The mean age of customers is 27.35 years.
It is well known that age has a normal distribution with a 5-year standard deviation. Additionally, 30% of the time, customers are under the age of 30.
Mathematically,
P (age ≤ 30) = 0.70
Let μ be the mean age of the customer.
P [z ≤ (30 - μ) / σ] = 0.70
The equivalent of "age" in a conventional normal distribution is the z-score or z. It is evident from the usual normal distribution table that when z=0.53, 0.70 probability is reached.
Thus,
z = (30 - μ) / σ
⇒ 0.53 = (30 - μ) / 5
⇒ μ = 27.35
As a result, the average consumer is 27.35 years old.
The probability at each z-score in a standard normal table is represented by the associated z-score. We will look for the number 0.70 in the table, then the row value of 0.5 and the associated column value of 0.03 will be examined. They add up to 0.53 when combined.
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A die is rolled and the spinner is spun. Find each probability.
Hello!
First, let's write the possible options:
Dice: 6 different results.
• 1, 2, , 4, 5, 6.
Spinner: 4 different results.
• A, B, C, D.
Knowing it, let's solve each alternative of your exercise:
a. 1 and AIn the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.
In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.
Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.
Solving:
[tex]\frac{1}{6}\times\frac{1}{4}=\frac{1\times1}{6\times4}=\frac{1}{24}[/tex]b. odd score and B.We'll solve it in a similar way.
We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.
For the spinner, the reasoning will be the same: 1/.
Let's calculate:
[tex]\frac{1}{2}\times\frac{1}{4}=\frac{1\times1}{2\times4}=\frac{1}{8}[/tex]c. number less than 5 and a consonant.In a dice, we have four numbers less than 5: 1, 2, 3,4.
In the spinner, there are 3 consonants (B, C, D).
Let's calculate:
[tex]\frac{2}{3}\times\frac{3}{4}=\frac{2\times3}{3\times4}=\frac{6}{12}=\frac{1}{2}[/tex]
to determine the number of trout in a lake, a conservationist catches 200 trout, tags them and throws them back into the lake. Later, 56 trouts are caught; 14 of them are tagged. how many trout would the conservationist expect to be in the lake
The conservationist expects to be in the lake would be; 142 trouts.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.
We have to find conservationists who expect to be in the lake.
Now, initially, trout count = 200
Then, again 56 trouts caught then, trout count = 200 + 56
But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.
So, trout count = 200 + 56 – 14 = 142.
Hence, the conservationist expects would be; 142 trouts.
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The angles of a triangle are in the ratio 2:8:5 find the size of each side
Answer:
24° , 60° , 96°
Step-by-step explanation:
sum the parts of the ratio, 2 + 8 + 5 = 15 parts
divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.
180° ÷ 15 = 12° , then
2 parts = 2 × 12° = 24°
5 parts = 5 × 12° = 60°
8 parts = 8 × 12° = 96°
the 3 angles in the triangle are 24° , 60° , 96°
O EQUATIONS AND INEQUALITIESSolving a word problem using a quadratic equation with rationa...
Answer:
[tex]\begin{gathered} length\text{ = 8 m} \\ width\text{ = 5.5 m} \end{gathered}[/tex]Explanation:
Here, we want to get the dimensions of the rectangle
Let us represent the length by l and the width by w
From the question:
The length of the rectangle is 3 m less than double the width
Mathematically:
[tex]l\text{ = 2w-3}[/tex]The product of the two represents the area
[tex]\begin{gathered} A\text{ = l }\times\text{ w} \\ lw\text{ = 44} \end{gathered}[/tex]Now, let us substitute the first equation with the second:
[tex]\begin{gathered} w(2w-3)\text{ = 44} \\ 2w^2-3w\text{ = 44} \\ 2w^2-3w-44\text{ = 0} \end{gathered}[/tex]Solving the quadratic equation, we have:
[tex]\begin{gathered} 2w^2-11w+8w-44\text{ = 0} \\ 2w^2+8w-11w-44\text{ = 0} \\ 2w(w\text{ + 4\rparen -11\lparen w+4\rparen = 0} \\ (2w-11)(w+4)\text{ = 0} \\ 2w=\text{ 11} \\ w\text{ = }\frac{11}{2} \\ \\ w\text{ = 5.5} \end{gathered}[/tex]Recall:
[tex]\begin{gathered} lw\text{ = 44} \\ 5.5l\text{ = 44} \\ l\text{ = }\frac{44}{5.5}\text{ = 8 } \end{gathered}[/tex]9. What is the value of x?
Answer:
A, 61.
Step-by-step explanation:
(2x+24). If we sub in 61 for x, we get (2(61)+24). Follow order of operations.
2 times 61= 122. Add 24 and you get 146. We can know this is correct because we are given the other angle and it's degrees, whch is also 146 degrees. Therefore, the answer is A, 61.
(2,-9) reflected over the y-axis
The new point is (-2, -9).
What happens when a point is reflected about an axis?
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given, the point to be reflected is : A : (2, -9)
Also, the axis through which the point is to be reflected is y-axis.
Following the statement established in the literature, we have:
The point (2, -9) when reflected over the y-axis, the x-coordinate is assumed to be the additive inverse, thus the new co-ordinate is (-2, -9).
The new point is (-2, -9).
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4x^2 -18x-5 factored form by grouping
4x² - 18x - 5 cannot be factored by grouping.
How to factor quadratic equations?Factoring a polynomial involves writing it as a product of two or more polynomials.
In other words, it is a process of finding the factor.
Therefore, let's factor the quadratic equation as follows:
4x² - 18x - 5
Factorization by grouping means that we need to group the terms with common factors before factoring.
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.
Hence,
4x² - 18x - 5 cannot be factorise by grouping because it has no common factor.
in other word, we cannot, however, use the grouping method to factor 4x² - 18x - 5 because factoring out the GCF from both groupings does not yield a common factor.
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write the answer in standard form(-3x^4 + x^6 – 9x^5+ 2x^2– 7) + (-2x^5 + x - 4x^2– x^4 + 12)
Simplify the expression and express in standard form.
[tex]\begin{gathered} (-3x^4+x^6-9x^5+2x^2-7)+(-2x^5+x-4x^2-x^4+12) \\ =-3x^4+x^6-9x^5+2x^2-7-2x^5+x-4x^2-x^4+12 \\ =x^6-11x^5-4x^4-2x^2+x+5 \end{gathered}[/tex]So answer is,
[tex]x^6-11x^5-4x^4-2x^2+x+5[/tex]The triangle shown is dilated with scale factor =2 which is the image of vertex m after the dilation
ANSWER
(-4, 2)
(Option D)
EXPLANATION
The triangle in the picture is dilated with scale factor 2.
This simply means that the size of the triangle was increased by 2.
To do this, first, let us write out the cordinates of the vertices of the original triangle:
M(-2, 1)
P(2, -2)
A(3, 5)
To dilate this, we will multiply the cordinates by 2, they become:
M' (-4, 2)
P' (4, -4)
A' (6, 10)
Therefore, the vertex M on the image after the dilation is (-4, 2).
(Option D)
You have a goal to practice the guitar for an average of at least 45 minutes per day for one week
An inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.
Given that, You have a goal to practice the piano for an average of at least 45 minutes per day for one week.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Let m be the number of minutes you need to practice on the seventh day
The inequality for the given situation is
245+m≤315
⇒ m≤315-245
⇒ m≤70
Therefore, an inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.
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"Your question is incomplete, probably the complete question/missing part is:"
You have a goal to practice the piano for an average of at least 45 minutes per day for one week. The first six days you practice a total of 245 minutes.
Write and solve an inequality that represents the number of minutes m you need to practice on the seventh day.
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters. She stands 23.1 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. -28.15 m (Diagram is not to scale.) T 1.85 m 23.1 m-
The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
What is the similarity law for triangles?It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.
It is given that:
Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
D = 39.75 m
d = 34.9 m
H:h = D:d
H/1.85 = 39.75/34.9
H = 2.11 m
Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.
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Finding Slope
HELP ME
Answer: slope is -3
Step-by-step explanation: (-5,6) and (-9,-6)
Take your Y values and subtract them -6-6=-12
Take your X values and subtract them -9-(-5) or -9+5= -4
Then your -12 will be your numerator and your -4 will be your denominator
Then Divide
-12/-4= -3
I hope this helps!
Three-inch pieces are repeatedly cut from a 42-inch string. The length of the string after x cuts is given by y = 42-3x. Find and interpret the x- and y-intercepts. The x-intercept is 14 The y-intercept is 42 ✓ This means that after Select Choice cuts, the length of the string is Select Choice ✓ This means that the Select Select Select Choice Choice inches. inches.
1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).
2) This means that after 3 cuts, the length of the string is 33 inches.
3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.
What are the x- and y-intercepts?The x-intercept is the point on the graph where a line crosses the x-axis.
The y-intercept is the point on the graph where a line crosses the y-axis.
The x- and y-intercepts are the coordinate points for graphing data.
Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.
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Could someone please help me this is due at 3 pm and it's allready 2:18 and i only need these questions and i am done please help me. if you answer all you get 20 points! PLEASE HELP
These are the solutions of all the questions
solve equationx^2-2x-7=0
After solving the equation x^2-2x-7=0, values of x are -1 + 2√2 and
-1 - 2√2.
A quadratic equation has a leading coefficient of the second degree.
What is a quadratic equation?
A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
After applying the quadratic formula to it we get,
[tex]x = \frac{-b +\sqrt{b^{2} - 4ac } }{2a} \\ x = \frac{-b -\sqrt{b^{2} - 4ac } }{2a}[/tex]
where a = 1
b = 2
c = -7
After putting the values of a,b, and c, we get
x = -1 + 2√2 and,
x = -1 - 2√2 .
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Complete the flow proof of the converse of the corresponding angles theorem. Fill in the blanks.
When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.
What are perpendicular lines?The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I
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Let f(x) = -3x³ + 9x² - 5x + 15. Use the Factor Theorem to help answer the
following questions.
a) Is a
O Yes
O No
b) Is x + 1 a factor of f(x)?
O Yes
No
1 a factor of f(x)?
c) Is a 3 a factor of f(x)?
O Yes
O No
Answer:
See below. I added words tro the first question "Is a" so that I could answer it.
Step-by-step explanation:
f(x) = -3x³ + 9x² - 5x + 15
f(x) = -(x-3)(3x² + 5)
x((9-3x)x-5)+15
-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16
=======
a) Is a [ghost happy]?
O Yes Yes, as long as it can haunt.
O No
b) Is x + 1 a factor of f(x)?
O Yes Yes
No
1 a factor of f(x)?
Always
c) Is a 3 a factor of f(x)?
O Yes
O No No, as far as I can see.
if covariance between two variables is near 0, it implies that group of answer choices a positive relationship exists between the variables. none of the choices. the variables are not linearly related. the variables are negatively related. the variables are strongly related.
If covariance between two variables is near 0, it implies that the variables are not linearly related.
In probability theory and statistics, covariance is a measure of the combined variability of two random variables in probability theory. The covariance is positive if the larger values of one variable mostly correlate with the greater values of the other variable, and vice versa for the smaller values.It is given that the covariance between two variables is near zero.In mathematical modelling, statistical modelling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.It clearly implies that the variables are not linearly related.To learn more about covariance, visit :
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Answer the question below in the picture please and thank you
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
What is meant by isotope?Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.
If we start with 180 g of the isotope, after one half-life the quantity will diminish to 180 g/2 = 90 g which exists half the original quantity.
This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]
After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]
After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]
But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.
The original quantity can then be rapidly computed for six half-lives using the formula below:
[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]
Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.
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A hyperbola has vertices (±5, 0) and one focus (6, 0). What is the standard-form equation of the hyperbola?show steps
The standard form of a hyperbola with center (h,k) is
We know the vertices are at (5,0) and (-5,0)
The vertices are at (h+a,k) and ( h-a,k)
The center must be at (0,0) and the a value is 5
The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)
c is equal to 6
We know that c^2 = a^2+b^2
6^2 = 5^2 + b^2
36 = 25+b^2
11 = b^2
We can write the equation
a spherical snowball is melting in such a way that its volume is decreasing at a rate numerically equal to twice the surface area. how quickly is the radius of the snowball decreasing?
The radius of the snowball decreasing by -2.
What is rate?
A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.
Let r(t) be a function of the radius of the sphere over time.
The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]
The rate of change of the volume is then [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]
Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex], it seems perfectly possible for the volume to decrease at a rate equal to 2s(t).
That just means that
[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]
Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.
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Kathy and Peter both drive older cars that dont always work in the wintertime. Suppose that Kathy's car works 80% of the time and Peter's works 65% of the time. What is the probability they will both be working on any given morning?
Find the tangent of the angle whose measure is negative pi. (-pi)
First convert the angle measure from radians to degrees using the formula
[tex]\theta\cdot\frac{180}{\pi}[/tex]Were θ represents the angle of interest
So for this exercise the angle is pi, so:
[tex]\pi\cdot\frac{180}{\pi}=180[/tex]Now using the calculator you can determine tha tangent of negative 180º
tan(-180º)=0
So the tangent of negative pi should also be zero
Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week?
True or false?
The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.
As given in the question,
If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them
a:b = c:d
a ÷b = c ÷d
ad = bc
let Sal earns $480 per week and he works 40hours per week
480÷40 = 12
Lidia earn $300 per week and she works 25 hours per week
300÷25 = 12
Cross product of their salaries is
480×25=1200
300×40=1200
The ratio of their salaries and their product are equal.
Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true
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HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP HELP HELP
Answer:
a) 1.6×10∧-6
b)2×10∧7
What is 3 2/5 plus 2 1/5?
Answer: 5 3/5
Step-by-step explanation:
3 + 2 = 5
2/5 + 1/5 = 3/5
5 + 3/5 = 5 3/5
Hope this helps!
How to rewrite the equation. Need the answers fast
Answer:
In this photo.
Put a heart and 5 mark for the answer.
Thanks ヽ(>∀<☆)ノ: o(≧▽≦)o
ヽ(・∀・)ﾉ: (´｡• ω •｡)
(o･ω･o): (＠＾◡＾)
(´• ω •: (＾▽＾)
Rhoni reads at a rate of 75 pages per hour. The number of pages Rie reads over time is shown in the table.
A table with two rows and five columns is shown. The first row is Time in hours. The second row is number of pages. Three hours, one hundred ninety-five pages. Five hours, three hundred twenty-five pages. Nine hours, five hundred eighty-five pages. Ten hours, six hundred fifty pages.
Question 1
Part A
Who has a greater rate of reading?
Select the answers from the drop-down lists to correctly complete the sentence.
The individual that has a greater rate of reading is Rhoni.
Who has a greater rate of reading?Rate measures how fast a person is reading a book. Rate is the total pages read per time. Rate is determined by dividing total pages read by the total time spent reading.
Division is the operation used in mathematics that is used to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.
Rie's rate = pages read / time
195 / 3 = 65 pages per hour
325 / 5 = 65 pages per hour
Rie's rate is 65 pages per hour. While Rhoni's rate is 75 pages per hour. This means that Rhoni reads faster than Rie.
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Algebra homework pls help
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.
Detailed explanation:Assume that a team has N players.
Each squad may have anywhere from 3 to 5 players, so
3 ≤ 5 ...(i)
Let P represent a player's total points in a single game round.
Each round of the game allows for a maximum of 10 points for each player, so
0 ≤ p ≤ 10 ....( i)
(1) Elena assembled a team of five people.
As a result, 5 players' points in 1 round equal 5P.
Equation (ii) yields the range of
0 ≤ 5p ≤ 50.
As a result, Elena's team's points total ranges from 0 to 50.
(2) If each shot is off by one point, then
One player's points in one round are equal to 10-1=9.
So, 9 x 5 = 45 points were collected by 5 players in 1 round.
(3) Assume that R represents the number of teams as an integer.
the game involves at least three teams, therefore
R ≥ 3 ...( iii)
Given that N players make up one team,
R team has NR players, where R is 3, 4, or more.
Next, using equation (i)
3R ≤ 5R
Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.
The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.
Answer:
(I) Between 0 and 50.
(ii) Between 3 and 5.
(iii) Between 3R and 5R, where R = 3,4,5,...
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sketch the graph or the inverse of the function pictured
Step 1:
Draw the table for the input x and output y.
Step 2:
From the table, we can see that the function is an exponential function.
[tex]\begin{gathered} y=x^2 \\ \text{for x = 0, y = 0} \\ \text{for x = 1, y = 1} \\ \text{for x = 2, y = 4} \\ \text{for x = 3, y = 9} \\ \text{Hence, y = x}^2 \end{gathered}[/tex]Step 2:
Find the inverse of the function.
[tex]\begin{gathered} y=x^2 \\ \text{The inverse of } \\ y=x^2 \\ is \\ y\text{ = }\pm\sqrt[]{x} \end{gathered}[/tex]Step 3:
The two graphs below, show the graph of the inverse for both negative and positive square roots of x.
[tex]\text{The blue graph above shows the graph for y = +}\sqrt[]{x}[/tex][tex]\text{The blue graph above shows the graph of y = -}\sqrt[]{x}[/tex]Final answer
The blue graph is the inverse of the red graph.