Since the ages of students at a university are normally distributed with a mean of 21, the percentage of the student body that is at least 21 years old is: 50%.
What is a normal distribution?A normal distribution is also referred to as the Gaussian distribution and it can be defined as a probability distribution that is continuous and symmetrical on both sides of the mean, which indicate that all data near the mean have a higher frequency than the data that are far from the mean.
For all normal distributions, the mean is always located at the center with 50 percent (50%) or 0.5 of the distribution to either side, which is right or left of the distribution.
In this context, the percentage of student body that is at least 21 years old is represented by the percentage to the left of the normal distribution, which is 50 percent (50%):
P(x ≤ 21) = 50%
P(x ≤ 21) = 50/100
P(x ≤ 21) = 0.5.
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a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error. the sample standard deviation. the estimated standard error. the population mean. the population standard deviation.
A parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is the population mean.
What is meant by population mean?The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The μ sign stands for the population mean.
The average calculated from the entire group, distribution, or population is known as the population mean. It is calculated by dividing the sum of all population variables by the total population of variables. Here, μ exists the population mean. ∑X exists the sum of all the observations in the population.
The population mean is a quantity that expresses the population's overall degree of individual variation, which is often unknown.
Therefore, the correct answer is option c) the population mean.
The complete question is:
a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error.
a) the sample standard deviation.
b) the estimated standard error.
c) the population mean.
d) the population standard deviation.
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Please help me with this
Does anyone know the answer to this question ?? PLS HELP.
Only answer if you know the answer !!!!
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to x³ -11x² +41x -51.
As given,
Standard form of the polynomial function:
f(x) = r(x-a)(x-b)(x -c)
r : leading coefficient
a, b, c are zeros
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is given by
f(x) = 1(x -3) (x -(4+i))(x - (4-i))
⇒ f(x) = (x -3) (x-4 -i)(x -4 +i)
⇒ f(x) = (x-3) [(x-4)² -i²]
⇒f(x) = (x-3)(x² -8x +16+1)
⇒f(x) =(x-3)(x² -8x+17)
⇒f(x) = x³-11x² +41x-51
Therefore, polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to
x³ -11x² +41x -51.
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solve (2x-3)²= 4x using the quadratic formula
Answer:
[tex]x = 2 \pm \frac12\sqrt7[/tex]
Step-by-step explanation:
Hello!
Expand the left-hand side of the equation:
(2x - 3)²(2x-3)(2x-3)(2x-3)(2x) +(2x-3)(-3)4x² - 6x - 6x + 94x² - 12x + 9Create the Equation:
4x² - 12x + 9 = 4x4x² - 16x + 9 = 0Solve using the quadratic formula:[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-(-16) \pm \sqrt{(-16)^2 - 4(4)(9)}}{2(4)}[/tex][tex]x = \frac{16 \pm \sqrt{256 - 144}}{8}[/tex][tex]x = \frac{16 \pm \sqrt{112}}{8}[/tex][tex]x = \frac{16 \pm 4\sqrt7}{8}[/tex][tex]x = 2 \pm \frac12\sqrt7[/tex]The roots of the equation are [tex]x = 2 \pm \frac12\sqrt7[/tex]
Lauren needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 3.75 hours and charged her $119
for parts. The total was $400.25. Write and solve an equation which can be used to
determine a, the cost of the labor per hour.
Answer:
3.75x + $119 = $400.25
x = $75
Step-by-step explanation:
Lauren needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 3.75 hours and charged her $119 for parts. The total was $400.25. Write and solve an equation which can be used to determine a, the cost of the labor per hour.
3.75x + parts = $400.25
so:
3.75x + $119 = $400.25
subtract $119 from both sides:
3.75x + $119 - $119 = $400.25 - $119
3.75x = $281.85
divide both sides by 3.75
3.75x/3.75 = $281.85/3.75
x = $75
so the tech charged $75 per hour.
Rewrite expression (4^-2)^3 using positive exponents
The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
The given expression is [tex](4^{-2})^3[/tex].
What is a positive exponent?A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
The given expression can be simplified as follows
[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]
So, the positive exponent = [tex]\frac{1}{4^6}[/tex]
Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
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How do the laws of exponents apply to algebraic expressions
The laws of exponents are useful to solve algebraic expression as shown below.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them. Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing. These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
The laws of exponents (sometimes referred to as the rules of exponents) allow us to simplify expressions by using our understanding of what an exponent implies.
The goal is to write algebraic expressions as simply as you can in both situations.
Recall that an exponent indicates the number of times to multiply a number, variable, or expression by itself.
[tex]x^4=x \cdot x\cdot x\cdot x[/tex]
and, [tex](x+5)^3=(x+5)(x+5)(x+5)[/tex]
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Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.The number of times a person exercises per week and their endurance.
Answer:
[tex]\text{Positive Correlation}[/tex]Explanation:
Here, we want to determine the type of correlation relationship
From science, we understand that engaging in exercise helps internal organs to function better. These are the sources of endurance
Exercising for a couple of more times, all things being equal means there will be more endurance. We can largely say that, for most people, it is expected that the higher the number of time spent exercising, the higher the endurance being built
Thus, we can conclude there is a positive correlation between the two
The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
Using the Pythagorean Theorem formula, the measurement of the unknown side (base) is 12 units.
How can the measurement of the unknown side of a right triangle be determined?According to the Pythagorean Theorem formula, c² = √a²+b², where c = hypotenuse, a = perpendicular, and b = base.
The hypotenuse is the longest side of a right triangle.
The shortest side is the perpendicular (adjacent side) while the other side is the base (opposite side).
Since the hypotenuse is given as equal to the square root of perpendicular squared and the base squared, we can compute the base, unknown side, using the following Pythagorean Theorem formula.
c² = √a²+b²
The perpendicular (shortest side) of a right triangle = 5
The hypotenuse (longest side) = 13
c² = √a²+b²
169 = √5²+b²
169 = √25 + b²
The base (unknown side):
b² = 169 - 25
b² = 144
The square root of √144 = 12
b = 12
Thus, the unknown side of the right triangle is the base, measuring 12 units.
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The length of the unknown side is 12 units, which is the base of the right triangle.
The right triangle's perpendicular (shortest side) = 5 units
The right triangle's hypotenuse (longest side) = 13 units
According to the Pythagorean Theorem,
H² = P² + B², Where H = hypotenuse, P = perpendicular, and B = base.
As per the given question, here H = 13 and P = 5
Substitute the values of H = 13 and P = 5 in the Pythagorean Theorem,
(13)² = (5)²+ B²
169 = 25 + B²
B² = 169 - 25
B² = 144
B = √144
B = 12 units
Therefore, the length of the unknown side is 12 units,
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Drag each label to the correct location on the table. Match each equation with its number of unique solutions. y = -52 – 41 +7 y = –202 + 91 - 11 y = 3.12 – 61 + 3 Two Real Solutions One Real Solution One Complex Solution Two Complex Solutions Reset Next reserved
When b²−4ac=0 there is one real root.
When b²−4ac>0 there are two real roots.
When b²−4ac<0 no real roots or two complex roots
First equation
-x²-4x+7
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-4\mright)^2-4\mleft(-1\mright)\cdot\: 7 \\ 16+28=44 \end{gathered}[/tex]b²−4ac>0, then equation -x²-4x+7 has two real roots.
Second equation
-2x²+9x-11
[tex]\begin{gathered} b^{2}-4ac \\ 9^2-4\mleft(-2\mright)\mleft(-11\mright) \\ 81-88=-7 \end{gathered}[/tex]b²−4ac<0, then equation -2x²+9x-11 has two complex roots.
[tex]x1=\frac{9}{4}-i\frac{\sqrt{7}}{4},\: x2=\frac{9}{4}+i\frac{\sqrt{7}}{4}[/tex]Third equation
3x²-6x+3
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-6\mright)^2-4\cdot\: \: 3\cdot\: \: 3 \\ 36-36=0 \end{gathered}[/tex]b²−4ac=0, then equation 3x²-6x+3 has one root.
Whats the answer to x + 23 12
A.8
B.-11
C.-6
D.6
Answer:
-11
Step by step explanation:
-11+23=12
Look at the attached image, that is the problem
Solve all 3 parts to the attached image
Question 1
1.If ABCD is a parallelogram then
_________________________?
A. Opposite sides of the parallelogram are congruent
B. Consecutive sides of the parallelogram are perpendicular
C. Consecutive sides of the parallelogram are congruent
D. Opposite sides of a parallelogram are parallel
Question 2
2. x=____?
A.9
B.8.5
C.9.5
D.1.9
Question 3
3. CD=____?
A.11.4
B.54
C.51
D.57
This can be solved using the properties of a parallelogram.
What is a parallelogram?
A parallelogram is a basic (non-self-intersecting) quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's opposing or facing sides are of equal length, and its opposite angles are of equal measure. The congruence of opposing sides and angles is a direct result of the Euclidean parallel postulate, and neither condition can be established without resorting to the Euclidean parallel postulate or one of its equivalent formulations. A quadrilateral having just one set of parallel sides is known as a trapezoid in American English or a trapezium in British English. A parallelepiped is a parallelogram's three-dimensional counterpart.
1. If ABCD is a parallelogram, then
(A) Opposite sides of the parallelogram are congruent
2. In a parallelogram opposite sides are equal, so
6x = 4x + 19
or, 6x - 4x = 19
or, 2x = 19
or, x = 19/2 = 9.5
Hence, x =
(C) 9.5
3. CD = 6x9.5 = 57 units
(D) 57
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Miss Davidson ran a sit-up competition among her P.E. students and monitored how many sit-ups each student could do. Number of sit-ups Number of students 76 3 79 5 175 2 X is the number of sit-ups that a randomly chosen student did. What is the expected value of X? Write your answer as a decimal.
Let the total number students be s. Then
s = 3 + 5 + 2= 10
x | Number of students(n) | Pr(x) | xPr(x)
---------------------------------------------------------------------------------
76 | 3 | 0.3 | 22.8
---------------------------------------------------------------------------------
79 | 5 | 0.5 | 39.5
--------------------------------------------------------------------------------
175 | 2 | 0.2 | 35
--------------------------------------------------------------------------------
[tex]\sum \text{xPr(x) = 22.8 + 39.5 }+\text{ 35 = 97.3}[/tex][tex]\text{ The expected value is }\sum \text{xPr(x)}[/tex]Therefore, the expected value of x is 97.3
2
Select the correct answer.
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?
A.
It is the graph of y = x where the slope is decreased by 8.
B.
It is the graph of y = x translated 8 units up.
C.
It is the graph of y = x translated 8 units to the left.
D.
It is the graph of y = x translated 8 units down.
Answer:
the answer of a question is option A
A rectangular gardan is surrounded by a walk of uniform width. The area of the garden is 200 square yards. If the dimensions of the garden plus the walkway are 18 yards by 26 yards, find the dimensions of the garden.
***NOTE*** This is a Quadratic Word Problem, so please use the Quadratic Method when solving and show all steps!!
Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards
Step-by-step explanation:
Let the length of the walkway be x yards. Then,
[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]
However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].
So,
[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]
the sum of the digits in a three digit mumber is 9. the tens digit is half the sum of the other two amd the hundreds digit is half the unit digit. fond the number.
The number is 234.
Step-by-step explanation:
Let the 3 digits be H , T and U so the number is HTU.
H + T + U = 9
T = 0.5H + 0.5U
U = 2H
So from the last 2 equations
T = 0.5H + 0.5(2H)
T = 0.5H + H
T = 1.5H
So substituting for T and H is the first equation:
H + 1.5H + 2H = 9
4.5H = 9
H = 2.
So T = 1.5*H = 1.5 *2 = 3.
PLS HELP WITH 15. (GIVING EXTRA POINTS)
Answer:
[tex]4^{6}[/tex] or 4096
Step-by-step explanation:
When the bases are the same, you add the exponents.
Answer:
Step-by-step explanation:
[tex]\boxed{\bf\\a^n*a^m=a^{n+m}}[/tex]
[tex]\displaystyle(4)^2\cdot(4)^4\cdot(4)^0=(4)^{2+4+0}=4^6=4096[/tex]
Here are some ingredients for bolognaise sauce 400g of minced beef 800g of tomato sauce 300 ml stock 300ml red wine. julia has 300g of minced beef. how much of the other ingredients does she need
Answer:
Step-by-step explanation:
she would have to use 3/4 of the ingrediants to the 400g of minced beef.
tomato sauce would be 600g
stock would be 225g
and red wine would be 225g
The quantity of chopped tomatoes is 600 g, of stock is 225 ml, and of red wine is 225 ml if Julie only has 300 g of minced beef.
The ratio is the comparison of two quantities to determine how frequently one quantity obtains the other. It can be shown as a fraction between two numbers.
Quantity of minced beef = 400 g
Quantity of chopped tomatoes = 800 g
Quantity of stock = 300 ml
Quantity of red wine = 300 ml
Taking ratios of all the quantities, we get:
minced beef: chopped tomatoes:stock: red wine
= 400:800:300:300
= 100:200:75:75 ( Dividing by 4, as a common factor)
Multiplying the above ratio by three to make the quantity of minced beef 300 g
= 300:600:225:225
Thus, the quantity of chopped tomatoes is 600 g, the quantity of stock is 225 ml, and the quantity of red wine is 225 ml if Julie only has 300 g of minced beef.
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3/4 - (-1/2) as a fraction
Answer:1/4
Step-by-step explanation:
If a rectangular solid has a volume of 32 and then each dimension is doubled, what happens to the volume? A. The volume is multiplied by 3.B. The volume is multiplied by 8.C. The volume is multiplied by 6.D. The volume is doubled.
To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height
V1=LWH= 32
[tex]\begin{gathered} V2=2L\cdot2W.2H \\ V2=8(\text{LWH)} \end{gathered}[/tex]Ex
2*4*4=32
Let's multiply all dimension by 2
4 * 8 * 8 =256
Answer:B. The volume is multiplied by 8.
a researcher is told that the average age of respondents in a survey is 49 years. she is interested in finding out if most respondents are close to 49 years or not. the measure most appropriate to answer this question is:
The measure that would most correctly answer this question is standard deviation.
What is standard deviation?
The standard deviation is measure of how spread out data from mean.
Step-by-step explanation:
Average age of respondents in a survey is [tex]49[/tex] years. Researcher interested in finding out if most respondents are close to [tex]49[/tex] years or not.
Hence here measures of dispersion fact will be used.
Measures of dispersion are range and standard deviation.
Range is nothing but the difference between maximum and minimum values of the data.
Standard deviation gives proper idea about how far the data values are scattered from the mean point [tex]49[/tex] years.
Therefore the correct option is standard deviation.
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Describe how to transform the graph of f(x)=x^2 into the graph of g(x)=4(3x-1)^2+5.
Please help me with this question! Thank You
The transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
The given functions are f(x) = x² and g(x)= 4(3x-1)²+5.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The transformation is
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 0.333 Units
Vertical Shift: Up 5 Units
Reflection about the x-axis: None
Reflection about the y-axis: None
Vertical Compression or Stretch: Stretched
Therefore, the transformation from the graph of f(x) to g(x) is horizontal shift right 0.333 units and vertical shift is up 5 units.
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write the linear equation in slope-intercept form passing through the point with the given slope. 1. (0,3):slope = -2 2. (-5,-3); slope = -3/5 3. (-8,6); slope 1/4 write the linear equation in slope-intercept form that passes through the given points. 4.
The equation of each line in slope-intercept form are:
1. y = -2x + 3
2. y = -3/5x - 6
3. y = 1/4x + 8
How to Write the Equation of a Line in Slope-intercept Form?If we are given a point (a, b) and the slope of a line (m), we can write the linear equation in slope-intercept form by first plugging in the given values into y - b = m(x - a), then rewrite it in the slope-intercept form as y = mx + b.
1. Slope (m) = -2
Point (a, b) = (0, 3)
Plug in the values into y - b = m(x - a):
y - 3 = -2(x - 0)
y - 3 = -2x + 0
y = -2x + 0 + 3
y = -2x + 3 [slope-intercept form]
2. Slope (m) = -3/5
Point (a, b) = (-5, -3)
Plug in the values into y - b = m(x - a):
y - (-3) = -3/5(x - (-5))
y + 3 = -3/5x - 3
y + 3 - 3 = -3/5x - 3 - 3
y = -3/5x - 6 [slope-intercept form]
3. Slope (m) = 1/4
Point (a, b) = (-8, 6)
Plug in the values into y - b = m(x - a):
y - 6 = 1/4(x - (-8))
y - 6 = 1/4(x + 8)
y - 6 = 1/4x + 2
y - 6 + 6 = 1/4x + 2 + 6
y = 1/4x + 8 [slope-intercept form]
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How can I work out the size of angle y?
Answer:
180 degrees converted is 3.14159 i think
Step-by-step explanation:
Answer:
< y = 17 degrees.
Step-by-step explanation:
x + y = 180 - 112 = 68 (as there are 180 degrees in a triangle)
Also, x = 3y, so substituting for x in the first equation:
3y + y = 68
4y = 68
y = 17.
So,
x = 3*17 = 51,
the cost of a computer repair is worked out using the formula C = 35 + 15h.
C represents the cost in dollars.
H is the time taken in hours.
use the formula to find the cost of repair that takes 3 hours.
Answer: C = 35 + 15 x 3 = 80
Step-by-step explanation:
15h = 15 x (h) = 15 x 3 = 45 + 35 = $80
C = (15 x 3) + 35 = 80
1) Find the volume of each cone.a. Estimate using 22 꼭 for n. Express theanswer as a fraction.
Volume of the cone = 50.29 mm³
Explanation:[tex]\text{Volume = 1/3}\pi r^2\text{ h}[/tex]radius = r = ?
height = 3mm
slant height = 5mm
To get the radius, we would apply pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
hypotenuse = 5mm
opposite = 3mm
adjacent = radius = ?
5² = 3² + radius²
25 = 9 + radius²
25 - 9 = radius²
16 = radius²
radius = √16
radius = 4
[tex]\text{Volume of the cone = }\frac{1}{3}\times\frac{22}{7}\times4^2\times3[/tex][tex]\text{Volume of the cone = }50.29mm^3[/tex]Please Help Please ASAP
214 ÷ 9 = ___.
Twenty-three and two-ninths
Twenty-three and five-ninths
Twenty-three and seven-ninths
24
Answer:
Twenty-three and seven-ninths
Step-by-step explanation:
Might not be correct I don't really remember how to do this
Decide whether each statement is sometimes true, always true, or never true. If the statement is sometimes true give one example of when it is true and an example of when it is not. See Instructions."The linear regression line passes through the average of the x-values and the average of the y-values."Your answer:See Instructions. "A positive correlation coefficient means that the points in the scatterplot are very close together."Your answer:See Instructions."A correlation coefficient close to 1 means that a linear model is most appropriate for the data."Your answer:
In general, the linear regression formula is shown below
[tex]undefined[/tex]the radius of a right circular cone is increasing at a rate of 5 inches per second and its height is decreasing at a rate of 4 inches per second. at what rate is the volume of the cone changing when the radius is 50 inches and the height is 10 inches?
The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.
The formula for the circular cone can be given as;
V = 1/3 πr²h
Now we take the derivative with respect to time as follows;
V = 1/3 πr²h
dV/dt = 1/3π d/dt(r²h)
dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]
Now we substitute the values in this equation as follows;
dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]
dV/dt = 1/3π [ 5000 - 10000]
dV/dt = 1/3π [-5000]
dV/dt = -5235.98
Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.
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