Answer:
28.26 square inches.
Explanation:
Given a waffle cone with the following properties:
• Height = 6 inches
,• Volume = 56.52 cubic inches.
[tex]\text{Volume of a cone}=\frac{1}{3}\pi r^2h[/tex]Note that the base of the cone is a circle and the area of a circle:
[tex]A=\pi r^2[/tex]Substitute the given values:
[tex]\begin{gathered} 56.52=\frac{1}{3}\times\pi\times r^2\times6 \\ 56.52=2\pi r^2 \\ \pi r^2=\frac{56.52}{2} \\ \pi r^2=28.26in^2 \end{gathered}[/tex]The area of the base is 28.26 square inches.
The heights of 8th grade boys are normally distributed with a mean of 50 inches and a standard deviation ofDraw and label a normal distribution curve below. 4 pts)2) pos) Approximately 99.7% of the heights fall betweenandb) pts) The middle 58% of heights fall betweenandps) What percentage of grade boys are between 55 and 50inches tall2 pts) What is the probability that an sgrade boy will beshorter than 55 inches
EXPLANATION
Let's see the facts:
Heights of 8th grade boys ---------------> Normally distributed
Mean= 50 inches
Standard deviation= 4 inches
d) Probability that boy shorter than 56 inches:
x=56
P(x<56)
We know that z-score=
[tex]z=\frac{x-\mu}{\sigma}[/tex]Replacing terms:
[tex]z=\frac{56-50}{4}=1.5[/tex]P-value from Z-table =
P(x<56) = 0.93319
Answer: The probability that an 8th grade boy will be shorter than 56 inches is 0.93319*100= 93.3%.
c) Percentage of 8th grade boys that are between 56 and and 60 inches tall is:
[tex]z-score_{56}=\frac{56-50}{4}=\frac{3}{2}[/tex]P-value from Z-table =
P(x<60) = 0.93319
[tex]z-score_{56}=\frac{60-50}{4}=\frac{5}{2}[/tex]P-value from Z-table =
P(x<60) = 0.99379
Then, subtracting both probabilities.
P(56
Answer: the percentage of 8th grade boys that are between 56 and 60 inches tall is 0.0606*100 = 6.06%.
a) We have that,
According to the Empirical Rule, we can assevere that 50+- 3σ = 50+- 3*4 ---->
50 + 12 = 62 inches
50 - 12 = 38 inches
About 99.7% of 8th grade boys height will fall between 38 inches and 62 inches.
Answer: Approximately 99.7% of the heights fall between 38 inches and 62 inches.
b) According to the Empirical Rule, we can assevere that around 68% of the data will fall within one standard deviation of the mean. As we already know, the standard deviation σ is a natural yardstick for any measurements that follow a normal distribution.
So, 50 +- σ = 50 +- 4 ---->
50 + σ = 50 + 4 = 54
50 - σ = 50 - 4 = 46
Answer: About 68% of 8th grade boys height will fall between 46 inches and 54 inches.
5.Mitchell's dog is 1 as old as Katie's cat. The sum of their ages is 123years. How old isMitchell's dog?A 3 years old8 years oldD. 9 years oldB. 4 years old
Given: Mitchell's dog is 1/3 as old as Katie's cat. The sum of their ages is 12 years.
Required: To find out how old is Mitchell's dog.
Explanation: Let Mitchell's dog be x years old. Then Katie's cat is 3x. Now according to the question-
[tex]\begin{gathered} x+3x=12 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}[/tex]Hence Mitchell's dog is 3 years old.
Final Answer: Mitchell's dog is 3 years old.
A simple random sample of 800 elements generates a sample proportion overline p =0.66 . ( Round your answers to four decimal places . ) ( a ) Provide a 90 % confidence interval for the population proportion . to ( b ) Provide a 95 % confidence interval for the population proportion . to
STEP - BY - STEP EXPLANATION
Whatto find?
• 90% confidence interval for the population proportion.
,• 95% confidence interval for the ppulation proportion.
Given:
n= 800
p=0.66
q=1- p= 1- 0.66 =0.34
a) Given a 90% confidence interval,
α =1- 0.90= 0.10
[tex]Z_{\frac{\alpha}{2}}=Z_{\frac{0.10}{2}}=Z_{0.05}=1.645[/tex][tex]C.I=\bar{P}\pm Z_{\frac{\alpha}{2}}\times\sqrt{\frac{\bar{P}\bar{q}}{n}}[/tex][tex]=0.66\pm1.645\times\sqrt{\frac{0.66\times0.34}{800}}[/tex][tex]\begin{gathered} =0.66\pm0.02755 \\ \\ =(0.6324,\text{ 0.6276\rparen} \end{gathered}[/tex]b)
Given 95% confidence interal.
1- 0.95 =0.
ANSWER
a) (0.6276, 0.6324)
Scott paid $13.24 for a 3.41 pound bag of shrimp at one store. The following week, he paid $18.99 for a 4.96 pound bag at another store. Find the unit price for each bag. Then state which bag is better buy based off the unit price. Round your answers to the nearest cent.
Solution:
Scott paid;
$13.24 for 3.41-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$13.24=3.41pound} \\ 3.41\text{pound}=13.24 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{13.24}{3.41} \\ \text{Unit price= \$3.88 to the nearest tenth} \end{gathered}[/tex]$18.99 for 4.96-pound bag of shrimp
This means,
[tex]\begin{gathered} \text{ \$18.99=4.96pound} \\ 4.96\text{pound}=18.99 \\ \text{The unit price means the price of 1pound.} \\ 1\text{pound=}\frac{18.99}{4.96} \\ \text{Unit price= \$3.83 to the nearest tenth} \end{gathered}[/tex]Therefore, the bag that is a better buy based on the unit price is the 4.96-pound because of the unit price which is lesser than the unit price for the 3.41-pound bag.
Thus, the 4.96-pound is a better buy.
Hi I need help with this question please thank you!
Answer:
• The factoring pattern: Difference of two squares (Option A)
,• The factored form: (a+9)(a-9).
Explanation:
Given the expression:
[tex]a^2-81[/tex]81 is the square of 9, thus, the expression above can be written in the form below.
[tex]=a^2-9^2[/tex]The expression is a difference of two squares.
By the factoring pattern of the difference of two squares:
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b) \\ \implies a^2-9^2=(a+9)(a-9) \end{gathered}[/tex]Thus, we have that:
• The factoring pattern: Difference of two squares (Option A)
,• The factored form: (a+9)(a-9).
mZPQT = ? 20 P O 5y - 36 30° T 810 55 s 4x – 12 R
Given the parallelogram in the attached image.
Recall that two adjacent angles in a parallelogram add up to 180 degrees.
So;
[tex]m\angle\text{PQR}+m\angle QRS=180^{\circ}[/tex]Given;
[tex]undefined[/tex]Wich of the following will be the coordinate of the vertices of triangle A'B'C'?
You have to translate the triangle ABC using the translation rule:
(x,y) → (x-1,y+2)
This rule indicates that the triangle will be translated 1 unit left and 2 units up. To determine the coordinates of each vertex after the translation, you have to subtract 1 to the x-coordinate of each point and add 2 to the y-coordinate.
Original → Translation
A(6,1) → A'(6-1,1+2) = A'(5,3)
B(1,7) → B'(1-1,7+2) = B'(0,9)
C(-3,-2) → C'(-3-1,-2+2) = C'(-4,0)
The coordinates of the vertices of triangle A'B'C' will be
A'(5,3)
B'(0,9)
C'(-4,0)
The correct option is C.
For what value of x is the parallelogram a rhombus?
The figure is a rhombus when x=?
The given parallelogram is a rhombus when x = 9 units
The parallelogram is a four sided plane with opposite sides parallel. So the opposite angles are equal. A parallelogram that has all angles are right angles is called rectangle.
The rhombus is a four sided plane with all of whose sides have the same length.
The sides are given,
9x-8 and 5x+28
In rhombus all the sides are equal
Then the equation will be
9x-8 = 5x+28
Rearrange the terms and solve it
9x-5x = 28+8
4x = 36
x = 36/4
x = 9
Hence, the given parallelogram is a rhombus when x = 9 units
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Devon lives in a city an estimated population of 240,000people which statement about this population is true
Part D: There are more than 200,000 people in this city is the correct option
The population of the city in which Devon lives <=240000
Data interpretation: The process of examining data through some predetermined processes in order to give it some meaning and reach a pertinent conclusion is known as data interpretation. It entails using the outcomes of the data analysis to draw conclusions about the relationships that were looked at.
Part a:
According to this part, more than 300,000 people live in this city, which may be possible but we cannot be sure about it.
Part b:
According to this part more than 250,000 people live in the city, which may or may not be possible as we are sure only about 240,000 people
Part c:
According to this part, more than 245,000 people live in this city, which is again a may or may not be possible situation given the fact
Part d:
According to this part, more than 200,000 people live in the city. We are sure about this because it is estimated that 240,000 people live in the city. Hence this is the correct option
Although a part of your question is missing, you might refer to this full question: Devon lives in a city with an estimated population of 240,000 people. Which statement about this population is true?
A) There are more than 300,000 people in this city.
B) There are more than 250,000 people in this city.
C) There are more than 245,000 people in this city.
D) There are more than 200,000 people in this city
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I have completed 33 problems on a 60 problem test. What percent of the test have I completed?
Answer:
You have completed about 55%
Answer: I would say you have completed about 55% on the test.
ii) A plate holds 7 cup cakes, each with a different colour icing,
and 4 brownies, each of a different size. Find the number of different
ways these 11 cakes can be arranged in a row if no brownie is next to
another brownie.
iii) A plate of biscuits holds 4 identical chocolate biscuits, 6
identical shortbread biscuits and 2 identical gingerbread biscuits.
These biscuits are all placed in a row. Find how many different
arrangements are possible if the chocolate biscuits are all kept
together.
Using the arrangements formula, the number of ways to organize the plates in each case is given as follows:
ii) No brownie next to another brownie: 570,240
iii) Chocolate biscuits kept together: 8,709,120.
What is the arrangements formula?The number of possible arrangements of a set of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In item a, if the brownies cannot be together, we have that:
In 8 of the 11 positions(combination), the arrangements will be of 4! and 4!, due to the 4 brownies and the 4 cupcakes.In the remaining 3 positions, they will be organized in 3! ways.Hence the number of ways to organize the cupcakes is:
[tex]C_{11,8} \times 4! \times 4! \times 3! = \frac{11!}{8!3!} \times 4! \times 4! \times 3! = 570,240[/tex]
In item b, the chocolate biscuits have to be kept together, hence:
The 4 biscuits can be ordered in 9 positions, from 1-4 to 9-12.In these positions, they are arranged in 4! ways.The remaining biscuits are arranged in 8! ways.Hence the number of ways that the biscuits can be arranged is:
9 x 4! x 8! = 8,709,120.
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A prospector graphed the locations of a gold vein and all of the gold dust strikes in the vicinity. He positioned the gold vein at ( − 8 , 9 ) ( - 8 , 9 ) and the farthest gold dust strike at ( 7 1 , 9 ) . ( 7 1 , 9 ) . If each unit on the graph represents 1 m i l e , then how far away from the gold vein is the farthest gold dust strike?
The actual distance between the golf vein and the farthest gold dust strike is; 79 miles.
What is the distance between the gold vein and the farthest gold dust strike?It follows from the task content that the actual distance between both locations is to be determined.
It follows from the distance formula in coordinates geometry that;
D = √{(x2 - x1)² + (y2 - y1)²}
Therefore, the distance between the gold vein and the farthest gold dust strike is;
D = √{(-9 -(-9))² + (71 - (-8))²}
D = √79²
D = 79.
Ultimately, the distance on the graph is 79 units and since each unit on the.graoh represents 1 mile, the actual distance between the gold vein and the farthest gold dust strike is; 79 miles.
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The table on the right gives the annual income for eight families, in thousands of dollars.Find the mean and standard deviation for family incomo.Family A B C D E F G HIncome 47 42 44 45 43 45 48 46The mean of the data set is thousand dollars. (Round to three decimal places as needed)
We can compute the mean by;
[tex]\operatorname{mean}=\frac{47+42+44+45+43+45+48+46}{8}=45[/tex]and the standard deviation by;
[tex]\frac{\sum ^{}_{}(x-\operatorname{mean})^2}{\sum ^{}_{}f}=\frac{28}{8}=3.5[/tex]So the mean of the data set is 45.
The standard deviation is 3.5
Write in CER format
C-claim
E-evidence
R-reasoning
Constructed Response: Answer the following _ question in CER format!
Why did the author of the Federal Pillars political cartoons use "pillars" to represent the states' ratification of the U.S. Constitution?
Claim - The vertical pillars represent a state that has ratified the new government.
Evidence - The evidence is given in the document itself and is reflected in the cartoon. See the image attached.
Reasoning - The Massachusetts Centinel, August 2, 1789, "The Federal Pillars," via Library of Congress. The Massachusetts Centinel published a series of cartoons illustrating the Constitution's ratification. Each vertical pillar indicates a state that has approved the new administration.
When was the US Consitution Fully Ratified?The Constitution became the formal structure of the government of the United States of America on June 21, 1788, when New Hampshire became the ninth of 13 states to ratify it.
The Constitution has been revised 27 times, the most recently in 1992, despite the fact that over 11,000 modifications have been suggested since 1789. Article V of the Constitution specifies two procedures for proposing revisions to the document.
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Liam bought 6 9/8 pounds of steak. He used 2 1/18 pound of steak for a cookoutfill in each blankRounded to the closest benchmark, Liam bought ??? pounds of steak.Rounded to the closest benchmark, Liam used about ??? pounds of steak for the cookout.Liam has about ??? pounds of steak remaining after the cookout.
Given:
[tex]\begin{gathered} \text{ Amount of steak Liam bought = 6}\frac{9}{8}\text{ pounds} \\ \\ \text{Amount of steak he used = 2}\frac{1}{18}\text{ pounds} \end{gathered}[/tex]Let's answer the following rounded to the closest benchmark.
Lisa’s car gets 31 miles per gallon of gasoline. How many miles can she drive on 22 gallons of gas? Lisa can drive ____ miles.
Lisa's car gets 31 miles per gallon.
Thus in 22 gallons she can drive,
22x31=682 miles.
Lisa can drive 682 miles.
Pls help me with this ill give brainlist
As per the graph, the line passes through coordinates - (1,0) and (0,3)
Since the line passes through both these coordinates, these are the solutions of the equation.
For Option b, 6x + 2y = 6,
If (1,0) is the solution of 6x + 2y = 6, then
⇒ 6(1) + 2(0) = 6
⇒ 6 + 0 = 6
⇒ 6 = 6
If (0,3) is the solution of 6x + 2y = 6, then
⇒ 6(0) + 2(3) = 6
⇒ 0 + 6 = 6
⇒ 6 = 6
Since, these two are solutions of this equation, hence the equation of the given line is: 6x + 2y = 6
What are Coordinates?Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. A point in a plane has specific coordinates, as we are aware. Any point's location on a plane can be described by an ordered pair of values (x, y), which are referred to as coordinates. In our daily lives, we employ coordinates for things like map locations and in-class seating arrangements.The cartesian coordinate system is used to find a point's location in a plane.The idea of two mutually perpendicular axes is used to represent a point's coordinate.To learn more about Coordinates, refer to:
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Under his cell phone plan, Logan pays a flat cost of $58 per month and $3 per gigabyte. He wants to keep his bill under $70 per month. Use the drop-down menu below to write an inequality representing gg, the number of gigabytes he can use while staying within his budget
Solve for x log 3x+4) = 2
Step 1:
Write the equation
[tex]\log ^{3x+4}_4\text{ = 2}[/tex]Step 2:
Express the equation in exponential form
[tex]\begin{gathered} \log ^{3x+\text{ 4}}_4\text{ = 2} \\ 3x+4=4^2 \\ 3x\text{ + 4 = 16} \\ 3x\text{ = 16 - 4} \\ 3x\text{ = 12} \\ x\text{ = }\frac{12}{3} \\ x\text{ = 4} \end{gathered}[/tex]Final answer
x = 4
Please help me help help me please help help me
1. Subtract 5 in both sides of the equation:
[tex]\begin{gathered} 5-5+2\ln (x)=4-5 \\ 2\ln (x)=-1 \end{gathered}[/tex]2. Divide both sides of the euqation into 2:
[tex]\begin{gathered} \frac{2\ln (x)}{2}=-\frac{1}{2} \\ \\ \ln (x)=-\frac{1}{2} \end{gathered}[/tex]3. Wrie the lograrithm in exponential form:
[tex]\begin{gathered} \ln (x)=b \\ x=e^b \\ \\ \\ \ln (x)=-\frac{1}{2} \\ \\ x=e^{-\frac{1}{2}} \end{gathered}[/tex]4. Use properties of powers to rewrite:
[tex]\begin{gathered} x=\frac{1}{e^{\frac{1}{2}}} \\ \\ x=\frac{1}{\sqrt[]{e}} \end{gathered}[/tex]5. Evaluate:
[tex]x\approx0.607[/tex]Then, the solution for the given equation is approximately 0.607The ratio of the length of Skylar's bridge to the length of Karen's bridge is 3.4. Karen's bridge measure 48 inches.How long is Skylar's bridge
Answer:
These points are mine :)))
Step-by-step explanation:
Please Help Quickly!
Karl spent $58.34 at the grocery store last week. This week he spent $72.78. How much more did he spend this week than last week on groceries?
(Type Answer)
He spent $14.44 more on groceries this week than last week
How to determine the additional amount that was spent this week?From the question, the given parameters are
Amount spent last week = $58.34
Amount spent this week = $72.78
The additional amount that was spent at the grocery store this week is calculated by subtracting the amount spent this week from the amount spent last week
This is represented as
Additional amount = Amount spent this week - Amount spent last week
Substitute the known values in the above equation
So, we have
Additional amount = 72.78 - 58.34
Evaluate the difference
Additional amount = 14.44
Hence, an additional of $14.44 was this week
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Hello, I need some help with this precalculus question for my homework, please HW Q12
In order to find the solution to this equation graphically, let's use each side of the equation as a function, and then graph both functions in the same coordinate plane:
[tex]\begin{gathered} y_1=e^x\\ \\ y_2=-3x \end{gathered}[/tex]Graphing y1 in red and y2 in blue, we have:
The intersection point between the graphs is located at (-0.26, 0.77), therefore the solution to the equation is:
[tex]The\text{ }solution\text{ }set\text{ }is\text{ }\lbrace x=-0.26\rbrace[/tex] Write four examples of ordered pairs, each
located in a different quadrant of the
coordinate plane.
The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.
Placing a concept on the Cartesian plane can help make it easier to visualize a point.
Numerical values of an ordered pair may be fractions or integers.
(x, y) represents an ordered pair, with x being the separation between a point and the primary axis (x).
In addition, y = ordinate calculates a location's separation from the secondary axis "y."
The point P will be represented mathematically as follows:
P = (6, 4) (6, 4)
The first number in the pair indicates the separation from the "x" axis, which is 6 pixels.
The second value in the ordered pair represents the 4 distance from the "y" axis.
Start from the origin and indicate the point on the Cartesian plane. Starting from the origin, move 6 steps in the direction of the "x" axis (to the right). Take 4 steps forward from this point to the "y" axis (upwards).
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Simplify √50 over √2
In order to simplify this expression, we need to use the following property:
[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So we have that:
[tex]\frac{\sqrt[]{50}}{\sqrt[]{2}}=\sqrt[]{\frac{50}{2}}=\sqrt[]{25}=5[/tex]So the answer is 5.
orm Effects?s
Countdown: Days:-2 Time:-06:43:38
Parking survey: For a class assignment, a group of statistics students set up a table near the the answer.
student parking lot. They asked students who passed by to complete a quick survey about
whether they support the building of a multi-level parking structure that would add 425 new spaces at the college.
to points
They used the information from the survey to calculate the 95% confidence interval: (0.53, 0.72). To which population
does the confidence interval apply?
A. O They apply to all students at the college.
B.O They apply only to the population of those who use the student parking lot.
C. The results do not apply to any population because this was a convenience sample.
D. O They apply only to the population of those students who drive to the college.
Answer:
Step-by-step explanation:
The results do not apply to any population because this was a convenience sample.
The confidence interval (0.53, 0.72) applies only to the population of those students who drive to the college. The correct answer is D.
The confidence interval is a statistical measure used to estimate an unknown population parameter, such as the proportion of students who support the building of a multi-level parking structure.
In this case, the students conducting the survey set up a table near the student parking lot and asked students who passed by to complete the survey. Therefore, the sample used for the survey consists only of students who use the student parking lot.
Since the survey was conducted exclusively among students who use the parking lot, the results and the subsequent confidence interval can only be generalized to that specific population.
The confidence interval (0.53, 0.72) represents the estimated range of proportions of students who support the parking structure within the population of students who drive to the college. It cannot be extended to the entire student body, students who do not use the parking lot, or any other population beyond those who drive to the college.
The correct answer is D.
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your dinner bill was $21.00 if you leave a 15% tip, how much will the tip be?
Solution:
Given:
The dinner bill = $21.00
The tip = 15% of the bill
Hence,
[tex]\begin{gathered} =15\text{ \% of \$21} \\ =\frac{15}{100}\times21 \\ =\frac{315}{100} \\ =\text{ \$3.15} \end{gathered}[/tex]Therefore, the tip will be $3.15
Seven more than the product of 14 and Mabel's ageUse the variable m to represent Mabel's age.
7+14m
Explanation
Step 1
Let
m represents Marbel's age
Then,
the product of 14 and Mabel's age=
[tex](m\cdot14)=14[/tex]now, Seven more than the product of 14 and Mabel's age
then
[tex]7+(m\cdot14)=7+14m[/tex]If I = prt, which equation is solved for t?
O 1-pr=t
O
1-P-1
I
pr
O 1+pr=t
The solution of the equation for t is t = i/pr
How to determine the equation for t?The equation is given as
i = prt
Divide both sides of the equation by p
So, we have the following equation
i/p = prt/p
Divide both sides of the equation by r
So, we have the following equation
i/pr = prt/pr
Evaluate the quotients
i/pr = t
Rewrite as
t = i/pr
By the above computation, we changed the subject of the formula in i = prt from i to t.
This implies that solving for t is a concept of subject of formula
Hence, the solution is t = i/pr
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Is ABC DEF? If so identify the similarity postulate or theorem that apples
ANSWER:
B. Similar - SAS
EXPLANATION:
Given:
Recall that the SAS Similarity Rule states that if two sides of one triangle are proportional to two corresponding sides of another triangle and the included angle in both triangles are congruent, then the two triangles are said to be similar.
Looking at triangles ABC and DEF, we can see that, we can see that;
[tex]\begin{gathered} \frac{AB}{DE}=\frac{BC}{EF} \\ \\ \frac{9}{3}=\frac{15}{5}=3 \end{gathered}[/tex][tex]\begin{gathered} m\angle B\cong m\angle E \\ 40^{\circ}\cong40^{\circ} \end{gathered}[/tex]Since the two corresponding sides of both triangles are in equal proportion and the included angle in both triangles are congruent, then triangles ABC and DEF are similar by the SAS Similarity Rule