Answer: the probability the mean weight will exceed 2.1 ounces is 0.09
Step-by-step explanation:
Let x be the random variable representing the amount of icing on a Cuppie Cake large cupcake. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = standard deviation
n = number of samples
From the information given,
µ = 2
σ = 0.3
n = 16
x = 2.1
the probability that the mean weight will exceed 2.1 ounces is expressed as
P(x ≥ 2.1)
For x = 2.1
z = (2.1 - 2)/(0.3/√16) = 1.33
We would determine the probability for the area above z = 1.33 from the normal distribution table. It would be
p = 1 - 0.91 = 0.09
P(x ≥ 2.1) = 0.09
Given the equation below, what is the value of 3 + 6(79 – s)?
7= -s+ 82
Answer:
1 expression) 477 - 6s
2 equation) s = 75
Step-by-step explanation:
Also, the first expression is simplified
What about this one y’all ?
Answer:
y decreases by half everytime
Step-by-step explanation:
» Aiden has 27 fewer
crayons this week than
last week. Last week he
had 56 crayons. How
many crayons does
Aiden have this week?
Show your work.
Answer:
He has 29 crayons left
Step-by-step explanation:
56-27=29
All you have to do is subtract since fewer means less and to find less you need to subtract
Sara cuts a pie into halves.How many pieces are there?
Answer:
2 Pieces
Mostly depends how much slices are there
Step-by-step explanation:
Every element is called half the whole by all equal sections. Similarly, the half fraction is defined as the whole half component of both of the two equivalent sections of the rectangle.
Hope this helps
- Consider the following sets:
P = {x|x is a parallelogram}
C = {x | x is a circle}
K = {x|x is a kite)
R = (x | x is a rectangle)
T = {x|x is a trapezoid)
Which set is a subset of set P? C K R T
Answer:
R
Step-by-step explanation:
A rectangle is a parrellagram. Also, got right on edg.
Answer:
R
Step-by-step explanation:
A person places $82100 in an investment account earning an annual rate of 4.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 2 years.
The future value of $82,100 invested at a 4.3% annual interest rate compounded continuously for 2 years using the formula V = Pe^{rt}, will be approximately $90,137.30.
Explanation:Your question involves the calculation of the future value of an investment using the formula for continuous compound interest, in this case $82,100 invested at an annual rate of 4.3%, over 2 years. This scenario relies on the mathematical concept of compound interest, which means the interest earned on the initial investment is added to the principal, and this combined amount earns interest as well.
Using the formula V = Pe^{rt}. where:
P = principal amount (initial investment) = $82,100,
r = annual nominal interest rate (decimal) = 4.3/100 = .043,
t = time the money is invested for = 2 years,
e = Euler's number (approx. 2.71828).
The calculation then becomes: V = $82,100 * e^(0.043 * 2) = $82,100 * e^(0.086). Using a calculator to do the exponentiation and the multiplication, the balance in the account after 2 years would approximately be $90,137.30.
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Find an integer, x, such that 2, 4, and x represent the lengths of the sides of an obtuse triangle.
A. 2
B. 3
C. 4
D. 6
Answer:
A
Step-by-step explanation:
As the administration looks ahead to next year, Kyra is concentrating on finishing up this year well. Students at her school receive 4 quarter grades, a mid-term exam grade, and a final exam grade for each class. The quarter grades are all weighted equally, the mid-term exam grade is double the weight of a quarter grade, and the final exam grade is four times the weight of a quarter grade. What fraction of the final course grade is the final exam grade? Express your answer as a common fraction.
Answer:
2/5
Step-by-step explanation:
Defining x the weight of each quarter grades (4x for the 4 quarter grades), then the weight of the mid-term exam grade is 2x, and the weight of the final exam is 4x. The addition of all grades is 4x + 2x + 4x = 10x (this represents the combination of grades that makes the final course grade).
So, the final exam grade represents 4x/10x = 2/5 of the final course grade.
Answer:
2/5
Step-by-step explanation:
just did the test
Someone please help. Someone please help.
Radius of the hemisphere and the cone base: R = 2 in
Height of the cone: H = 6 - 2 = 4 in
π ≈ 3,14
Ice inside cone:
[tex]V_1=\frac13\pi R^2\cdot H=\frac13\pi\cdot2^2\cdot 4=\frac{16}3\pi[/tex]
Ice outside cone:
[tex]V_2=\frac12\cdot\frac43\pi R^3=\frac23\pi\cdot2^3=\frac{16}3\pi[/tex]
Total of ice:
[tex]V=V_1+V_2=\frac{16}3\pi+\frac{16}3\pi=\frac{32}3\pi\approx\frac{32}3\cdot3,14=33,49(3)\approx33,5[/tex]
There are 33,5 cubic inches of ice in the cone.
Find the value of r .
Answer:
0.5
Step-by-step explanation:
hypotenuse/adjacent=r
7/14=0.5
11
Adimas found the mean of her 11 math test scores for the first semester.
(76 +87 +65 +88 +67+84 +77 +82 +91 +85 +90) 892
81
11
Using 81 as the mean, find the variance of her grades rounded to the nearest hundredth.
02=
Find the standard deviation of her grades rounded to the nearest hundredth.
Answer:
Variance = 78.5
Standard Deviation = 8.86
Step-by-step explanation:
Given
Mean = 81
Required
Find the variance and standard deviation of the given set of data.
Provided that we already know the mean; to calculate the variance, follow the steps below.
1. Subtract the mean from each data.
76 - 81 = -5
87 - 81 = 6
65 - 81 = -16
88 - 81 = 7
67 - 81 = -14
84 - 81 = 3
77 - 81 = -4
82 - 81 = 1
91 - 81 = 10
85 - 81 = 4
90 - 81 = 9
2. Square these results
-5² = 25
6² = 36
-16² = 256
7² = 49
-14² = 196
3² = 9
-4² = 16
1² = 1
10² = 100
4² = 16
9² = 81
3. Sum these results
Sum = 25+36+256+49+196+9+16+1+100+16+81
Sum = 785
4. Calculate variance by dividing the sum by n - 1 where n = 11
So, n - 1 = 11 - 1 = 10
Variance = 785/10
Variance = 78.50
5. Calculate standard deviation by finding the square root of variance
S.D = √78.50
S.D = 8.86 (Approximated)
Answer:
71.36 and 8.45
Step-by-step explanation:
Show that (x+1)(x+3)(x+5) can be written in the form ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer
The expression (x+1)(x+3)(x+5) can be expanded to the form ax^3+bx^2+cx+d with a, b, and c as positive integers and d as negative by first multiplying (x+1) and (x+3) to get x^2+4x+3, which is then multiplied by (x+5) to obtain x^3+9x^2+23x+15.
Explanation:To show that
(x+1)(x+3)(x+5)
can be written in the form
ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer, perform multiplication for the given factors as follows:
Firstly, multiply (x+1) and (x+3) which yields x^2+4x+3.
Then, multiply this result by (x+5) which gives the final form: x^3+9x^2+23x+15.
So, a=1, b=9, c=23, and d=15 proving the original expression can be written in the stated form.
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The ___ of a two-dimensional figure can be any side.
Answer:
The area I believe.
Step-by-step explanation:
The Length of a two-dimensional figure can be any side.
What is the length?length is the measure of some distance from one end to another end.
The side is a distance between two vertexes joined with another part of the figure.
We can measure that distance which means it could be a length.
Thus, The Length of a two-dimensional figure can be any side.
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You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h= 4t(2)+ 2t models her jump where h is her jumps height in feet t seconds after the mummy scares her. Where did she reach her maximum.
Answer:
She reaches her maximum height after 0.25 secondsStep-by-step explanation:
The question is not properly structured and the equation is also incorrect. Here is the correct question.
You and some friends went to a haunted house on Halloween. The mummy scared one friend so much that she jumped into the air! The equation h= -4t²+ 2t models her jump where h is her jumps height in feet t seconds after the mummy scares her. When did she reach her maximum.
Give the equation h= -4t²+ 2t that models my friend jump where h is her jumps height in feet t seconds, At maximum height, her velocity will be zero i.e
Vmax = 0m/s
Velocity is the rate of change in distance of a body i.e V = dh/dt
Given h= -4t²+ 2t
V = dh/dt = -8t+2
Since v = 0m/s
0 = -8t+2
-8t = -2
t = -2/-8
t = 0.25 secs
She reaches her maximum height after 0.25 seconds
Factor the expression 25x2 – 1.
Answer:
(5x + 1) • (5x - 1)
Step-by-step explanation:
Step 1:
Equation at the end of step 1:
5^2x^2 - 1
Step 2:
Trying to factor as a Difference of Squares :
Factoring: 25x^2-1
Theory :
A difference of two perfect squares,
A difference of two perfect squares, A^2 - B^2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B)
= A^2 - AB + BA - B^2
= A^2 - AB + AB - B^2
= A^2 - B^2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 25 is the square of 5
Check : 1 is the square of 1
Check : x^2 is the square of x^1
Factorization is :
(5x + 1) • (5x - 1)
Final result :
(5x + 1) • (5x - 1)
Answer:
Step-by-step explanation:
(5x-1) (5x+1)
Identify two factors that have a product of 1 7/8.
Will give Brainliest
Answer:
17×1= 17, and 8×1= 8
17 and 8 is ur answer
i hope its right...
Step-by-step explanation:
1 7/8 into an improper fraction is 15/8
You can say that
3 5
---- x ----
2 4
What is the domain of the function y=3x?
Answer:
The domain is all real numbers
Step-by-step explanation:
if y = 3x and x can be any number
you can do 3 times -29 or 3 times 1/3
Solve |x| + 7 < 4.
A) {x | x < -11 or x > -3}
B) {x | -3 < x < 3}
C) Ø
Answer:
C
Source:
Trust me
Percent change
Original amount: 165
End amount: 222.75
Answer:
35%
Step-by-step explanation:
The percent change is calculated as
[tex]\frac{change}{original}[/tex] × 100%
change = 222.75 - 165 = 57.75, thus
% change = [tex]\frac{57.75}{165}[/tex] × 100% = 0.35 × 100% = 35%
The percent change in value is 35%, and it is a percentage increase.
To calculate the percent change in value, we use the formula: ((new value - original value) / original value) * 100. In this case, the new value is $222.75 and the original value is $165. Plugging in these values, we get ((222.75 - 165) / 165) * 100 = 35%. Therefore, the percent change in value is 35%. Since the value has increased, it is a percentage increase.
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The probable question may be:
If the original amount is $165, and it has increased to $222.75, what is the percent change in the value, and is it a percentage increase or decrease?
If the perimeter of a square is 60 inches, how long is each side?
Answer:
15
Step-by-step explanation:
Since a square has 4 sides, that means that each side is equal to the other three sides because it is a square. If so, we do 60/4 to get is 15. To check the answer 15x4 is equal to 60.
Answer:
each side will be 15
Step-by-step explanation:
because if its a square and all the sides are the same lengh and one of the sides are 15 then all of the other sides will also be 15,so that will equal 60.
A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle θ to the horizontal is given by R(θ)=672sin(2θ), where R is measured in feet. Round to two decimal places. Write DNE if the solution does not exist.
A) At what angle θ should the ball be hit if the golfer wants the ball to travel 450 feet (150 yards)?
degrees
B) At what angle θ should the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)?
degrees
" role="presentation" style="position: relative;">C) At what angle θ should the ball be hit if the golfer wants the ball to travel at least 480 feet (160 yards)?
degrees
D) At what angle θ should the ball be hit if the golfer wants the ball to travel 720 feet (240 yards)?
Answer:
A) 21.02°
B) 26.74°
C) 22.79°
D) DNE
Step-by-step explanation:
We can solve the equation for the angle:
D = 672·sin(2θ)
D/672 = sin(2θ)
arcsin(D/672) = 2θ
θ = arcsin(D/672)/2
A) For D = 450, θ = arcsin(450/672)/2 = 21.0198° ≈ 21.02°
B) For D = 540, θ = arcsin(540/672)/2 = 26.7363° ≈ 26.74°
C) For D = 480, θ = arcsin(480/672)/2 = 22.7923° ≈ 22.79°
D) For D = 720, θ = arcsin(720/672)/2 = DNE
Which of the following can have a NEGATIVE impact on your credit score
1) paying bills on time
2) paying down balances on your credit card accounts
3) applying for multiple credit cards in a short period of time (e.g., a week)
The answer option which can have a negative impact on your credit score is: 3) applying for multiple credit cards in a short period of time (e.g., a week).
A credit score refers to a numerical expression between 300 to 850, that typically represents an individual's financial history and credit worthiness.
This ultimately implies that, the higher your credit score, the higher and better it is to obtain a credit (money) from a potential lender.
Generally, the ratings of a credit score by FICO include the following;
A credit score ranging from 670 to 739 is considered to be a good credit score.A credit score of 740 to 799 is better.A credit score of 800 to 850 is considered to be excellent.Generally, the best ways to improve your credit score are;
1. You should ensure you don't pay less than the minimum amount due.
2. You should ensure you pay your bills on time or as at when due.
3. You shouldn't move credit card debt around.
4. You should pay down balances on your credit card accounts.
However, when you apply for multiple credit cards in a short period of time (e.g., a week), it is most likely to have a negative impact on your credit score.
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A student was given the equation x^2+2x-16=0 to solve by completing the square. The first step that was written is shown below. ——> X^2 + 2x=16<—— The next step in the student’s process was x^2 +2x+c =16+c. State the value of c that creates a perfect square trinomial.
Answer:
[tex]x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}[/tex]
Step-by-step explanation:
Quadratic Equation Given:
[tex]x^2+2x-16=0[/tex]
[tex]x^2 + 2x=16[/tex]
[tex]$c=\left( \frac{b}{2} \right)^2 $[/tex]
[tex]x^2 + 2x+1=16+1[/tex]
[tex](x+1)^2=17\\[/tex]
[tex]x+1=\pm \sqrt{17} \\[/tex]
[tex]x=-1 \pm \sqrt{17} \\[/tex]
[tex]x_{1}=-1+\sqrt{17},\:x_{2}=-1-\sqrt{17}[/tex]
Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.
We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], with a vertex at point (h,k).
Let us write equation of parabola using our given information as:
[tex]y=a(x-(-8))^2-7[/tex]
[tex]y=a(x+8)^2-7[/tex]
Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:
[tex]-4=a(-7+8)^2-7[/tex]
[tex]-4=a(1)^2-7[/tex]
[tex]-4+7=a-7+7[/tex]
[tex]3=a[/tex]
Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex].
if one letter is chosen at random from the word substitute, what is the probability that the letter chosen will be a "t"?
Please show the work. Thank you
Answer:
3/10
Step-by-step explanation:
there are 10 letters in substitute
there are 3 t's
3/10
The probability of choosing the letter 't' will be 3 / 10.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
If one letter is chosen at random from the word substitute.what is the probability that the letter chosen will be a "t"?The probability will be calculated as:-
There are 10 letters in the word SUBSTITUTE.
Out of these 10 letters, t is three times in the word
So probability will be:-
P = 3 / 10
Therefore the probability of choosing the letter 't' will be 3 / 10.
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$ 20,000 is invested at a rate of 5% compounded quarterly. Identify the compound interest function ta model the situation. Then find the balance after 5 years.
Answer:
the balance after 5 years is: 26540.744
Step-by-step explanation:
Given the information:
P = initial balance = $ 20,000r = interest rate (decimal) = 5% = 0.05n = number of times compounded annually = 4t = time = 5We have the compound interest function ta model the situation is:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
<=> A = [tex]20000(1+\frac{0.05}{4} )^{4*5}[/tex]
<=> A = $26540.744
Hence, the balance after 5 years is: $26540.744
Answer:
$25,640.74
Step-by-step explanation:
The total compound interest is $5,640.74.
The final balance is $25,640.74.
with zero additional deposits
hope this helps:)
Find the percent of change. Round to the nearest tenth of a percent if necessary. 10 inches to 25 inches. ___ % increase.
Answer:
150% change
Step-by-step explanation:
Formula for Percent change = C =[ (new - old)/ old ]* 100%
C = [ (25 in. - 10 in.) / 10 in. ] = [15/10 ] * 100% = 150 %
work out the perimeter of a semicircle with radius 3cm.Give answer in terms of pi.
Answer:
15.42477796
Step-by-step explanation:
1/2π x 6 + 6
- sorry if its wrong
Answer:
3pi
Step-by-step explanation:
refer to the picture for steps.
Helen is using glass tiles that each measure one square centimeter to make a
decorative square plate. The plate will use 144 square centimeters of glass tiles.
How many glass tiles will Helen use in one row of her plate?
Answer: 12
Step-by-step explanation:
12 times 12 is 144 so 12.in each row
Helen will use 12 glass tiles in one row of her plate, as the square plate has a total area of 144 square centimeters and each tile measures one square centimeter.
Explanation:The student's question involves calculating the number of glass tiles Helen would use in one row of a square plate, given that she has 144 square centimeters of glass tiles and each tile measures one square centimeter. To determine the number of tiles in one row, we need to remember that the area of a square is equal to the side length squared. Since the total area is 144 square centimeters, we take the square root of 144 to find the length of one side, which is 12 centimeters. Therefore, Helen will use 12 glass tiles in one row of her plate, as there would be 12 tiles lengthwise and 12 tiles widthwise to make up the total area of 144 square centimeters.
If you sleep 6 hours out of 24 hours, what percent of the time do you sleep?
Thanks and be quick!
Answer:
I'm not sure which one 25% i put the wrong number in
If you sleep 6 hours out of 24 hours, you sleep for 25% of the time.
To find the percentage of time spent sleeping, one must divide the number of hours slept by the total number of hours in a day and then multiply by 100. In this case, a person sleeps for 6 hours in a 24-hour day. The calculation is as follows:
Percentage of time spent sleeping = (Number of hours slept / Total number of hours in a day) × 100%
Percentage of time spent sleeping = (6 hours / 24 hours) × 100%
Percentage of time spent sleeping = 0.25 × 100%
Percentage of time spent sleeping = 25%
Therefore, sleeping for 6 hours in a 24-hour period means a person spends 25% of their time sleeping.