There are 6 such paths, so there are 6 outcomes in the sample space that show Casey winning.
We can use a tree diagram to visualize the different outcomes of Casey's rolls:
Each branch of the tree represents one roll of the number cube.
The first two rolls are independent and equally likely to be any of the six numbers.
If the first two rolls are the same number, then Casey gets to roll again. If the third roll is a 6, she wins.
We can count the number of outcomes in the sample space that show Casey winning by counting the number of paths in the tree that lead to a 6 on the third roll.
These are:
1-1-6
2-2-6
3-3-6
4-4-6
5-5-6
6-6 (rolls again)-6
Therefore, the answer is 6.
To learn more about the sample space;
https://brainly.com/question/28043513
#SPJ1
Abigail is making a jewelry box and covering the entire box with decorative tape. How many square inches of tape will Abigail use to cover the jewelry box?
The amount of tape that Abigail will use to cover the jewelry box is given as follows:
298 in².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.
The dimensions of the box are given as follows:
6 in, 12.5 in and 4 in.
Hence the amount of tape, given by the surface area, is obtained as follows:
S = 2 x (6 x 12.5 + 6 x 4 + 12.5 x 4)
S = 298 in².
Missing InformationThe dimensions of the box are given as follows:
6 in, 12.5 in and 4 in.
More can be learned about the surface area of a rectangular prism at https://brainly.com/question/1310421
#SPJ1
If m26=85°, what is the measure of 23?
The measure of angle 3 is 95°
What are angles in parallel line?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
When we have two parallel lines and they are intersected by a transversal , the angles on the parallel lines are corresponding and equal.
Therefore angle 3 = angle 7
angle 7 = 180-(angle 6) (angles on a straight line)
angle 7 = 180-85
= 95°
angle 3 = angle = 7 = 95°
Therefore the value of angle 3 is 95°
learn more about angles on parallel lines from
https://brainly.com/question/24607467
#SPJ1
Use the diagram to complete the proportion. (Geometry)
FDBGEC
Answer:
The answer is
13)CE
14)EG
15)BD
16)BF
Principle interviewed all math and english teachers and asked them to rank his school leadership on a scale of 1 to 10. He will use the result of the survey to report to his boss to show his school management abilities
1.Non response and household bias
2.Sampling and household bias
3.Response and non response bias
4.Response and sampling bias
The correct answer is 3. Response and non-response bias.
Response bias occurs when the way that questions are asked or worded, or the context in which they are asked, influences how respondents answer them. This can lead to inaccurate or incomplete information being collected.
Non-response bias occurs when some individuals selected to participate in a survey do not respond. This can happen for various reasons, such as being unavailable, unwilling, or unable to participate. Non-response bias can skew the results of a survey because the characteristics of those who do not respond may differ from those who do respond.
In this scenario, the principal has asked all math and English teachers to rank his school leadership on a scale of 1 to 10. If some teachers do not respond to the survey or are unavailable, unwilling, or unable to participate, this could lead to non-response bias.
Additionally, if the principal has a reputation for being well-liked or well-respected, some teachers may feel pressured to give a higher rating than they otherwise would, which could lead to response bias.
To know more about Response and non-response bias follow
https://brainly.com/question/28047176
#SPJ1
Pls help
A storage bin has the shape of a cylinder with a
conical top. What is the volume of the storage bin
Answer:
V = π(5.1^2)(7.1) + (1/3)π(5.1^2)(8.6)
= 184.671π + 74.562π
= 259.233π cubic feet
= about 814.4 cubic feet
17. What is the name of the shape Kimberly forms by connecting the points? Be as specific as possible.
The name of the shape Kimberly forms by connecting the points is a plane shape
The name of the shape Kimberly forms by connecting the points?From the question, we have the following parameters that can be used in our computation:
A shape is formed by connecting points
As a general rule; shapes formed by connecting points are referred to as plane shapes, and examples of them are:
SquaresTrianglesCircleTrapezoidParallelogramEtcRead more about plane shape at
https://brainly.com/question/9721576
#SPJ1
A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is
orange. Determine P(not blue) if the spinner is spun once. (answer in percentage please)
Answer: Therefore, the probability of not landing on blue when spinning the spinner once is 62.5%.
Step-by-step explanation: There are 8 sections on the spinner, and 3 of them are blue. Therefore, the probability of landing on blue is:
P(blue) = 3/8 = 0.375
The probability of not landing on blue is the complement of the probability of landing on blue:
P(not blue) = 1 - P(blue) = 1 - 0.375 = 0.625
To convert this probability to a percentage, we can multiply by 100:
P(not blue) = 0.625 x 100% = 62.5%
The stem-and-leaf plot displays the amount of time, in minutes, that 10 players spent practicing their serving skills for an upcoming tennis tournament.
1| 2, 2, 9
2| 0, 2, 6
3| 1, 1
4| 0
5|
6| 8
Key: 3|1
means 31
Part A: Calculate the mean, median, mode, and range for the data given. Show your work.
Part B: Should the tennis players report the mean or median value to show they are less prepared for the tournament? Explain based on the scenario.
Part(A),
The value of the mean is 27.1, the value of the mode is 12 and median is 27.5.
Part(B),
Tennis players should report the median value to show they are less prepared for the tournament.
Part A:
To calculate the mean, we need to find the sum of all the data values and divide by the total number of values:
Sum of the data = 12 + 12 + 29 + 20 + 22 + 26 + 31 + 31 + 40 + 68 = 271
Number of data values = 10
Mean = sum of the data/number of data values
Mean = 271 / 10
Mean = 27.1
Therefore, the mean time spent practicing is 27.1 minutes.
To find the median, we need to arrange the data in order from smallest to largest:
12, 12, 20, 22, 26, 29, 31, 31, 40, 68
There are 10 data values, so the median is the average of the two middle values:
Median = (26 + 29) / 2
Median = 27.5
Therefore, the median time spent practicing is 27.5 minutes.
To find the mode, we need to identify the data value that occurs most frequently. In this case, there are two modes:
Mode = 12 and 31
Therefore, the modes for the time spent practicing are 12 and 31 minutes.
To find the range, we need to subtract the smallest data value from the largest data value:
Range = largest data value - smallest data value
Range = 68 - 12
Range = 56
Therefore, the range of time spent practicing is 56 minutes.
Part B:
Based on the scenario, it is more appropriate for the tennis players to report the median value to show they are less prepared for the tournament. This is because there is one outlier value of 68, which is much larger than the other data values.
The mean is affected by outliers and may not represent the typical amount of time spent practicing for the tournament. On the other hand, the median is not affected by outliers and represents the middle value of the data set, which is a more accurate measure of the typical amount of time spent practicing.
Therefore, tennis players should report the median value to show they are less prepared for the tournament.
To know more about mode mean and median follow
https://brainly.com/question/31211262
#SPJ1
Sydney has 1 1/5 yards of ribbon to make bows. Each bow is made from a piece of ribbon that is 2/5 yard long. How many bows can Sydney make?
Group of answer choices
2 3/5
3
2 1/5
2
The number of bows can Sydney make are 3, we get by division.
Given that Sydney has [tex]1\frac{1}{5}[/tex] yards of ribbon to make bows
Each bow is made from a piece of ribbon that is 2/5 yard long
We have to find the number of bows can Sydney make
To find this we have to divide the total length of ribbon by 2/5
[tex]1\frac{1}{5}[/tex]/(2/5)
6/5×5/2
We get 3
Hence, the number of bows can Sydney make are 3
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ1
confusing. someone please help! (there are 2 questions)
Answer:
Step-by-step explanation:
The rule for a triangle is that if you add the 2 shorter sides, it must be greater than the longest side (can't even be =, must be bigger.
A. 36+48>60 true yes triangle
B 6.2+5.7>9.4 yes triangle
C. 20+20 is not greater than 50 no not at triangle
D. 12+24>32 yes triangle
Vertical angles mean angles across from each other when 2 lines intersect.
So:
B, C, D are vertical angles
[tex]x^2=225[/tex]
Use the square root property to solve the equation. The equation has real number solutions.
PLEASE HELP ME , I NEED TO PASS !
The number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
Using the sine rule;
29/sin20° = 32°/sinT
T = (33 × sin20°)/29° {cross multiplication}
m∠T = 23 {to the nearest degree}
m∠S = 180 - (20 + 23)° {sum of interior angles of a triangle}
S = 127°
Therefore, the number of triangle that can be formed is one, with angles m∠S and m∠T derived to be 127° and 33° using the sine rule.
Read more about sine rule here: https://brainly.com/question/4372174
#SPJ1
if x=4 units, y=12 units, and h=8 units find the area of the parallelogram
The area of a parallelogram with the given base and height is 96 square units.
Given that, x=4 units, y=12 units, and h=8 units.
From the given figure,
Area of parallelogram = Base×Height
Here, b=4+12 =16 units and h=8 units
Now, area of parallelogram = 16×8
= 96 square units
Therefore, the area of a parallelogram with the given base and height is 96 square units.
Learn more about the area here:
https://brainly.com/question/27683633.
#SPJ1
9.
Refer to the figure to complete the proportion.
a h
C7
O
O
h
a
The proportion when completed for the triangles is a/c = h/b
Completing the proportionFrom the question, we have the following parameters that can be used in our computation:
The right triangles
The first expression in the proportion is a/c
This proportion represents leg/hypotenuse expression
Using this as a guide, we can make use of the following proportion
h/b
So, the complete equation is a/c = h/b
Read more about right triangles at
https://brainly.com/question/2437195
#SPJ1
2. A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and an opening 6 cm wide. If all the ice melted in the cup, would it overflow?
3.A family-sized box of cereal with dimensions 3x9x12 inches costs $6, while the regular size with dimensions 2 x 8 x 9 inches costs $4.50. What is the difference in price per cubic inch?
4. How does the volume of a cylinder with a radius of 6 inches and a height of 8 inches compare to the volume of a cylinder with radius of 8 inches and height of 6 inches?
Part(2),
The volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.
Part(3),
The difference in price per cubic inch is $0.0128/in³.
Part(4),
The volume of the cylinder with a radius of 8 inches and a height of 6 inches.
Part(2)
The volume of a cone is given by the formula V = (1/3)πr²h,
where r is the radius and h is the height. The volume of the snowcone is therefore V = (1/3)π(4 cm)²(12 cm) = 201.06 cubic cm.
V = (1/3)π(3 cm)²(12 cm) = 113.1 cubic cm.
Since the volume of the snowcone is larger than the volume of the paper cup, the snowcone will overflow when it melts.
Part(3)
To compare the cost per cubic inch of the two sizes of cereal boxes, we need to calculate the volume of each box and divide the cost by the volume.
The volume of the family-sized box is V = 3 in x 9 in x 12 in = 324 cubic inches.
The cost per cubic inch is therefore $6/324 in³ = $0.0185/in³.
The volume of the regular-sized box is V = 2 in x 8 in x 9 in = 144 cubic inches. The cost per cubic inch is, therefore, $4.50/144 in³ = $0.0313/in³.
The difference in price per cubic inch is $0.0313/in³ - $0.0185/in³ = $0.0128/in³.
Part(3)
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
For the cylinder with a radius of 6 inches and a height of 8 inches, the volume is V = π(6 in)²(8 in) = 904.78 cubic inches.
For the cylinder with a radius of 8 inches and a height of 6 inches, the volume is V = π(8 in)²(6 in) = 1206.37 cubic inches.
Therefore, the volume of the cylinder with a radius of 8 inches and a height of 6 inches.
To know more about volume follow
https://brainly.com/question/23029382
#SPJ1
Miss Kenny teaches a chemistry class. She finds that she has 7/8 of a pound of clay for a project. The project requires 1/6 of about how many projects can, Miss Kenny complete without running out of clay
Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.
We know that,
A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
To find out how many projects Mrs. Kenny can complete with 7/8 pound of clay, we need to divide 7/8 by 1/6:
= (7/8) ÷ (1/6)
To divide fractions, we need to invert the second fraction and multiply:
= (7/8) × (6/1)
Simplifying the fractions, we get:
(7 × 6)/(8 × 1) = 42/8 = 5 1/4
Thus, Mrs. Kenny can complete 5 projects with 1/4 of a pound of clay left over.
Learn more about fractions here:
brainly.com/question/24370499
#SPJ1
4. Use the formula found in Exercise #31 to calculate
the initial deposit of an account that is worth
$14,472.74 after earning 5.5% interest compounded
monthly for 5 years. (Round to the nearest dollar.)
The amount that was initially deposited is obtained as $10,100.
What is Compound interest?Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods.
The interest earned in each subsequent period is added to the principal, and the interest is then calculated on the new, larger amount.
We have that;
A = P (1 + r/n)^nt
Then we have;
A = amount
P = principal
r = rate
n = number of times compounded
t = time in years
Then;
14,472.74 = P(1 + 0.055/12)^12 * 5
P = $10,100
Learn more about compound interest:https://brainly.com/question/14295570
#SPJ1
Find each angle and arc measure.
m∡RST = ______ degrees
m∡RUT = ______ degrees
(50 POINTs will give BRAINIEST FOR EFFORT)
m∡RST angle is 146 degrees and m∡RUT is 157 degrees are the arc measures.
Let us find angle RVT
The sum of four angles should be 360 degrees
∠RVS +∠SVU+∠UVT+∠RVT=360
64+139+75+x= 360
278+x=360
x=360-278
x=82 degrees
Arc measure m∡RST =64+82
m∡RST = 146 degrees
m∡RUT = 82+75
m∡RUT = 157 degrees
Hence, m∡RST is 146 degrees and m∡RUT is 157 degrees are the arc measures.
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ1
What is the product of the matrices Matrix with 1 row and 3 columns, row 1 negative 3 comma 3 comma 0, multiplied by another matrix with 3 rows and 1 column. Row 1 is negative 3, row 2 is 5, and row 3 is negative 2.?
Matrix with 2 rows and 1 column. Row 1 is 9, and row 2 is 15.
Matrix with 1 row and 3 columns. Row 1 is 9 and 15 and 0.
Matrix with 3 rows and 3 columns. Row 1 is 9 comma negative 9 comma 0, row 2 is negative 15 comma 15 comma 0, and row 3 is 6 comma negative 6 comma 0.
[24]
The product of the matrices is [24].
Given is a row matrix and a column matrix, we need to find the product of both,
So,
A = [-3, 3, 0]
B = [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]
Now, the product will be =
AB = [-3, 3, 0] × [tex]\left[\begin{array}{ccc}-3\\5\\-2\end{array}\right][/tex]
AB = [9 + 15 + 0]
AB = [24]
Hence the product of the matrices is [24].
Learn more about matrices click;
https://brainly.com/question/11367104
#SPJ1
analyze the diagram below, and complete the instructions that follow
Find the unknown side length, x. Write your answer in simplest radical form.
A. 15
B. 5√10
C. 2√70
D. 4√37
The value of the length x is 2√70. Option C
How to determine the value
To determine the value of the length of the triangle, we need to consider the different trigonometric identities, they are;
sinecosinetangentcotangentsecantcosecantNow, using the Pythagorean theorem, we have;
17² = x² + 3²
Find the square values and substitute
289 = x² + 9
collect the like terms
x² = 289 - 9
Subtract the values
x² = 280
Find the square root of both sides
x = √280
Find the values
x = √4× 70
x = 2√70
Learn about trigonometric identities at: https://brainly.com/question/22591162
#SPJ1
L Pretest: Unit 2
Question 16 of 45
A relation is called a function when each element in the domain is paired with
just one element from which of the following?
OA. Range
OB. Solution variables
OC. Independent variables
OD. Inputs
SUBMIT
A relation is called a function when each element in the domain is paired with just one element from the A. Range
Completing the statementFrom the question, we have the following parameters that can be used in our computation:
The incomplete definition of relation
A relation takes the form
Domain : x
Range : y
The values from the domain are then paired with the range
If these values are paired just once, then it is a function
Read more about relation at
https://brainly.com/question/10283950
#SPJ1
carly and ramil want to draw a line on the coordinate plane that is parallel to line a. carly uses the rule multiply by 1 add 2 to generate her y coordinates. ramil uses the rule multiply by 2 and add 1 to generate his y-coordinates. which students line will be parallel to line d? without graphing the lines explain how you know
The students' line that will be parallel to line d is the line with the same slope as d
Which students line will be parallel to line d?The rules are given as
Carly uses the rule multiply by 1 add 2 to generate her y coordinates. Ramil uses the rule multiply by 2 and add 1 to generate his y-coordinatesThis means that the equations of the function are
Carly: y = x + 2
Ramil: y = 2x + 1
If the slope of line d is 1, Carly's line will be parallel to line d and if the slope of line d is 2, Ramil's line will be parallel to line d
This is because parallell lines have equal slopes
Read more about linear relation at
https://brainly.com/question/30318449
#SPJ1
alberto sights the top of a building at an angle of elevation of 70°. if the building is 40 foot tall and alberto's eyes are 6 feet from the ground, how far is alberto from the base of the building?
Answer:
Step-by-step explanation:
pls complete a and b!
a. The error is that the two factors should be 5s and 3s-7s²+1
b. The student out to multiply the two factors if the product will be 15s²-35s³+5s
What is factorization?Factorization or factoring consists of writing a number or another mathematical object as a product of several factors.
For example, if we are given an expression , 2x +6. The expression consist of two terms and the common factor between them is 2 . Therefore we bring the 2 out . i.e 2( x+3). This means the two factors are 2 and x+3
Similarly , 15s²-35s³+5s can be factorized by bring out the common factors between the three terms
= 5s( 3s-7s²+1)
This means that the student omitted +1 and she ought to have cross checked by multiplying the two factors back if the product will be the polynomial.
learn more about factorization from
https://brainly.com/question/25829061
#SPJ1
at age 20 someone sets uo an IRA retirement account with an apr of 5% . at the end of each month he deposits $65 in the account how much will the ira conrian when he retires at age 65? Comprare
That amount to the total deposit made over
The time period
When someone aged 20 sets up an IRA retirement account with an APR of 5% and deposits $65 at the end of each month, when he retires at age 65, the account will have a future value of $131,718.42.
b) Compared to the total deposit he made over time ($35,100.00), he generated a total compounded interest of $96,618.42.
How is the future value determined?The future value can be determined using an online finance calculator, which compounds the interest at 5% over a period of 540 months or 45 years.
Number of years = 45 years (65 - 20)
N (# of periods) = 540 months (45 years x 12)
I/Y (Interest per year) = 5%
PV (Present Value) = $0
PMT (Periodic Payment) = $65
Results:
Future Value (FV) = $131,718.42
Sum of all periodic payments = $35,100.00 ($65 x 540 months)
Total Interest = $96,618.42
Learn more about the future value at https://brainly.com/question/24703884.
#SPJ1
answer for all please need this today worth 50 brianly points
The expression V2 (V2Z) is called _________ ?
The expression [tex]V^2 (V^2_Z)[/tex] is called mean-square speed.
What is mean-square speed?In Mathematics and Science, mean-square speed is sometimes referred to as root-mean-square speed and it can be defined as a measure of the average value of square-speed of particles that are found in a molecule, gas, or liquid.
Mathematically, the mean-square speed of any particle is denoted or represented by this expression [tex]V^2 (V^2_Z)[/tex].
This ultimately implies that, mean-square speed is always calculated as the square root of the average value of the squares of the speeds (velocities) of each particles in thermodynamics and kinetic theory of gases.
Read more on mean-square speed here: https://brainly.com/question/31609540
#SPJ1
Complete Question:
The expression [tex]V^2 (V^2_Z)[/tex] is called ______?
Question 10 of 10
How does the graph of f (x) 3x +2 +4 relate to its parent function?
A. The parent function has been compressed.
B. The parent function has been translated up.
C. The parent function has been stretched.
D. The parent function has been translated to the left.
SUBMIT
The graph of f(x) relate to its parent function by B. The parent function has been translated up.
How does the graph of f(x) relate to its parent function?Given that
f(x) = 3x +2 +4
When evaluated, we have
f(x) = 3x + 6
The parent function of the above is
f(x) = 3x
When f(x) = 3x is compared to f(x) = 3x + 6, we have
Difference = 6
This means that the parant function is translated up by 6 units
Read more about transformation at
https://brainly.com/question/1548871
#SPJ1
supply a polynomial, and a monomial
The monomials in the expression are given as follows:
x², xy, -8y².
The simplified polynomial is given as follows:
9x² + 9xy - 72y².
What is the distributive property?With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.
The expression for this term are given as follows:
9(x² + xy - 8y²).
The inner term is a polynomial composed by the sum/subtraction of the monomials presented as follows:
x², xy, -8y².
Applying the distributive property, the simplified polynomial is given as follows:
9x² + 9xy - 72y².
More can be learned about the distributive property at brainly.com/question/2807928
#SPJ1
Pls, Help due TODAY!!
After the vertical stretch by factor 3 the function becomes g(x)=3x².
The given function is f(x)=x² is vertically stretched by the factor 3.
When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).
Here, g(x)=3×x²
g(x)=3x²
Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².
To learn more about the translation visit:
https://brainly.com/question/17485121.
#SPJ1