The temperature decreased by 41°F during the overnight hours.
What is scalar and vector quantity?Physical quantities with merely magnitude and no direction are called scalar quantities. Scalar values encompass things like mass, volume, temperature, and time. Real numbers, such as positive or negative integers or decimals, are frequently used to represent scalar quantities in mathematics.
In contrast, a vector quantity is a physical quantity that possesses both magnitude and direction. The terms displacement, velocity, force, and acceleration are all examples of vector quantities. Typically, vector values are represented by a number or symbol for the magnitude and an arrow or boldface letter for the direction.
Given that, the temperature went from 28 to -13.
The expression that represent this change are:
Expression 1: -13°F - 28°F
Expression 2: | -13°F - 28°F |
The temperature change can be calculated as:
| -13°F - 28°F | = |-41°F| = 41°F
Hence, the temperature decreased by 41°F during the overnight hours.
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help ASAP PLSSSS
The table of values represents a linear function.
Enter the rate of change of this function.
The rate of change (or slope) of this linear function is -1/2.
Describe Linear Function?A linear function is a mathematical function that has a constant rate of change, meaning that the output (y-value) changes at a constant rate for every unit increase in the input (x-value). In other words, the graph of a linear function is a straight line.
The general form of a linear function is y = mx + b, where m is the slope of the line (the rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The slope represents how much the y-value changes for every one-unit increase in the x-value.
Linear functions can be used to model many real-world situations, such as distance vs. time or cost vs. quantity. They are also commonly used in economics, physics, and engineering.
The rate of change of a linear function represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y) / (change in x)
Let's use the points (0, -3) and (2, -4) to calculate the slope:
slope = (-4 - (-3)) / (2 - 0)
slope = -1 / 2
Therefore, the rate of change (or slope) of this linear function is -1/2.
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Graph the system of linear equations.
4x + 3y = 24
-2x + 6y = 18
Use the Line tool to graph the lines.
An inlet pipe on a swimming pool can be used to fill the pool in 16
hours. The drain pipe can be used to empty the pool in 24
hours. If the pool is 13
filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
Answer:
Step-by-step explanation:
Find the prime factorization of 792. What is the sum of the distinct prime factors?
The sum of the distinct prime factors is 16.
Solution:There are overall 24 factors of 792 among which 792 is the most significant factor and its prime factors are 2, 3, and 11.
Hence sum = 2 + 3 + 11 = 16
Figure ABCD is a parallelogram.Parallelogram A B C D is shown. The length of A D is 5 x + 3 and the length of B C is 38.What is the value of x?6789
ABCD is a parallelogram, the value of x is 7
A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.
The opposing sides of a parallelogram are equal and parallel.
AD = BC
5x + 3 = 38
Take 3 away from both sides.
5x + 3 - 3 = 38 - 3
5x = 35
Subtract 5 from both sides.
5x/5 = 35/5
x = 7
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
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The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 grams find the weight that corresponds to each event(use excel or appendix c to calculate the z value. Round your final answers to 2 decimal places)
URGENT
the weight that corresponds to each of the events are:
a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].
b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].
c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].
How to deal with Normal distribution?Let X be the weight of a small Starbucks coffee. We are given that X is normally distributed with mean [tex]$\mu=385$[/tex] grams and standard deviation [tex]$\sigma=8$[/tex].
We want to find the weight that corresponds to each of the following events:
a) The weight is less than 380 grams.
b) The weight is between 375 and 395 grams.
c) The weight is greater than 400 grams.
To solve these problems, we first standardize the distribution by finding the corresponding z-scores using the formula:
[tex]$z=\frac{X-\mu}{\sigma}$$[/tex]
a) The weight is less than 380 grams.
We want to find P(X<380). We can find the z-score for X=380 as follows:
[tex]$z=\frac{380-385}{8}=-0.625$$[/tex]
Using a standard normal table or calculator, we find that the probability P(Z<-0.625)=0.266. Therefore,
[tex]$P(X < 380)=P\left(Z < -\frac{0.625}{1}\right)=0.266$$[/tex]
b) The weight is between 375 and 395 grams.
We want to find [tex]$P(375 < X < 395)$[/tex]. We can find the z-scores for X=375 and X=395 as follows:
[tex]$z_1=\frac{375-385}{8}=-1.25,\quad z_2=\frac{395-385}{8}=1.25$$[/tex]
Using a standard normal table or calculator, we find that the probability P(-1.25<Z<1.25)=0.7887. Therefore,
[tex]$P(375 < X < 395)=P\left(-1.25 < Z < 1.25\right)=0.7887$$[/tex]
c) The weight is greater than 400 grams.
We want to find P(X>400). We can find the z-score for X=400 as follows:
[tex]$z=\frac{400-385}{8}=1.875$$[/tex]
Using a standard normal table or calculator, we find that the probability P(Z>1.875)=0.0304. Therefore,
[tex]$P(X > 400)=P\left(Z > \frac{1.875}{1}\right)=0.0304$$[/tex]
Therefore, the weight that corresponds to each of the events are:
a) The weight is less than 380 grams: [tex]$P(X < 380)=0.266$[/tex].
b) The weight is between 375 and 395 grams: [tex]$P(375 < X < 395)=0.7887$[/tex].
c) The weight is greater than 400 grams: [tex]$P(X > 400)=0.0304$[/tex].
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A photography student took portrait photos of people from his hometown. He wants to
develop 21 of the photos, 9 of which were photos of babies.
If he randomly chooses to make 4 of the photos black and white, what is the probability that
all of them are of babies?
Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:
Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985
Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:
C(9, 4) = (9!)/((4!)(9-4)!) = 126
Therefore, the probability that all 4 photos chosen are of babies is:
P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)
P = C(9, 4)/C(21, 4)
P = 126/5985
P ≈ 0.021
So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.
Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y = mx + b.
x 1 2 3 4 5 6
y 102 114 131 152 176 206
Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50
What is linear regression?
Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.
To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:
The mean of x is 3.5 and the mean of y is 150.
The variance of x is 2.5 and the variance of y is 2203.5.
The covariance of x and y is 607.5.
Using these values, we can calculate the slope of the regression line:
m = covariance of x and y / variance of x = 607.5 / 2.5 = 243
We can also calculate the y-intercept of the regression line:
b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5
Therefore, the equation for the linear function that best fits the given data is:
y = 243x - 16.5
Rounding both numbers to two decimal places, we get:
y = 243x - 16.50
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Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50
What is linear regression?
A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.
To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:
The mean of x is 3.5 and the mean of y is 150.
The variance of x is 2.5 and the variance of y is 2203.5.
The covariance of x and y is 607.5.
Using these values, we can calculate the slope of the regression line:
m = covariance of x and y / variance of x = 607.5 / 2.5 = 243
We can also calculate the y-intercept of the regression line:
b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5
Therefore, the equation for the linear function that best fits the given data is:
y = 243x - 16.5
Rounding both numbers to two decimal places, we get:
y = 243x - 16.50
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You are the marketing manager at The Best Candy Shop where the top sales item is the Dream Pop bags of flavored candies. You have been getting complaints from customers that there are not enough lemon or blueberry flavored candies, which are favorites, and too many grape and strawberry flavored candies. Your boss wants you to create an advertisement indicating, “all bags have equally likely flavors.” (That is, the probability of getting a strawberry flavored candy piece is the same as getting a blueberry flavored candy piece, etc.). As the marketing manager, you want to make sure you are advertising truthful information, so you pull a sample bag of Dream Pop candy and find the following pieces: • 16 grape flavors • 12 strawberry flavors • 6 lemon flavors • 6 blueberry flavors • Explain how you could communicate to your boss that his advertising suggestion (all bags have equally likely flavors) would be incorrect. You must include at least two (2) probabilities from your sample bag of candy that would deem his advice inaccurate.
We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
Based on the sample bag of Dream Pop candy, we can calculate the probability of getting each flavor.
If all bags have equally likely flavors, then each flavor should have the same probability of being selected.
However, we can see from the sample that this is not the case.
To communicate this to the boss, we can calculate the probability of getting two different flavors and compare them.
For example:
The probability of getting a grape flavor is 16/40 or 0.4
The probability of getting a lemon flavor is 6/40 or 0.15
These probabilities are not equal, indicating that the flavors are not equally likely.
We can also compare the probabilities of getting two other flavors, such as:
The probability of getting a strawberry flavor is 12/40 or 0.3
The probability of getting a blueberry flavor is 6/40 or 0.15
Again, these probabilities are not equal, further indicating that the flavors are not equally likely.
Therefore,
We can explain to the boss that the advertising suggestion of "all bags have equally likely flavors" would be inaccurate based on the sample bag of candy.
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Which of the following tables represents a linear relationship that is also proportional?
x 2 3 4
y −3 0 3
x 4 2 0
y −2 −1 0
x −2 1 4
y 0 1 2
x 0 1 2
y −4 0 4
Answer:
This table represents a linear relationship that is also proportional:
x 0 1 2
y −4 0 4
Answer:
The second table represents a linear relationship that is also proportional.
To check if a relationship is proportional, we need to see if the ratio of y to x is constant for all values of x and y. In other words, if we divide any y value by its corresponding x value, we should get the same number for all values.
Let's check the ratio for each table:
Ratio for the first table:
-3/2 = -1.5
0/3 = 0
3/4 = 0.75
The ratio is not constant, so this relationship is not proportional.
Ratio for the second table:
-2/4 = -0.5
-1/2 = -0.5
0/0 = undefined
The ratio is constant (-0.5), so this relationship is proportional.
Ratio for the third table:
0/(-2) = 0
1/1 = 1
2/4 = 0.5
The ratio is not constant, so this relationship is not proportional.
Ratio for the fourth table:
-4/0 = undefined
0/1 = 0
4/2 = 2
The ratio is not constant, so this relationship is not proportional.
Therefore, the second table is the only one that represents a linear relationship that is also proportional.
Which graph matches the function given:
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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please help with with this math
The slope of this linear function is equal to: B. -2/9.
The volume of a cylinder with a height of 10 m and a radius of 5 m is equal to 785 m³.
The value of each expression is: C. a) 2, b) 1/2, c) 2/9.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (8 - 10)/(6 - (-3))
Slope (m) = (8 - 10)/(6 + 3)
Slope (m) =
Slope (m) = -2/9.
How to calculate the volume of a cylinder?In Mathematics, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.By substituting the given parameters, we have:
Volume of cylinder, V = 3.14 × 5² × 10
Volume of cylinder, V = 785 m³
(√2)² = 2
(1/√2)² = 1/2
(√2/3)² = 2/9
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I give brainliest for the answer
The intersection of two parallel lines; x = 10 metres.
Describe another angle using an example.Alternate angles are created when two parallel lines are intersected by a transversal. Have a look at the given illustration; the two parallel lines are EF and GH. When a transversal splits two parallel lines, the alternate angles are equal.
The alternate interior angles are equal because of the parallel lines characteristic.
Angle STQ (denoted as 2x+10) and angle RQS are hence equal. Angle QRP (shown as x+20) and angle RQS are likewise equal.
Setting these two angles equal to each other, we can get:
x+20 = 2x+10
Simplifying this equation, we get:
x = 10.
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Help what’s the answer
Answer:
Difference=£2.4
Step-by-step explanation:
Here in shop A
130 cm=£1.82
1 cm=£1.82/130
1 cm=0.014
Now
400 cm=0.014*400
=£5.6
Again, In shop B
235cm=£1.88
1 cm=£1.88/235
1 cm=£0.008
Now
400cm=0.008*400
=£3.2
Now,
Difference=£5.6-£3.2
=£2.4
Can you help me, please!?
Answer:
The correct answer is (b+2)
Step-by-step explanation:
(3b-7) + (-2b+9)
3b-7-2b+9
3b-2b+9-7
b+2 Ans
Answer:
b+2 is the answer of this expression.
Step-by-step explanation:
(3b-7) and (-2b+9)
3b+(-2b) + (-7+9)
(3b-2b) + 2
b+2
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
√9+25 = 28
π-4 = -0.8571
³√-27 = -3
2 / 3 = 0.6667
18÷2 = 9
√-27 = 5.196
What is surdsIn mathematics, a surd is a term used to describe an irrational number that is expressed as the root of an integer. Specifically, a surd is a number that cannot be expressed exactly as a fraction of two integers, and is usually written in the form of a radical (e.g. √2, √3, √5, etc.).
We have √9+25 = 28
find the square root of 9 = 3
3 + 25 = 28
π-4 = 3.14 - 4
= -0.8571
³√-27 = ³√3³
= 3
2÷3 = 0.6667
18÷2 = 9
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question:
given :√9+25 : π-4 : ³√-27 : 2÷3 : 18÷2 : √-27
find the value of the terms
Please help me on this geometry question. Use a trig function to find the missing side to the nearest 10. Please show step by step
Answer:
x = 42.9
Step-by-step explanation:
We can let 34 represent the reference angle. Using this angle, we see that the side measuring 24 units is the opposite side and the side measuring x is the hypotenuse.
Thus, we can use the sine trig function which is
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
We plug in what we have into the equation above and solve for x:
[tex]sin(34)=\frac{24}{x}\\ x*sin(34)=24\\x=\frac{24}{sin(34)}\\ x=42.9189996\\x=42.9[/tex]
sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
I’m the forest there were lions and tigers and bears the ratio of lions to tigers was 3 to 2 the ratio of tigers to bears was 3 to 4 if there were 9 lions how many bears were there
Answer:
There were 8 bears
Step-by-step explanation:
Letting L = number of lions, T = number of tigers and B = number of bears
L : T = 3 : 2
We can rewrite this as
L/T = 3/2
Cross multiply:
L x 2 = 3 x T
Divide by 3 to get
T = 2/3 L
Since L = 9
T = 2/3 x 9 = 6
In the other ratio we have
T : B = 3 : 4 which we can write as
T/B = 3/4
Cross multiply to get
4T = 3B
B = 4/3 T
Since T = 6, B = 4/3 x 6 = 8
Check
L : T = 9 : 6 = 3: 2 (by dividing both sides of : by 3)
T : B = 6 : 8 = 3:4 (by dividing both sides of : by 2)
$690 is invested in an account earning 2.2% interest (APR), compounded quarterly.
Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
a) A function showing the value of the account after t years, where the annual growth rate can be found from a constant, is f(x) = 690 (1+0.0055)^4t.
b) The percentage of growth per year (APY) is 2.2%.
What is a function?A function is a mathematical expression that shows the relationship between variables.
An example of a mathematical function is an equation that shows the relationship between y and x variables.
Principal = $690
APR = 2.2%
APR per quarter = 0.0055 (2.2%/4)
Compounding = Quarterly
Investment period = t years
Let f(x) = the value of the account after t years.
Future value function, (FV) = PV × (1 + r) ^ n
Where PV = present value or investment
r = compounding rate per period
n = the investment period
Therefore, f(x) or FV = 690 (1+0.0055)^4t.
APY = 100 [(1 + Interest/Principal)(365/Days in term) - 1]
2.2% = 100 [(1 + $15.18/$690)(365/365) - 1]
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Prove that for every real number if c is the root of a polynomial with rational coefficients then root ofa polynomial with integer coefficients: It may be helpful to suppose that is a solution to the polynomial equation: GnXn An-1xn-1_ +q1* + 4o Where qi € Q
Every real root of a polynomial with rational coefficients is also a root of a polynomial with integer coefficients.
Suppose that c is a root of the polynomial equation:
[tex]q_n[/tex] × [tex]x^n[/tex] + q_{n-1} × [tex]x^{n-1}[/tex] + ... + q1 × x + q0 = 0
where [tex]q_i[/tex] are rational coefficients. Since c is a root of this polynomial equation, we have:
[tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0 = 0
Multiplying both sides of the equation by the common denominator of the coefficients [tex]q_i[/tex], we can obtain an equation with integer coefficients. Let d be the least common multiple of the denominators of the coefficients [tex]q_i[/tex]. Then we can write:
d × ([tex]q_n[/tex] × [tex]c^n[/tex] + [tex]q_{n-1}[/tex] × [tex]c^{n-1}[/tex] + ... + q1 × c + q0) = 0
Expanding the left-hand side of the equation, we obtain a polynomial with integer coefficients:
d × [tex]q_n[/tex] × [tex]x^n[/tex] + d × [tex]q_{n-1}[/tex] × [tex]x^{n-1}[/tex] + ... + d × q1 × x + d × q0 = 0
Since c is a root of the original polynomial equation, it is also a root of this polynomial with integer coefficients. Therefore, we have shown that if c is a root of a polynomial with rational coefficients, then it is also a root of a polynomial with integer coefficients.
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Jina rolled a number cube 40 times and got the following results.
Outcome Rolled
1
Number of Rolls 7
2
6
3
9
4
6
5
3
Answer the following. Round your answers to the nearest thousandths.
6
9
(a) From Jina's results, compute the experimental probability of rolling a 3 or 6.
0.45
(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 3 or 6.
0
(c) Assuming that the cube is fair, choose the statement below that is true.
With a small number of rolls, it is surprising when the experimental probability is much
greater than the theoretical probability.
With a small number of rolls, it is not surprising when the experimental probability is much
When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.
what is probability ?The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.
given
(a) The result of rolling 3 or 6 times is 6 + 9 = 15.
Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375
(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).
(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.
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Suppose that an individual has a body fat percentage of 16.3% and weighs 163 pounds. How many pounds of his weight is made up of fat? Round your answer
to the nearest tenth.
pounds
X
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
what is unitary method ?By determining the value of a single unit or quantity and then scaling that value up or down to determine the value of another quantity, the unitary method is a mathematical strategy used to solve problems. According to the unitary method's guiding concept, if one quantity or unit has a certain value, then a predetermined number of those same quantities or units will have a proportionate value. For instance, 5 apples would cost $5 if 1 fruit cost $1.
given
We can use the person's weight and body fat proportion to determine how many pounds of body fat they have. We can commence by calculating the decimal weight of the body fat:
weight of body fat Equals body fat percentage * weight
= 0.163% * 163 lbs.
= 26.509 lbs.
Consequently, the person's weight is roughly 26.5 pounds of fat (rounded to the nearest tenth).
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For numbers 3, 4, and 5, find the value of the indicated length(s) in ⨀C. A and B are points of tangency. Simplify all radicals.
I just need help with these three problems!
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
what is circle ?A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.
given
AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.
We can apply the Pythagorean theorem to segment AB as follows:
[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]
AB² = 50
AB = √50 = 5√2
As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .
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Determine whether the subset of M is a subspace of M with the standard operations of matrix addition and scalar inn nn multiplication The set of all n x n invertible matrices O subspace O not a subspace
The set of all n×n invertible matrices with the standard operations of matrix addition and scalar multiplication is (b) not a subspace.
A Subspace is defined as a subset of a vector space that is itself a vector space under the same operations of addition and scalar multiplication defined on the original vector space.
To be a subspace of Mₙ,ₙ, a subset of Mₙ,ₙ must satisfy three conditions:
(i) The subset must contain the zero matrix,
(ii) The subset must be closed under matrix addition, meaning that if A and B are in the subset, then (A + B) is also in the subset.
(iii) The subset must be closed under scalar multiplication, meaning that if A is in the subset and c is any scalar, then cA is also in the subset.
The set of all n×n invertible matrices does not contain the zero matrix, as the zero matrix is not invertible.
Therefore, it fails to meet the first condition and cannot be a subspace, the correct option is (b).
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The given question is incomplete, the complete question is
Determine whether the subset of Mₙ,ₙ is a subspace of Mₙ,ₙ with the standard operations of matrix addition and scalar multiplication.
The set of all n×n invertible matrices is
(a) Subspace
(b) Not a subspace.
The result of adding 15 to x and dividing the answer by 4 is the same as taking x from 80. a Express this statement as an algebraic equation. b Hence find the value of x.
Answer:
(15+x)÷4 = 80-x
by criss cross we'll get:
15+x = 4(80-x)
15+x = 320-4x
x+4x=320-15
5x = 305
x = 61
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
Answer:
To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:
P(positive|disease) = P(positive and disease) / P(disease)
From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.
We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.
Substituting these values into the formula, we get:
P(positive|disease) = 136 / 144
Simplifying, we get:
P(positive|disease) = 0.944
Rounding to three decimal places, we get:
P(positive|disease) ≈ 0.944
Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.
The table below shows the number of painted pebbles of Claire and Laura. If Greg chooses a pebble at random from the box 75 times, replacing the pebble each time, how many times should he expect to choose a yellow pebble?
A) 11
B) 33
C) 32
D) 22
Answer:
B) 33 times.
Step-by-step explanation:
The total amount of pebbles is 50. There is 22 yellow pebbles.
Note that 3/2 * 50 is 75. 3/2 * 22 = 33.
He should expect to choose a yellow pebble B) 33 times.
First-year students at a university must take history or philosophy during their first semester. 400 are enrolled in both out of a total of 1200 first-year students. If 600 are enrolled in philosophy, how many are taking history?
Answer: I really don't know I'm just trying to get a quest done sorry
Between which two consecutive integers does [tex]\sqrt138[/tex]lie?
The square root of 138 lies between 11 and 12, as 11²=121 and 12²=144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
This is because the square root of a number is the number that, when multiplied by itself, produces the original number. Therefore, to find the square root of 138, we need to identify two consecutive integers such that one of them squared is smaller than 138 and the other squared is larger than 138.
To do this, we can work our way up from the integer closer to 0, in this case 11. 11 squared is 121, which is smaller than 138, so we know that the square root of 138 must be between 11 and a larger integer. Then, if we square 12, we get 144, which is larger than 138. Therefore, we can definitively say that the square root of 138 lies between 11 and 12.
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The square root of 138 lies between 11 and 12, as 11² is 121 and 12² is 144.
What is number?Number is a mathematical object used to count, measure, and label. Numbers are used in almost every field of mathematics and science, including algebra, calculus, geometry, physics, and computer science. Numbers can also be used to represent data, such as population, income, temperature, or time. In addition, numbers are used to represent abstract concepts, such as love, truth, beauty, and justice.
To calculate this, we can divide 138 by 11 and 12, and see which integer is closer to the answer.
138 divided by 11 is 12.545454545454545454545454545455.
138 divided by 12 is 11.5.
Since 11.5 is closer to the answer, the square root of 138 lies between 11 and 12.
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