The percent of young men that are shorter than the mean height of young women is 2.5%.
What is a normal distribution?A data set with a normal distribution has the majority of its values clustered in the middle of the range and the remaining values tapering off symmetrically toward either end.
A continuous probability distribution for a real-valued random variable is known as a "normal distribution" in statistics.
Based on the information, the percentage will be calculated thus:
Z = (69.3 - 64) / 2.7 = 1.9630
So P(Z>1.96)= 1-P(Z<1.96)
(check standard normal table)
= 1-0.975
= 0.025
= 2.5%
The percentage is 2.5%.
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PLEASE HELP NOW!!!!!!!!!!! (03.04 MC)
Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane.
Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power minus 1 going through points 0 comma 0 and 1 comma 1.
What effect does subtracting 1 from the parent function have on the transformed function?
a
Subtracting 1 from the parent function shifts the function up one unit.
b
Subtracting 1 from the parent function shifts the function down one unit.
c
Subtracting 1 from the parent function shifts the function right one unit.
d
Subtracting 1 from the parent function shifts the function left one unit.
Subtracting 1 from the parent function will transform the function in the following way: b Subtracting 1 from the parent function shifts the function down one unit
what is transformation?This refers to as movement of object in an organized way such that the movement can always be calculated from the initial position.
The movement involved in transformation on images is ordered and there are some terms used to classify such movements. some of the terms are:
ReflectionDilationTranslation and so onThe movement done in the question is a translation. This is a linear movement towards a particular direction. the movement is translation is usually:
Up: adding numbers to the y directiondown: subtracting number in the y directionRight: adding number to the x directionLeft: subtracting number or value from the x directionSubtracting 1 from the parent function. the parent function as used refers to the y direction hence option b is the correct answer
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Please answer asap please and thank you
Answer:
Step-by-step explanation:
Mary paid $16 for her 12 month subscription to Word Up magazine. How much did Mary pay per magazine?
Answer: 1.3333333333....
Step-by-step explanation: 16 divided by 12 is 1.3333333333333333333333333333333333333333333333333333333333333333333333333333..................................................................
If Mary spent 16 dollars for 12 magazines, it would be $1.33 for each.
help needed asap!! will award brainiest
let in the region where . explain why must have a global minimum at some point in (note that is unbounded---how does this influence your explanation?). then find the global minimum. minimu
the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is y= 5е¹ ⁻ ˣ +5 x
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
First Derivative Test
-a .е⁻ˣ +b = 0 (1)
b=a .е⁻ˣ
Second Derivative Test
y''= a . .е⁻ˣ (2)
Where y'' >0
If we know that ( x,y) = 9 1,10) , then we have the following system:
10 = a е⁻¹ +b (3)
b= a е⁻¹ (4)
y'' = a е⁻¹ (5)
By (4) in (3):
10= 2aе⁻¹
a=10/2е⁻¹
a= 5е
By (5) we prove that y''>0, and we get the value of by (4):
b=5
Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is . y= 5е¹ ⁻ ˣ +5 x
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The complement of an angle is half of it’s size. Find the angle
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:The \:\: angles \:\: are \:\: 60° \:\: and \:\:30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Sum of two complementary angles is 90°
Let's assume one of them to be x, the other one will be x/2 as one of the angles is complementary to other one.
[tex]\qquad \tt \rightarrow \: x + \dfrac{x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: \dfrac{2x + x}{2} = 90[/tex]
[tex]\qquad \tt \rightarrow \: 3x = 90 \times 2[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 \div 3[/tex]
[tex]\qquad \tt \rightarrow \: x = 60 \degree[/tex]
and
[tex]\qquad \tt \rightarrow \: \dfrac{x}{2} = 60 \div 2 = 30 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The graph is a function. + O True O False
the provided graph is not a function .
s
Write an equation for the line parallel to the given line that contains C.
5
C(1,7); y=x+4
The equation of the line parallel to the given line that contains C is obtained as y = x + 6.
What is termed as the parallel lines?Parallel lines are two or more lines which lie within the same plane but never intersect. They are equal in distance and have the same slope. Parallel lines have been straight lines which never meet, no matter how far they are extended. Numerous pairs of angles are formed when two parallel lines have been intersected by another line known as a transversal.For the given question;
The equation of the line is given as;
y = x + 4
The standard form of the equation of line in slope intercept form is;
y = m x + c
where, m is the slope and c is the y intercept.
On comparing;
m₁ = 1
Now, the other lien is parallel to the given line.
Thus, slopes of both lines will be equal.
m₁ = m₂ = 1
The passing points of the line are;
(x₁, y₁) = C(1, 7)
Now, the equation of lien will be;
y - y₁ = m₂(x - x₁)
Put the values;
y - 7 = 1(x - 1)
Simplifying.
y = x + 6
Thus, the equation of the line parallel to the given line that contains C is obtained as y = x + 6.
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19. the sum of twelve and sixteen divided by the sum of three and four
20.the difference of twenty-two and six divided by the sum of five and three
21.the sum of thirty-six and fourteen divided by the product of two and five
22.the quotient of thirty-two and four divided by the sum of one and three
23.the sum of six and fifteen divided by 24.the difference of thirteen and nine
25.the difference of thirty-one and seventeen divided by the product of ten
Answer:
they require the use of fractions.
Step-by-step explanation:
sum means to add both numbers
difference means to subtract the small number from the big number
quotient means to divide
product means to multiply
24. 13-9= 4
not sure what you meant by q23 and q25.
19. the sum of twelve and sixteen divided by the sum of three and four = 4
20. the difference of twenty-two and six divided by the sum of five and three = 2
21. the sum of thirty-six and fourteen divided by the product of two and five = 4
22. the quotient of thirty-two and four divided by the sum of one and three = 2
23. the sum of six and fifteen divided by 24 = 21/24
24. the difference of thirteen and nine = 4
25. the difference of thirty-one and seventeen divided by the product of ten = 7/5 = 1.4
A line has a slope of 1/3 and includes the points (6,1) and (9,j). What is the value of j?
Answer:
j = 2
Step-by-step explanation:
Slope of a line is given by:
[tex]\medium \text{$\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$}[/tex]
where (x₁, y₁) and (x₂, y₂) are two points on the line
This is commonly referred to as rise/run
Given the two points (6, 1) corresponding to (x₁, y₁) and (9, j) corresponding to (x₂, y₂)
[tex]\text{Slope = }\dfrac{\ensuremath{j}-1}{9-6}=\dfrac{j-1}{3}[/tex]
But we are given the slope as 1/3
So we get
[tex]\dfrac{j-1}{3} = \dfrac{1}{3}[/tex]
Multiplying by 2 on both sides gives us:
j - 1 = 1
Adding 1 to both sides gives us
j - 1 + 1 = 1 + 1
j = 2
Simplify.
Rewrite the expression in the form z^n
z^7/z^-14
In the form exponent function zⁿ, the above equation z⁷/z⁻¹⁴ would equal z²¹.
What are exponential functions?The term "exponential function" refers to a function whose expression calls for the input to exist as an exponent (power) of some constant. The following describes their typical form. There are numerous equivalent forms in which they are written.
Briefing:The negative exponent rule instructs us to place a number with a negative exponent in the denominator and the opposite is also true.
State product of power property of exponents.
Keep the bases the same when multiplying two bases with the same value, and then add the exponents to find the answer.
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]\frac{z^7}{z^{-14}}[/tex]
[tex]z^{7-(-14)}[/tex]
z²¹.
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Each droplet that you sneeze is approximately 7 x 10-3 mm in diameter. If you wear an N95 mask, which filters virus particles as small as 8 x 10-5, will you sufficiently protect those around you? Explain your reasoning.
Answer:
Yes, 7 x [tex]10^{-3}[/tex] in standard form is 0.007mm
8 x [tex]10^{-5}[/tex] in standard form is 0.00008 mm. The mask will catch particles that are much smaller than 0.007 in diameter.
Step-by-step explanation:
a binomial experiment consists of trials. the probability of success for each trial is . what is the probability of obtaining - successes? approximate the probability using a normal distribution. (this binomial experiment easily passes the rule-of-thumb test for approximating a binomial distribution using a normal distribution, as you can check. when computing the probability, adjust the given interval by extending the range by 0.5 on each side.)
The trials in a binomial experiment are the steps. the likelihood of each trial being successful is. What is the likelihood of success? The probability of success is P=1.42.
What in mathematics is a binomial?The binomial distribution is used to summarise the number of trials or observations where each trial has the same probability of attaining a certain value.. When flipping a coin, the probability of witnessing a certain number of successful outcomes in a specified number of trials is determined by the binomial distribution; as there are only two possible outcomes, the likelihood of flipping a coin is 12 or 0.5 for each trial we do.
based on the facts provided;
here ,
n=500 ,p=0.4,q=0.6, X=number of successes
when n*p and n*q>5 then we can use normal approximations
here n*p=500*0.4=200 >5 ,n*q=500*0.6=300>5
so we can use normal approximation
mean =200
variance =200*0.6=120,
std. deviation=120^1/2
we need to find
P(185<=X<=220), applying continuity correction factor
P(184.5<=X<=220.5)
Z=(X-mean)/std. dev~N(0,1)
P((184.5–200)/10.95<=Z<=(220.5–200)/10.95)
=P(-1.42<=Z<=1.87)
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5. Which of the following functions has a graph with the largest positive x-intercept?
A. f(x) = 2(x+5)-1
B. f(x) = 8(x+8)
c. f(x) = 2(x-8) +1
D. f(x)=13(x-3)
The function which has a graph with the largest positive x-intercept is C. f(x) = 2(x-8) +1
What is a x-intercept?The value of the x coordinate at the point where the graph crosses the x-axis is known as the x-intercept for any curve. Alternatively, we can say that the x-intercept is the value of the x coordinate at the point where the value of the y coordinate equals zero.
Let y be 0, so lets find the x-intercept of
A. 2(x+5)-1 = 0
⇒ 2(x+5) = 1
⇒ 2x + 10 = 1
⇒ 2x = -9
⇒ x = -9/2
B. 8(x+8) = 0
⇒ x+8 = 0
⇒ x = 0 −8
⇒ x = −8
C. 2(x-8) +1 = 0
⇒ 2x − 15 = 0
⇒ 2x = 15
⇒ x = 15/2
⇒ x = 7.5
D. 13(x-3) = 0
⇒ x − 3 = 0/13
⇒ x − 3 = 0
⇒ x = 0 + 3
⇒ x = 3
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The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?
The dimensions are 24 by 13.5 cm
How to determine the dimensions of the rectangle?The given parameters are
Length = 3 cm less than twice the width
This means that
L = 2W - 3
Where
L represents Length and W represents Width
The perimeter is given as
P = 75 cm
The perimeter is calculated as
P = 2*(L + W)
So, we have
2*(L + W) = 75
This gives
2*(2W - 3 + W) = 75
Evaluate
2*(3W - 3) = 75
Divide by 2
3W - 3 = 37.5
So, we have
3W = 40.5
Divide by 3
W = 13.5
Recall that
L = 2W - 3
So, we have
L = 2 * 13.5 - 3
Evaluate
L = 24
Hence, the dimensions of the rectangle are 24 by 13.5 cm
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A drilling crew dug to a depth of 26 ½ feet during their first day of drilling. On the second day, the crew dug down 9½ feet more than on the first day. Describe the depth of the bottom of the hole after the second day.
The depth of the bottom of the hole after the second day is 36 feet using addition operation.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the sum refers to the outcome of the operation.
Given the depth on the first day is 26 ½ feet.
Depth on the second day = 9½ feet more than on the first day i.e. 9½ feet + depth on the first day
This implies, depth on the second day = 9½ + 26 ½
= 36 feet
Therefore, the depth of the bottom of the hole after the second day is 36 feet.
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What is the relationship between translations, reflections, and ridgid motion?
The relationship between translations, reflections, and rigid motion is that they are all types of rigid motions, which means their size does not change.
What exactly is rigid motion?Rigid motion is the movement of a set in which the distance between points remains constant.
What is translation?Translation is a type of rigid motion in which an object simply slides while maintaining its direction.
What do you mean by reflection?A reflection, like a mirror, causes an image to flip to another location.
We must establish a connection between translations, reflections, and rigid motion.
We can conclude from the above definitions that the size of the object remains constant, but it is undergoing different transitions.
Therefore, Translations, reflections, and rigid motion all belong to the category of transformations that are rigid motions, which means that their sizes don't change.
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Factorise the following:
a) x^2 + 10x + 16
b) x^2 + 7x + 12
c) x^2 + 13x + 12
Answer:
Step-by-step explanation:
a)
[tex]x^2+10x+16=\\x^2+2x+8x+16=\\x(x+2)+8(x+2)=\\(x+2)(x+8)[/tex]
b)
[tex]x^2+7x+12=\\x^2+3x+4x+12=\\x(x+3)+4(x+3)=\\(x+3)(x+4)\\[/tex]
c)
[tex]x^2+13x+12=\\x^2+x+12x+12=\\x(x+1)+12(x+1)=\\(x+1)(x+12)[/tex]
Answer:
[tex]\textsf{(a)} \quad (x+8)(x+2)[/tex]
[tex]\textsf{(b)} \quad (x+4)(x+3)[/tex]
[tex]\textsf{(c)} \quad (x+12)(x+1)[/tex]
Step-by-step explanation:
Factoring quadratics
To factor a quadratic in the form [tex]ax^2+bx+c[/tex] find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].Rewrite [tex]b[/tex] as the sum of these two numbers.Factor the first two terms and the last two terms separately.Factor out the common term.Part (a)[tex]\textsf{Given}: \quad x^2+10x+16[/tex]
Two numbers that multiply to 16 and sum to 10 are: 2 and 8.
[tex]\implies x^2+2x+8x+16[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+2)+8(x+2)[/tex]
Factor out the common term (x + 2):
[tex]\implies (x+8)(x+2)[/tex]
Part (b)[tex]\textsf{Given}: \quad x^2+7x+12[/tex]
Two numbers that multiply to 12 and sum to 7 are: 3 and 4.
[tex]\implies x^2+3x+4x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+3)+4(x+3)[/tex]
Factor out the common term (x + 3):
[tex]\implies (x+4)(x+3)[/tex]
Part (c)[tex]\textsf{Given}: \quad x^2+13x+12[/tex]
Two numbers that multiply to 12 and sum to 13 are: 1 and 12.
[tex]\implies x^2+x+12x+12[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x+1)+12(x+1)[/tex]
Factor out the common term (x + 1):
[tex]\implies (x+12)(x+1)[/tex]
assuming the ocean’s level is currently rising at about 1.6 millimeters per year, create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
40 millimeters; the ocean will have risen each year for the next 25 years.
ocean’s level is currently rising at about 1.6 millimeters per year.
create an application that displays the number of millimeters that the ocean will have risen each year for the next 25 years.
IN, 1 year —> 1.6 millimeters;
25 years —> 25*1.6 millimeters;
= 40 millimeters;
40 millimeters; the ocean will have risen each year for the next 25 years.
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write the mixed expression as a rational expression: 2+9/g
mixed expression as a rational expression will be [tex]\frac{2g+9}{g}[/tex]
WHAT IS FRACTION ?In mathematics, a fraction is a number that is expressed as a quotient in which the numerator and denominator are divided. In a simple fraction, both are integers. A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator.
CALCULATIONto convert mixed fraction into rational fraction
we multiply denominator with whole number and add it with numerator and the result of this gives numerator . and the denominator is same as mixed fraction .
so for the given expression ,
2 * g + 9 is numerator
and g is denominator .
= [tex]\frac{2g+9}{g}[/tex]
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HELP! EZ MATH!! ANSWER QUICK PLEASE!!!
Answer:
The correct answer is 57. 4^3 was misidentified as 4×3.
Step-by-step explanation:
[tex] {4}^{3} - 7 = 64 - 7 = 57[/tex]
Whats 6% of 583! Because its very confusing and if you can help that would be great
Answer:
34.98is the answer ............ .............
Answer: 34.98
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
6% = 6 'out of one hundred',
p% is read p 'percent',
6% = 6/100 = 6 ÷ 100
What does it mean to calculate the percentage of a number?
6% of 583 = ?
... is equivalent to multiplying them:
6% × 583 = ?
6% of 583 =
6% × 583 =
6/100 × 583 =
(6 ÷ 100) × 583 =
6 × 583 ÷ 100 =
3,498 ÷ 100 =
34.98
Show the relationship between -5/6 and -7/10. Use an inequality symbol
[repost]
From the inequality concept ( -7 / 10) > ( -5 / 6).
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
Given fractional numbers are -5/6 and -7/10. The numbers in the form of inequality will be calculated as:-
-7 / 10 = -0.7
-5 / 6 = -0.84
-0.7 > -0.84
-7 / 10 > -5 / 6
Therefore, from the inequality concept ( -7 / 10) > ( -5 / 6).
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What is the product of the common prime factors 24 and 32?
Answer:
2*2*2
That's the prime product of their common factors
Anais bought
2 1/2 yards of ribbon. She had
feet 1
6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains
The inches of ribbon that Anais use to trim the curtains is 12 inches.
How to illustrate the information?From the information, Anais bought 2 1/2 yards of ribbon and then he had 1 feet 6 inches of ribbon left after trimming some curtains.
It should be noted that 12 inches = 1 feet
Therefore, the inches that will be left will be:
= 2 1/2 - 1 6/12
= 2 1/2 - 1 1/2
= 1 feet
It should be noted that 1 feet = 12 inches.
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can someone help me with this please
Answer:
x=4
Step-by-step explanation:
15-9=6
10-6=4
Answer:
x = 6 cm
Step-by-step explanation:
The two shapes are similar. That means one figure is exactly a multiple of the other figure
We can see that the ration of the length of the bigger rectangle to the length of the smaller rectangle is 15/9 = 5/3
Therefore the ratio of the width of the bigger rectangle to the width of the smaller rectangle must also be 5/3
Given width of big rectangle = 10 and that of small rectangle is x
We get
10/x = 5/3
Multiply by x both sides:
x × 10/x = x × 5/3
10 = 5x/3
Multiply by 3 both sides
30 = 5x
5x = 30
Dividing by 5 both sides
5x/x = 30/5
x = 6 cm
x y
7 11
8 13
9 15
10 17
27
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
The correct answer is that y does not vary directly with x.
If y and x are directly related, then the equation y=kx would be true for each point in the set.
What is the explanation:
If y is directly related to x, then every point in the set would fit the equation y=kx.
For the first point, we would have 11=7k, which would imply that k=11/7.
For the second point, we would have 13=8k, which would imply that k=13/8.
By utilizing proportions to check, we can see that 11/7 does not equal 13/8.
Cross multiplying yields 11*8=7*13, or 88=91
Since this is untrue, k is not a constant and y does not change in accordance with x.
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Please explain!!
A DVD has a diameter of 12 centimeters. What is the area of the dvd? Round your answer to the nearest hundredth.
Answer:
Given diameter (D) = 12Radius = D = 26Circumference = πD= 12π= 37.699111843078Area = π(D)22= 36π= 113.09733552923
Complete the statements below to explain two ways to convert miles to kilometers.
1 mile ≈1.61 kilometers
1 kilometer ≈0.62 mile
CLEARCHECK
Kilometers are ____
miles.
That means the number of kilometers in a distance will always be
_____ the number of miles in that distance.
We can convert miles to kilometers by ______
by 1.61.
We can convert kilometers to miles by ______
by 0.62.
The statements below to explain two ways to convert miles to kilometers is
Kilometers are 0.62 miles , That means the number of kilometers in a distance will always be 0.62 the number of miles in that distance.We can convert miles to kilometers by multiply by 1.61.We can convert kilometers to miles by multiply by 0.62.What is unit conversion?Unit conversion can be described as the conversion that can be made to convert an item in a particular unit to another unit.
From above the conversion rate for the conversion of miles to kilometer and there conversion of kilometer was given , which can be used in making the conversion.
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Will plays a game at a theme park.
There are 20 cards numbered from 1 to 20.
Will takes a card at random.
He wins if the card he chooses shows a prime number.
Work out the probability that Will wins.
Give your answer as a fraction in its simplest form.
Answer:
find prime numbers between 1-20:
= 2,3,5,7,11,13,17,19
=8 prime numbers
probability of winning = 8/20=2/5
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