Lets say the number is ab. Its value is 10a + b
When it is reversed it is 10b + a = 12a+1.2b (from the condition its value should increase 0.2 times).
11 a = 8.8b
a/b = 8.8/11 = 0.8/1 = 8/10 = 4/5 ( we do this because a and b should be natural numbers less than 10).
answer is 45.
A two-digit number less than 100 that increases by one-fifth of its original value, when its digits are reversed, can be found by setting up an equation. By defining the tens digit as 'a' and the unit digit as 'b', the equation 6a = 9b is derived. Solving for the digits within their possible values, the number 12 is found.
Explanation:To find a number less than 100 that increases by one-fifth of its value when its digits are reversed, we need to set up an equation. Let's call the tens digit a and the units digit b. The number can be written as 10a + b. When the digits are reversed, the number becomes 10b + a. The problem states that reversing the digits increases the number by one-fifth of its original value, which gives us the equation:
(10a + b) + \frac{1}{5}(10a + b) = 10b + a
Now solving the equation:
6a = 9b
As a and b are digits, their possible values range between 0 and 9. We find that a = 1 and b = 2 satisfy the equation. Hence, the number is:12
When we reverse the digits, we get 21, which is greater than 12 by \frac{1}{5} of 12, as required.
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Which expression is equivalent to 10k+17–7j-18-11k
A. -8jk-1
B. -7j-k-1
C. -7j+k+1
D. -8j-k
Answer:
B
Step-by-step explanation:
An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.
10k + 17 - 7j - 18 - 11k
10k -11k + 17 - 18 - 7j Move to group like terms together.
-k - 1 - 7j
This is the same solution as B written in a different order.
Answer:
BBBBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:)
To the nearest hundredth, what is the value of x?
Question 2 options:
36.08
41.51
47.81
72.88
➷ cos41 = x/55
x = cos41 x 55
x = 41.50902
The correct option would be 41.51
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
41.51
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]
Multiply both sides by 55
55 × cos41° = x
⇒ x = 41.51 ( to the nearest hundredth )
The rule for a pattern is add 6. The first term is 5. Write the first five terms in a pattern
Consider two events such that P(A)=1/4, P(B)=2/5, and P(A∩B)=1/10. Are events A and B independent events?
Yes, they are independent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)≠P(A∩B)
Yes, they are independent because P(A)×P(B)≠P(A∩B)
Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).
To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:
P(A AND B) = P(A)P(B)
Given:
P(A) = 1/4
P(B) = 2/5
P(A∩B) = 1/10
Let's calculate the product of P(A) and P(B):
P(A)P(B) = (1/4) × (2/5) = 1/10
Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:
P(A AND B) = P(A)P(B)
This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.
Look at the function f(x)=x^2-2. Which of the following describes the domain and range of the function and its inverse?
Answer:
A
Step-by-step explanation:
The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.
This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.
An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.
Answer:
A.
Step-by-step explanation:
I just got 100% on the quiz.
Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
i.e. 0.2<0.42<0.7<0.87
Step-by-step explanation:
Since we have given that
1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]
2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]
3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]
4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]
We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:
So, 0.2<0.42<0.7<0.87
Hence, it becomes
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?
3 + 9 + 15 + ...
3 + 9 + 27 + ...
3, 9, 27, ...
3, 9, 15, ...
The first answer is correct
Answer:
3 + 9 + 27 + ...
Step-by-step explanation:
3 + 9 + 15 + ... is not a geometric series because it has no common ratio.
[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]
3 + 9 + 27 + ... is a geometric series because there is a common ratio;
[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]
3, 9, 27, ... is a geometric sequence and not a series. The sum of all the terms in a geometric sequence forms a geometric series.
3, 9, 15, ... is a not a geometric series.
The mean number of words per minute (WPM) read by sixth graders is 81 with a standard deviation of 17 WPM. If 130 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 77.21 WPM? Round your answer to four decimal places.
Answer:
The probability that the sample mean would be greater than 77.21 WPM = 0.9945
Step-by-step explanation:
Mean number of Words per Minute = u = 81
Standard Deviation = s = 17
sample size = n = 130
Target value = x = 77.21
we can find the probability by converting x to z-score.
The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
using given values, z-score = [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]
=> -2.54
using the z table, we can find the find the probability of -2.54, that is 0.9945.
Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945
The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).
To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.
Here's the step-by-step process:
1. Identify the given information:
Population mean [tex](\(\mu\))[/tex]: 81 WPM
Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM
Sample size [tex](\(n\))[/tex]: 130
Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM
2. Calculate the standard error of the mean (SEM):
[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]
3. Find the Z-score for the sample mean:
[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]
4. Use the Z-score to find the probability:
We look up the Z-score of -2.543 in the standard normal distribution table.
[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]
This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.
[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]
I will mark brainliest
Answer:
On the surface of the sea
Step-by-step explanation:
Six feet below sea level is marked as -6
Go up 6 feet
-6+6 =0 feet below sea level
That would mean we are at 0, which would be sea level
We would be on the surface of the sea
Instead of 1/4 an hour ellen spent 1/3 of an hour to meet each applicant how much more time did she spend meeting all applicants
Answer:
5 more minutes (total of 20 minutes per applicant)
Step-by-step explanation:
Divide an hour by 1/3 (60/3 = 20 minutes)
Divide an hour by 1/4 (60/4= 15 minutes)
By spending 1/3 of an hour (20 minutes) instead of 1/4 of an hour (15 minutes), she spent 5 more minutes meeting all applicants.
Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange x + 5y = 10 into this form
Subtract x from both sides
5y = - x + 10 ( divide all terms by 5 )
y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{5}[/tex]
• Parallel lines have equal slopes, hence
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (1, 3) into the partial equation
3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line
Answer:
A) y = − 1 /5 x + 16/ 5
Step-by-step explanation:
A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 2125 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answer:
Car 1 : 40 gallons
Car 2 : 15 gallons
Step-by-step explanation:
F = Car 1 Fuel Efficiency
S = Car 2 Fuel Efficiency
F + S = 55
40F + 35S = 2125
Using the first equation...
S = 55 - F
Then substitute into the second equation.
40F + 35(55 - F) = 2125
Simplify
40F + 1925 - 35F = 2125
5F + 1925 = 2125
5F = 200
F = 40
Then plug it back into S = 55 - F
S = 15
Plug it back into F + S = 55 to check.
Hope this helps.
Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
Let car 1 fuel efficiency = x
Let car 2 fuel efficiency = y.
Based on the information given,
x+ y = 55 ...... i
40x + 35y = 2125 ...... ii
Therefore, y = 55 - x ..... iii
Put equation iii into ii
40x + 35(55 - x) = 2125
40x + 1925 - 35x = 2125
Collect like terms
40x - 35x = 2125 - 1925
5x = 200
x = 200/5
x = 40
Since x + y = 55.
y = 55 - 40 = 15
Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
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Solve for x.
x/7 = -3
x = -21
explanation: a trick i used was just do -3 times 7 and get my answer -21. if you are unsure if the answer is right just check your work with a calculator. -21 divided by 7 is -3 so -21 is the value of x. please mark brainliest !!
PLS HELP SQDANCEFAN!!!!!!! Given: circle k(O), the measure of arcs PL=80°, PY=150°
Find: m∠YPL
Thx :)))
Answer:
∠P = 65°
Step-by-step explanation:
The measure of arcs LP and PY are given as 80° and 150°, so their sum is 230°. Arc LY completes the circle of 360°, so is 130°. Inscribed angle P is half that measure, so ...
∠P = 130°/2 = 65°.
URGENT
Let x1 = 6, y1 = 8, and y2 = 2. Let y vary inversely as x. Find x2.
A x2 = 1.5
B x2 = 24
C x2 = 2.67
D x2 = 46
i think the answer is B
The value of x2 is 24.
What is inversely varying?Two variables are inversely varying if one variable value increases then other variable value decreases. We can represent this relation with an equation
y ∝ 1/x
⇒ y=k/x
where k is a constant.
According to asked problem y is varying inversely with x.
given, x1=6
y1=8
putting these values in the above equation,
8=k/6
⇒k=48
Now we have the value of k.
So the inversely varying equation will become,
y=48/x
By putting the value y2=2
2=48/x
⇒x=48/2
⇒x=24
The value of x2 is 24.
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There are 5 brown horses and 4 tan horses in a barn. Sonia will randomly select two horses to ride with her friend. What is the probability that the first horse selected is tan and the second horse selected is brown?
The first one is 4/9 and the second one is 5/9
Final answer:
The probability that the first horse selected is tan and the second horse selected is brown, out of a total of 5 brown horses and 4 tan horses, is 5/18.
Explanation:
The question asks for the probability that the first horse selected is tan, and the second horse selected is brown when there are 5 brown horses and 4 tan horses in a barn. To find this probability, we will multiply the probability of each event happening in sequence.
First, the probability of selecting a tan horse out of the total 9 horses (5 brown + 4 tan) is 4/9. Once a tan horse is selected, there are now 8 horses left, 5 of which are brown. Therefore, the probability of then selecting a brown horse is 5/8.
To find the total probability of both events occurring in sequence (first selecting a tan horse, then a brown horse), we multiply the two probabilities together: 4/9 * 5/8 = 20/72, which simplifies to 5/18.
One surface of a wheel on a toy wagon has an area of 36 square inches. What is the circumference of the wheel?
Answer:
I'm pretty sure the answer is 21.26
I hope thats right if not sorry mark me brainliest
The circumference of the wheel is 21.26 inch
What is circumference?The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.Given:
Area of wheel= 36
πr² = 36
r²= 36/ 3.14
r = 3.385
Now,
Circumference of the wheel is
=2πr
=2*3.14*.3.385
=21.264 inches
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Plsss Urgent !! A container at the petting zoo holds 8138.88 cubic centimeters of grain. Visitors can fill paper cones with grain from the container. The cones have a radius of 4 centimeters and a height of 9 centimeters. How many times can you fill a cone with the grain that is stored in the container? Use 3.14 to approximate the value of Pi.
Answer:
54 times you can fill a cone with the grain that is stored in the container
Step-by-step explanation:
step 1
Find the volume of the paper cone
The volume of the cone is
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=4\ cm[/tex]
[tex]h=9\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{1}{3}(3.14)(4)^{2} (9)=150.72\ cm^{3}[/tex]
step 2
Divide the total volume of the container by the volume of one paper cone
[tex]\frac{8,138.88}{150.72}=54[/tex]
Answer:
Its 54
Step-by-step explanation:
Jen started her homework at 3:45 and she worked for 2 hours and 37 minutes, What time did she finish her homework?
If there are 42 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.
Explanation:The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.
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Triangle with a height of 25 feet and base of 12 feet. What is the area of the triangle?
Answer:
150 ft
Step-by-step explanation:
triangle area formula= (b*h)/2
25 time 12 is 300. divide 300 by 2 and get 150.
Answer:
A = 150 ft^2
Step-by-step explanation:
The area of a triangle is found by using
A = 1/2 b*h where b is the base and h is the height
A = 1/2 (12)*25
A = 6*25
A = 150 ft^2
CALCULUS HELP NEEDED PLEASE!!!!
1.) Find the area or the region bounded by the curves y = x^3 and y = 9x.
a. 0
b. 10.13
c. 40.50
d. 20.25
2.)The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?
a. 1.219
b. 3.830
c. 1.786
d. 5.612
1. The given curves intersect one another three times:
[tex]x^3=9x\implies x(x^2-9)=0\implies x=0,\pm3[/tex]
The area of the bounded region is
[tex]\displaystyle\int_{-3}^3|x^3-9x|\,\mathrm dx[/tex]
[tex]x^3-9x[/tex] is odd, but the absolute value makes it even. More formally,
[tex]|(-x)^3-9(-x)|=|-x^3+9x|=|x^3-9x|[/tex]
which means the integral is equivalent to
[tex]\displaystyle2\int_0^3|x^3-9x|\,\mathrm dx[/tex]
For [tex]0\le x\le 3[/tex], the definition of absolute value tells us that
[tex]|x^3-9x|=9x-x^3[/tex]
so the integral evaluates to
[tex]\displaystyle2\int_0^3(9x-x^3)\,\mathrm dx=\left(9x^2-\frac{x^4}2\right)\bigg|_{x=0}^{x=3}=\frac{81}2=40.5[/tex]
2. Using the disk method, the volume is given by the integral
[tex]\displaystyle\pi\int_0^\pi\sin^2(\sin x)\,\mathrm dx[/tex]
Use a calculator to get the result 1.219.
Identify the graph of x^2-8y=0 for theta=90º and write and equation of the translated or rotated graph in general form.
Answer:
The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* x² - 8y = 0
∵ A = 1 , B = 0 , C =
∴ B² - 4AC = (0)² - 4(1)(0) = 0
∵ B² - 4AC = 0
∴ it will be a parabola.
∵ Ф = 90°
* The point (x , Y) will be (x' , y')
∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ
∵ cos(90) = 0 and sin(90) = 1
∴ x = -y' and y = x'
* lets substitute x and y in the first equation
∴ (-y')² - 8(x') = 0
∴ (y')² - 8x' = 0
* We notice that the x' took the place of y and y' took the place of x
∴ The parabola rotated around the origin by 90°
∴ The equation of the parabola is (y')² - 8x' = 0
* The answer is parabola, with angle of rotation 90°
* The equation is (y')² - 8x' = 0
* Look to the graph
- The blue is x² - 8y = 0
- The green is (y')² - 8x' = 0
Answer:
the correct answer is D)
parabola
Write an equivalent exponential equation for the following three problems.
Answer with step-by-step explanation:
We are given three different expressions and we are to write an equivalent exponential equation for them.
We know that the standard form of a logarithmic expression is given by:
[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form [tex]x = a ^ y[/tex].
1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]
2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]
3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]
public relations is part of business and administrative support true or false
Answer: true :))
Step-by-step explanation:
Public relations is part of business and administrative support as it helps manage a business's image and relationship with the public. Meanwhile, bureaucracy plays a role in not only enforcing policies but also in policy formation.
Explanation:Public relations is indeed a part of business and administrative support. Businesses use public relations to manage and protect their image and relationship with the public. It's a key component to business administration as it helps businesses improve their brand awareness, manage crises, and strengthen relationships with stakeholders.
The question about bureaucracy is a separate query and in this context, the statement is false. Bureaucracy is not only involved in enforcing policies to ensure people comply, but it is also involved in the process of policy formation. Through different departments and offices, information is gathered, policy proposals are developed and recommendations are made to decision-makers.
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Un the morning a farm worker packed 4 pints of strawberries every 5 minutes in the afternoon she packed 3 pints of strawberries ev ery 4 minutes what was the diference between her morning and afternoon packing rates in pints per hour
Answer:
In the morning, the packing rates per hour was 45. In the afternoon, the packing rates per hour was 40. The difference is 5.
10=16(x-2)^2+10
show work
Answer:
x=2
Step-by-step explanation:
10=16(x-2)^2+10
Subtract 10 from each side
10-10=16(x-2)^2+10-10
0 =16(x-2)^2
Divide by 16
0/16 = 16/16 (x-2)^2
0 = (x-2)^2
Take the square root of each side
sqrt(0) = sqrt( (x-2)^2)
0 = x-2
Add 2 to each side
0+2 = x-2+2
2 =x
[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]
Anita earns 60 points every time she shops at a grocery store. She needs a total of 2,580 points to receive a free prize. So far, she has earned 480 points. How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a free prize?
Answer:
35 times
Step-by-step explanation:
The points Anita has remaining for a prize is 2580 - 480 = 2100 points
Since each time she earns 60 points, to get 2100 points, she needs to go:
[tex]\frac{2100}{60}=35[/tex] times
She needs to go 35 times
Answer:
35 times
Step-by-step explanation:
Plz help!
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
What is the equation of the new function g(x) ?
Enter your answer in the box.
g(x)= ____
Answer:
g(x) = 2sin(x) + 3
Step-by-step explanation:
f(x) = sin(x)
transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
so
g(x) = 2sin(x) + 3
The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. (a) What is the probability that a randomly selected bag contains between 10001000 and 15001500 chocolate chips? (b) What is the probability that a randomly selected bag contains fewer than 10251025 chocolate chips? (c) What proportion of bags contains more than 11751175 chocolate chips? (d) What is the percentile rank of a bag that contains 10501050 chocolate chips?
Answer:
A) 0.947; B) 0.0392; C) 0.7257; D) 6th
Step-by-step explanation:
For part A,
We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.
[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]
Using a z-table, we see that the area to the right of z = -1.95 is 0.0256. The area to the right of z = 1.92 is 0.9726. This means the area between them is
0.9726 - 0.0256 = 0.947.
For part B,
To find the probability that fewer than 1025 chips are in the bag, we find the z-score:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]
Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.
For part C,
Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this. To find the proportion greater than this, we subtract from 1:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]
In the z-table, we see that the area under the curve less than this is 0.2743. This means that the area greater than this is 1-0.2743 = 0.7257.
For part D,
We again find the area under the curve less than this. This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.
[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]
In the z-table, we see the area to the right of this is 0.0582. This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.
These questions are solved by converting the specified number of chips to a Z-score and using it to find the corresponding probability in a standard normal distribution table. The various calculated probabilities provide the answers to the different parts of the question.
Explanation:In order to answer these questions, we need to convert the number of chips to a Z-score, which is a measure of how many standard deviations an element is from the mean, and then find the corresponding probability from a standard normal distribution table.
(a) To calculate the probability of a bag containing between 1000 - 1500 chips, you subtract the mean from each and divide by the standard deviation to get Z-scores. Then one can find the corresponding probabilities in a Z-table and subtracting the smaller probability from the larger. This will give you the probability of number of chips falling between those two amounts.
(b) Similarly, to compute the probability of a bag containing fewer than 1025 chips, find the Z-score for 1025 and look it up in the Z-table. The probability that corresponds to that Z-score is the likelihood of having fewer than 1025 chips.
(c) For the the proportion of bags that contains more than 1175 chips, first compute the Z-score for 1175. The corresponding probability in the Z-table gives the proportion for those with numbers equal or less than 1175. To get the proportion for bags with more than 1175 chips, you need to subtract that value from 1 (since the total probability is always 1).
(d) Finally, for the percentile rank, it's again the same process. You find the Z-score for 1050, look up its corresponding probability and multiply it by 100 to convert it into percentile rank.
Learn more about Normal Distribution here:https://brainly.com/question/30390016
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