary angles add to 180 degrees
Let x be the supplement to the 55 degree angle
55+ x =180
Subtract 55 from each side
55+x-55 =180-55
x = 125
What is the maximum number of miles that Joseph can drive in order for Company B to be a better buy? The company charges only for whole number mileage (not fractional increments of miles driven).
The question is incomplete. Here is the complete question:
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that offer different pricing
options for car rentals. Company A charges $0.25 per mile plus a $50 rental fee. Company B charges $0.45 per mile plus a $20
rental fee.
What is the minimum number of miles that Joseph must drive in order for Company A to be a better buy? The company charges only
for whole number mileage (not fractional increments of miles driven).
Answer:
149 miles.
Step-by-step explanation:
Please kindly check the attached files for explanation.
Answer:
the correct answer is d) 151
Step-by-step explanation:
In scaling, the number by which you multiply is called the_________
Answer: Multiplicand.
Abigail invested $29,000 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 8 years?
Final answer:
Using the formula for continuous compounding A = Pert, the amount in the account after 8 years will be approximately $34,305 when $29,000 is invested at a 2.1% interest rate, compounded continuously.
Explanation:
Abigail invested $29,000 in an account with an interest rate of 2.1% compounded continuously. To calculate the amount of money that would be in the account after 8 years, we use the formula for continuous compounding: A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), e is the base of the natural logarithm, r is the annual interest rate (as a decimal), and t is the time in years. Plugging in the values: A = 29000e0.021×8.
The calculation results in A ≈ 29000×e0.168≈ 29000×1.18301 = $34305.29. After rounding to the nearest dollar, the amount in the account after 8 years will be $34,305.
Final answer:
To the nearest dollar, there would be approximately $36,884 in Abigail's account after 8 years.
Explanation:
To calculate the future value of an investment with continuous compounding, we can use the formula: A = Pe^(rt), where A is the future value, P is the initial amount, e is a mathematical constant approximately equal to 2.71828, r is the interest rate, and t is the time in years.
For Abigail's investment, P = $29,000, r = 0.021 (2.1% as a decimal), and t = 8 years. Plugging those values into the formula, we get:
A = 29000 * e^(0.021 * 8) ≈ 29,000 * e^0.168 ≈ $36,883.65
Therefore, to the nearest dollar, there would be approximately $36,884 in Abigail's account after 8 years.
The volume of a cone is 7351 cubic millimeters and the height is 5 millimeters. What is the radius of the cone?
Answer:
The radius of the cone is 37.47 mm
Step-by-step explanation:
[tex]V= \frac{1}{3}\pi } r^{2}h[/tex] Substitute values given V=7351 h=5
[tex]7351 = \frac{1}{3} \pi r^{2}(5)[/tex] solve for r^2 by dividing volume by [tex]\frac{15.7}{3}[/tex] which is 7351/5.2333 to get
[tex]1404.65=r^{2}[/tex] Take square root of both sides [tex]\sqrt[2]{1404.65} =37.47[/tex]
r = 37.47
Donation Amounts (in dollars) A charity receives donations ranging from 5 to 35 dollars. The donation amounts from 10 different people were used to create the box plot shown above. Which of the sets of donation amounts below matches the given box plot? A. Donation Amounts: 5, 10, 15, 15, 15, 25, 25, 25, 30, 35 B. Donation Amounts: 5, 10, 15, 15, 15, 15, 25, 25, 35, 35 C. Donation Amounts: 5, 10, 15, 15, 15, 25, 25, 30, 35, 35 D. Donation Amounts: 5, 10, 10, 15, 15, 25, 25, 25, 35, 35
Without an actual box plot to reference, it's impossible to accurately determine which set of donation amounts correctly corresponds to the box plot in question.
Explanation:The question seeks to identify the set of donation amounts that matches a given box plot. When analyzing sets of donation amounts to determine which one aligns with a box plot, we look for key features such as the minimum, the maximum, the median, and the quartiles. These features divide the data set into four parts of equal importance, helping us understand the distribution of the data.
Given that there isn't an actual box plot provided, we would typically compare the given options against the features one would expect to find in a box plot:
Minimum and maximum values to set the range.Quartiles that split the data into four equal parts.Median as the middle value when the data is sorted.However, without the specific details of the box plot, such as the exact median or quartile values, we cannot accurately determine which set of donations matches the box plot. Typically, an analysis would involve calculating or identifying these characteristic numbers from each option and then seeing which one fits the description given by the box plot.
Identify the volume of a cone with diameter 18 cm and height 15 cm.
Answer:
405π
Step-by-step explanation:
π[tex]r^2\frac{h}3}[/tex]
Diameter is twice the radius. So divide 18 by 2 which is 9.
π[tex]9^2\frac{15}{3}[/tex]
Now just simplify:
π·81·5
405π
Volume of cone is 1272.34502 [tex]cm^{3}[/tex]
What is volume of cone?The volume of a cone is defined as the amount of space or capacity a cone occupies. The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone.
Given
Diameter of cone = 18 cm
Radius of cone = [tex]\frac{18}{2}[/tex] = 9 cm
Height of cone = 15 cm
Volume of cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
= [tex]\frac{1}{3} \pi (9)^{2} (15)[/tex]
= 1272.34502 [tex]cm^{3}[/tex]
Hence, volume of cone is 1272.34502 [tex]cm^{3}[/tex]
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C is the center of the circle. Find the length of OPR.
A. S = 23.55
B. s = 47.10
C. S = 70.65
D. S = 141.30
Answer: 141.30
Step-by-step explanation:
The length of [tex]\( \overline{OPR} \)[/tex] cannot be determined without additional information about the circle's radius or the angle [tex]\( \angle OCR \).[/tex]
To find the length of [tex]\( \overline{OPR} \),[/tex] we need to calculate the circumference of the circle, since [tex]\( \overline{OPR} \)[/tex] is an arc of the circle.
The circumference of a circle is given by the formula [tex]\( C = 2\pi r \),[/tex] where \( r \) is the radius of the circle.
However, we are not given the radius of the circle. Therefore, without additional information about the circle's radius or the angle [tex]\( \angle OCR \),[/tex] we cannot determine the length of [tex]\( \overline{OPR} \).[/tex]
Since we cannot determine the length of [tex]\( \overline{OPR} \)[/tex] with the given information, none of the provided options are correct.
Miguel is comparing the probabilities of two spinners.
Which of the following statements is true? Select all that apply.
A is False, there are three 1's on A and 1 on B, so it is 3 times more likely.
B is True, there are 4 total numbers and 2 are even, so 2/4 = 1/2
C is True, there are three 1's and 8 total numbers so 3/8 is true.
D is False, there are different quantities of different numbers so it's not fair.
E is True, there is a /2 probability of each spinner landing on odd.
(-3p^3+ 5p^2- 2p) +(-p^3- 8p^2 – 15p) =
Answer:
[tex]-4p^3-3p^2-17p[/tex]
Step-by-step explanation:
Combine like terms:
[tex]-3p^3+ 5p^2- 2p -p^3 - 8p^2-15p=-4p^3-3p^2-17p[/tex]
The (-3p³ + 5p² - 2p) +(-p³ - 8p² – 15p) can be simplified as -4p³ - 3p² - 17p
What are polynomials?Polynomials are expression that can have constant, variables and exponents.
Therefore,
(-3p³ + 5p² - 2p) + (-p³ - 8p² – 15p)
we have to use the positive value outside to open the bracket.
-3p³ + 5p² - 2p - p³ - 8p² - 15p
-3p³ - p³ + 5p² - 8p² - 2p - 15p
Hence,
-3p³ - p³ + 5p² - 8p² - 2p - 15p = -4p³ - 3p² - 17p
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The World Health Organization analyzed generic drugs in 45 countries. It collected 3,575 samples. The sample proportion that tested as placebo was 0.01. What can you conclude about generic drugs from the population proportion? Answer in complete sentences.
Answer:
People's health benefits from the drug is very low.
Step-by-step explanation:
From the question, the generic drugs from the population proportion has 1% placebo effect which is very low. This means that the beneficial health outcome resulting from people ’s anticipation that an intervention will help from the generic drug is very low.
Look at the following numbers:
−3, −1, 0, 3
Which pair of numbers has a sum of 0? (5 points)
Group of answer choices
0, −1
−3, 3
−1, 3
−1, 0
Answer:
-3 and 3
Step-by-step explanation:
when -3 and and 3 are added it sums up to 0. For example, any number that's positive (ex. 5) and the same number with the opposite sign (ex. -5) are added it will always be 0.
What is the value of X?
Answer:
Step-by-step explanation:
x^2=4^2+4.7^2
x^2=38.09
x=√38.09
x=6.1717
x=6.2(nearest tenth)
Note that x=radios of the circle
A chest of drawers was originally priced at $100, but Sam waited to buy it until the chest of drawers was on sale for 80% off. If he paid 10% sales tax on the sale price, how much did he pay in total?
Answer:
$25
Step-by-step explanation:
Since it was originally $100, 80% off would mean he would only have to pay $20 for it. But sales tax, you would have to add 10% back of the sale price which was $20. so, 10% of 20 is $5. The sale price, $20, plus the $5 is 25 dollars he had to pay.
After waiting for a 80% off discount, Sam purchased the dresser for $20. Including a 10% sales tax, he paid a total of $22.
Explanation:In this problem, we first need to figure out what 80% off of the original $100 price is. This can be done by converting the 80% discount to a decimal (0.8) and then multiplying it by the original cost ($100). This gives us $80.
However, since this is the amount discounted, we subtract it from the original price to get the sale price of the chest of drawers, so $100 - $80 = $20. This is how much Sam paid before sales tax.
Next, we need to calculate the sales tax amount. We first convert the 10% sales tax to a decimal (0.10), and then we multiply it by the sale price ($20). This gives us $2 in sales tax.
Finally, we add the sales tax to the sale price to get the total amount Sam paid for the chest of drawers: $20 + $2 = $22. So, Sam paid a total of $22 for the chest of drawers.
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A rectangular prism has a length of 6 meters, a height of 8 meters, and a width of 5
meters. What is its volume, in cubic meters?
Answer: V =
meters
Submit Answer
help me pls give u a brainlest
The table shows the results of rolling a number cube, with sides labeled 1 through 6, several times.
What is the experimental probability of rolling a 2 or a 4?
Enter your answer as a fraction in simplest form, in the box.
Answer:
P(2 or 4) = 6/40 + 8/40 = 14/40 = 7/20
A portion of the graph of f(x) = −x2 − 10x − 21 is shown. Which of the following describes all solutions for f(x)?
(x, x2 − 10x − 21), where −7 ≤ x ≤ −3
(x, y), where −7 ≤ x ≤ −3
(x, x2 − 10x − 21), where −8 ≤ x ≤ −2
(x, y) for all real numbers
Answer: C because x is greater then it.
The function that describes all solutions for f(x) is C. (x, x2 − 10x − 21), where −8 ≤ x ≤ −2 because x is greater than it.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given equation of the function is;
-x²-10x-21=0
To solve for x;
x²+10x+21=0
x²+7x+3x+21=0
(x+7)(x+3)=0
thus, the solution is x=-7 OR -3.
Hence, The function that describes all solutions for f(x) is C. (x, x2 − 10x − 21), where −8 ≤ x ≤ −2 because x is greater than it.
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Suppose you double the radius length of a circle. What happens to the circumference and to the number of radii that will fit around the circle?
If you double the radius of a circle, the circumference also doubles; however, the number of radii that can fit around the circumference remains unchanged.
Explanation:If you double the radius of a circle, the circumference of the circle also doubles because the formula for the circumference of a circle is 2πr (`r` being the radius). Thus if `r` becomes 2r, the circumference becomes 2(2πr) or 4πr, which is twice the original circumference.
Similarly, if you try to fit radii around the circle, you would find that exactly the same number of radii will fit around the circle as before. This is because the radius is the distance from the center of the circle to the circumference, and no matter how long the radius is, you can always fit exactly 2π radii around the circumference. Doubling the radius length therefore does not alter the number of radii that can fit around the circle.
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An image of a rectangular pyramid is shown below:
A right rectangular pyramid is shown.
Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer.
Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer.
Answer:
b
Step-by-step explanation:
Answer:
The shape of the cross-section is a square. The plane is parallel to the base of the triangular pyramid and the base is a square.
Step-by-step explanation:
two data sets have similar variabilities. suppose the measures of center of the data sets differ by 4 times the measure of variation. describe the visual overlap of the data.
Answer:
When two data sets have similar populations, the value of difference measures at the center as a measure of multiple variation will tend to overlap.
Step-by-step explanation:
When two data sets have similar variables, at the center as a multiple, the value of the difference measures of of variation explains the visual overlap.
Normally, the higher the value, the less the overlap populations . since it is known that the value is 4 which is small, the population should have an amount that is large of overlap.
Final answer:
When measures of center differ from measures of variation by 4 times, it implies significant differences in data sets, visually showing minimal overlap with separated distributions.
Explanation:
Measures of center and variation: When the measures of center of two data sets differ by 4 times the measure of variation, it indicates a significant difference in the central tendencies of the data sets. The visual overlap of the data sets would be minimal, with the distributions of the two data sets largely separated rather than overlapping.
How many distinguishable 5-letter combinations are possible of the letters of the word TIGHT?
A. 40
B. 60
C. 72
D. 120
Answer:
A. 40 combinations
we have 8 x 5 = 40
Step-by-step explanation:
Would be 60 as 3 letter words with 5 letters.
The logic is that all letters are being used to their maximum and with numbers 3 within 5 or 5 within 5 the maximum that cna be used is 12 rotation for 3 per letter or 8 rotaion for 5. Then we have 5 rotations = 60 for 3 and 40 for 5. Another logic is the many combinations can you make from the numbers 1 2 3 4 5 not multiplying?
The rearrangement of 5 figure numbers will be 5x4x3x2x1 which is 120 combinations, when you don't repeat a number.
We see that 4+3 +2+1 = 10 and shows less than 5 number combinations at 120, and then we have 5
5:10 ratio = 5/15 = 1/3
This = 1/3 of 120 =40
Then we find answer is 40 as compact 5 letter words from the word tight.
Solve the equation.Find the product of each sum and difference. (2c + 8)(2c – 8)
Answer:
4c^2 - 16c + 16c - 64
4c^2 - 64
Step-by-step explanation:
Answer:
= 4c² - 64
Step-by-step explanation:
(2c + 8)(2c – 8)
= 4c² - 16c + 16c - 64
= 4c² - 64
Use the following terms to complete the following statements: integers, rational
numbers, and whole numbers. Use each term only once.
The counting numbers and zero are ___
The counting numbers and their opposites, along with zero,
are ___
Integers and the decimal equivalents of fractions are ___
Answer:
the counting numbers and zero are whole numbers.
the counting numbers and their opposites, along with zero, are integers.
integers and decimal equivalents of fractions are rational numbers.
Answer:
Answer:
the counting numbers and zero are whole numbers.
the counting numbers and their opposites, along with zero, are integers.
integers and decimal equivalents of fractions are rational numbers. hoped this helped
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
x = −5
x = −1
x = 1
x = 5
Answer:x=5
Step-by-step explanation: x^2−2x−15=0
(x−5)=0 x−5=0 x=5
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Explain the steps in calculating the mean absolute deviation of a set of data.
Step-by-step explanation:
1. To find the mean absolute deviation of the data, start by finding the mean of the data set.
2. Find the sum of the data values, and divide the sum by the number of data values.
3. Find the absolute value of the difference between each data value and the mean: |data value – mean|.
4. Find the sum of the absolute values of the differences.
5. Divide the sum of the absolute values of the differences by the number of data values.
Answer:
Sample Answer: First, find the mean of the data set by averaging. Next, find the absolute deviations for each data point. That is, find the distance each point is from the mean. Then find the mean of the absolute deviations.
Which did you include in your explanation? Check all that apply.
Find the mean of the set of data.
Find the absolute deviations for each point.
Absolute deviation is a data point’s distance from the data set’s mean.
Find the mean of the absolute deviations.
The diameter, D, of a sphere is 8.4 mm. Calculate the sphere's volume, V.
Use the value 3.14 for a, and round your answer to the nearest tenth
Answer:
73.8 cubic mm.
Step-by-step explanation:
The volume of a square V is given by the formula:
[tex]V= \frac{4}{3}\pi r^{2}[/tex] where r is the radius of the sphere.
We also know that the diameter is two times the radius, so in this case if the diameter is 8.4 mm, then the radius is 4.2 mm.
Now we substitute the information in the formula, taking into account that we are going to use the value of 3.14 for [tex]\pi[/tex].
[tex]V= \frac{4}{3}\pi r^{2}\\ V= \frac{4}{3}(3.14)(4.2)^{2} \\V=\frac{(4)(3.14)(17.64)}{3} \\V=\frac{221.55}{3}=73.8528[/tex]
Which rounded to the nearest tenth is 73.8. Thus, the sphere's volume is 73.8 cubic mm.
Answer:
V = 310.2 mm³
Step-by-step explanation:
The formula for volume of a sphere is given as:
V = 4/3 * π * r³
where r is the radius of the sphere.
We are given the diameter in the question. Diameter is twice the radius. So, radius = diameter/2
radius = 8.4/2
radius = 4.2 mm
V = 4/3 * π * r³
= 4/3 * 3.14 * (4.2)³
V = 310.181
V = 310.2 mm³
Order which number is the greatest?
−1925, −0.33, −0.680, −520
Answer:
-0.33 is the greatest
Step-by-step explanation:
help fast will mark as brainlist Which formula should be used to find the circumference of a circle?
C = pi d
C = 2 pi d
C = pi r
C = StartFraction pi over d EndFraction
Answer:
The correct answer is 2 pi d
Step-by-step explanation: