Given:
A prism is completely filled with 72 cubes that have edge lengths of 1/2 in.
Required:
To find the volume of the prism.
Explanation:
The volume of the each cube is
[tex]\begin{gathered} =(\frac{1}{2})^3 \\ \\ =\frac{1}{8}in^3 \end{gathered}[/tex]So the volume of the complete prism is
[tex]\begin{gathered} =72\times\frac{1}{8} \\ \\ =9in^3 \end{gathered}[/tex]Final Answer:
The volume of the prism is
[tex]9in^3[/tex]Use the spinner to find the theoretical probability of the event 6 2 The theoretical probability of spinning a multiple of 2 is
The spinner has six possible outcomes, 3 of them are multiples of 2 (2, 4 and 6). Then the probability is:
[tex]P=\frac{3}{6}=\frac{1}{2}[/tex]Therefore the probability is 1/2.
What is the probability of flipping a coin 11 times and getting heads 5 times?Round your answer to the nearest tenth of a percent.O A. 16.1%B. 8.1%O C. 22.6%O D. 0.5%SUBMIT
If you flip a coint there are two possible outcomes, "head"
can someone help me set it up im very confused.
let h be the height of the television set
4: 3 = 46 : h
[tex]\frac{4}{3}=\frac{46}{h}[/tex]cross multiply
4h = 138
Divide both-side of the equation by 4
h = 34.8 inches
What is 7×312 using mental math
Step-by-step explanation:
2184 simple ..... .............
Answer:
Its 2184
Step-by-step Explained
A company is going to make a storage container with sheet steel walls. The container will be in the shape of a rectangular prism, as shown below. If the sheet steel costs $30 for each square meter, how much will the sheet steel cost in total?
ANSWER
$3060
EXPLANATION
Each steel sheet used for the prism costs $30 per square meter.
To find the total cost of the sheet, we have to find the surface area of the rectangular prism. Then we multiply the surface area by the cost per square meter.
The surface area of a rectangular prism is:
[tex]\begin{gathered} A\text{ = 2(}wh\text{ + wl + hl)} \\ \text{where h = height} \\ w\text{ = width} \\ l\text{ = length} \end{gathered}[/tex]From the diagram:
l = 7 m ; w = 3 m ; height = 3 m
Therefore, the surface area of the prism is:
[tex]\begin{gathered} A\text{ = 2\lbrack(3 }\cdot\text{ 3) + (3 }\cdot\text{ 7) + (3 }\cdot\text{ 7)\rbrack} \\ A\text{ = 2(9 + 21 + 21)} \\ A\text{ = 2(51)} \\ A\text{ = 102 square meters} \end{gathered}[/tex]Now, we multiply by the cost per square meter:
[tex]\begin{gathered} C\text{ = 102 }\cdot\text{ 30} \\ C\text{ = \$3060} \end{gathered}[/tex]That is the total cost of the steel sheet.
A rectangular field is 300 meters long and 150 meters wide.What is the area of the field in square kilometers? Do notround your answer.km²XG?Conversion facts for length1000 millimeters (mm) = 1 meter (m)100 centimeters (cm) = 1 meter (m)10 decimeters (dm) = 1 meter (m)1 decameter (dam) = 10 meters (m)1 hectometer (hm)100 meters (m)1 kilometer (km)1000 meters (m)I need help with this math problem.
Given:
A rectangular field is 300 meters long and 150 meters wide.
Required:
Find the area of the field in square kilometer.
Explanation:
The area of the rectangle is given by the formula:
[tex]\begin{gathered} A=length\times width \\ A=300\times150 \\ A=45000\text{ m}^2 \end{gathered}[/tex][tex]1m=\frac{1}{1000}km[/tex][tex]\begin{gathered} A=45000\times\frac{1}{1000000} \\ A=0.045\text{ km}^2 \end{gathered}[/tex]Final Answer:
The area of the
Part A Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression.Part BSolve 10/12 - 3/8Part Ccalculate the difference between your stimate in Part A and the actual value calculated in Part B.Show the solution as an equation Based on the results was your estimate in Part A reasonable?
Answer:
[tex]\begin{gathered} A\text{. 1/2} \\ B\text{. 11/24} \\ C\text{. }\frac{1}{24} \\ \end{gathered}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Step-by-step explanation:
For part A,
-estimate the fraction 10/12 using 1/2 as our benchmark
The lower range is 1/2 and the upper range is 1
The halfway point is:
[tex]\begin{gathered} \frac{1}{2}\cdot\frac{(1+2)}{2} \\ \frac{1}{2}\cdot\frac{3}{2}=\frac{3}{4} \end{gathered}[/tex]Therefore, our range is 1/2 < 3/4 < 1
10/12 ≥ 3/4, we round up to 1
-estimate the fraction 3/8 using the 1/2 as our benchmark:
The lower range is 0 and the upper range is 1/2
The halfway point is:
[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore, our range is 0 < 1/4 < 1/2
3/8 ≥ 1/4, we round up to 1/2
[tex]\frac{2}{2}-\frac{1}{2}=\frac{1}{2}[/tex]For part B, the denominators are 12 and 8, so the LCM would be;
[tex]\text{LCM}=24[/tex]Then, we make a common denominator and subtract the numerators
[tex]\begin{gathered} \frac{10}{12}-\frac{3}{8}=\frac{20}{24}-\frac{9}{24} \\ \frac{10}{12}-\frac{3}{8}=\frac{11}{24} \end{gathered}[/tex]For part C, compute the difference between the two results from parts A and B:
[tex]\frac{1}{2}-\frac{11}{24}=\frac{1}{24}[/tex]Yes, the calculations in A were reasonable because the difference is pretty close to 0.
Jeremy says this dilation can be represented by (X+3\4,Y+3\4)Julie says this dilation can be represented by (3\4X, 3\4Y)whoo is correct and why
The scale factor for dilation is 3/4. Therefore, the dilation can be represented below
[tex](\frac{3}{4}x,\frac{3}{4}y)[/tex]This means Julie is correct.
The image of the point (-2,2) under a translation is (-3,5). Find the coordinatesof the image of the point (-3,1) under the same translation.Submit Answer
We have an inital coordinate given (-2,2) and after a translation we got a new coordinate called (-3,5)
We can find the transformation like this:
-3= -2-1
5= 2+3
So then the transformation is given by:
[tex]T\rightarrow(x-1,y+3)[/tex]If we apply this transformation to the (-3,1) coordinate we got:
[tex](-3-1=-4,1+3=4)[/tex]So then the final answer would be (-4,4)
1. A company supplies pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins and normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy pins with lengths in the interval 25.00 ± 0.50 mm.
The percentage of the pins that will be acceptable to the customer is 63.16%.
What will the percentage be?Based on the information, the probabilty that the pin lies is between 24.5 and 25.5. This will be illustrated as P(24.5 <x < 25.5).
So convert this into Z score, will be:
P(24.5 <x < 25.5):
= P((24.5-25.3)/0.45 <Z < (25.5-25.3)/0.45)
Solving this, we will get
P(-16/9<Z < 4/9) = P(-1.77 <Z < 0.44),
By looking at the z table and solving for Z by using P (Z<0.44)-P(Z>-1.77) will be:
= 0.67 -(1-0.9616)
= 0.6316
= 63.16%
Learn more about probability on:
https://brainly.com/question/24756209
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Complete question
A company supplies pins to a customer. It uses an automatic lathe to produce the pins. Due to factors such as vibration, temperature and wear and tear, the lengths of the pins and normally distributed with a mean of 25.30 mm and a standard deviation of 0.45 mm. The customer will only buy pins with lengths in the interval 25.00 ± 0.50 mm. What percentage of the pins will be acceptable to the customer?
Translate the following word phrase to an algebraic expression and simplify: “8 times the difference of 6 times a number and 3”
Given the word phrase
8 times the difference of 6 times a number and 3
Let the number = x
6 times the number = 6x
The difference of 6 times the number and 3 = 6x - 3
8 times the difference of 6 times a number and 3 will be:
[tex]8(6x-3)[/tex]Find the area the sector.arc circle 7A. 1083π4 in²B. 1083π8 in²C. 57π4 in²D. 38π in²
Solution:
Given:
A circle with the sector details;
[tex]\begin{gathered} r=19\text{ }in \\ \theta=135^0 \end{gathered}[/tex]The area of a sector is given by;
[tex]\begin{gathered} A=\frac{\theta}{360}\times\pi r^2 \\ A=\frac{135}{360}\times\pi\times19^2 \\ A=\frac{1083\pi}{8}\text{ }in^2 \end{gathered}[/tex]Therefore, the area of the sector is;
[tex]\frac{1083\pi}{8}\text{ }in^2[/tex]marh questions i need to solve and i have problems with it
7.
Given the side ratio as:
[tex]5:13[/tex]The area ratio is the second power of the above, which is:
[tex]\begin{gathered} 5^2:13^2 \\ =25:169 \end{gathered}[/tex]Given the area ratio of:
[tex]36:49[/tex]The perimeter ratio is:
[tex]\begin{gathered} \sqrt{36}:\sqrt{49} \\ \\ =6:7 \end{gathered}[/tex]what is 9×9 can you pls tell me
ANSWER
9X9 is a product of two integers numbers.
It's equal to 81.
Rewrite 9/11 and 6/7 so that they have a common denominator.Then use <, =, or > to order 9/11 and 6/7
Answer:
• 9/11=63/77
,• 6/7=66/77
,• 9/11<6/7
Explanation:
Given the fractions: 9/11 and 6/7
First determine the lowest common multiple of the denominators: 11 and 7
L.C.M of 11 and 7 = 77
Next, make this the common denominator as follows:
[tex]\begin{gathered} \frac{9}{11}=\frac{9}{11}\times\frac{7}{7}=\frac{63}{77} \\ \frac{6}{7}=\frac{6}{7}\times\frac{11}{11}=\frac{66}{77} \end{gathered}[/tex]Comparing the numerators, since 63<66:
[tex]\implies\frac{9}{11}<\frac{6}{7}[/tex]What is the first quartile of the data displayed in this box-and-whisker plot?O 49O 41O 37O 353436403844424648T54 56525058
1) In any box and whiskers plot we can tell the following about how to read it:
3) So, reading that box and whiskers plot, we can tell the first quartile is:
[tex]Q_1=37[/tex]Find the point-slope equation of the line using the point (7, 4) and slope of2Use the slash key (/) to indicate a fraction.
The general equation of a line is given as:
y = mx + c where
m = slope
c = intercept on y axis.
We are given a point (x,y) so we use the relation below to develop the equation.
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=slope \\ \text{where:} \\ y_1=\text{ 4} \\ x_1=7 \end{gathered}[/tex][tex]\frac{y-4}{x-7}=2[/tex]Crossmultiplying, we have:
2x - 14 = y - 4
Adding 4 to both sides,
y = 2x - 14 + 4
y = 2x - 10
In the items below a physical property is identified along with two objects/figures. For each item identity whether the property applies to one, both, or neither of the objects/figures listed and explain why it does or does not.1) Property: MassCylinder Square
Background
• Mass: ,is the quantity of matter in a physical body.
,• Cylinder: ,a three-dimensional solid.
,• Square: ,a one-dimensional figure (flat shape).
As a square is just a one-dimensional figure, it cannot have mass, then...
Answer: the property applies only to the Cylinder.
What is the value of x?2445°X=(Simplify your answer. Type an exact answer, using radicals as needed.)
Given the figure of a right-angle triangle
As shown, the given triangle is a 45-45-90 triangle
The relation between the hypotenuse (h) and the length of one leg (l) is as follows:
[tex]h=(\sqrt{2})l[/tex]As shown, h = 24, and l = x
[tex]\begin{gathered} 24=\sqrt{2}*x \\ \\ x=\frac{24}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{24\sqrt{2}}{2}=12\sqrt{2} \end{gathered}[/tex]So, the answer will be:
[tex]x=12\sqrt{2}[/tex]Yusuf is going to the amusement park, where he has to pay a set price of admission and another price for tickets to go on each of the rides. The total amount of money Yusuf will spend is given by the equation y=4x+20y=4x+20, where yy represents the total amount of money, in dollars and cents, and xx represents the number of rides Yusuf goes on. What could the number 20 represent in the equation?A.The total amount of money Yusuf will spend if he goes on 1 ride.B.How much it cost for a ticket to go on one of the rides.C.The total amount of money Yusuf will spend if he goes on 0 rides.DThe total amount of money Yusuf will spend if he goes on 100 rides.
Given the equation:
[tex]y=4x+20[/tex]If x = 0, then:
[tex]\begin{gathered} y=4\cdot0+20 \\ \Rightarrow y=20 \end{gathered}[/tex]Answer: C
write a multiplication equation for the area of the square with side lengths of 1 meter
Area of a square is expressed using the formula;
A = L^2
L is the side length of the square
From the question, we are given;
L = 1 meter
The multiplication equation for the area of the square will be;
A = 1 meter * 1 meter
A = 1m^2
how do I solve an angle in right triangles. what is angle B?AB=7BC=3
To find the value of the b angle.
First, label the sides of the right angle
The biggest side is always the hypotenuse
The side between the right angle and angle A is the adjacent side.
and the other side it's my opposite side.
Let's use the trigonometric function to find the value of b
I have the value of the hypotenuse
h = 7
and the value of my opposite side
opp = 3
So we need a trigonometric function that involves my hypotenuse and the opp
sin = opp/ hyp
Replace the values
sin b = 3/7
Solve the equation for b
b = arcsin (3/7)
b = 25.376
Rounded to hundredths
b = 25.37
The ages (in years) of the 5 doctors at a local clinic are the following30, 40, 39, 36, 30Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places
Solution
For this case we have the following data:
30, 40, 39, 36, 30
Representing the ages (in years) of the 5 doctors at a local clinic
these values represent an entire population, and we want to find the standard deviation of the population
1) First we need to calculate the mean
[tex]\mu=\frac{30+40+39+36+30}{5}=35[/tex]2) Now we can find the population variance like this:
[tex]\sigma^2=\frac{(30-35)^2+(40-35)^2+(39-35)^2+(36-35)^2+(30-35)^2}{5}=\frac{92}{5}=18.4[/tex]3) Calculate the population standard deviation
[tex]\sigma=\sqrt[]{18.4}=4.29[/tex]then the answer would be:
4.29
Diego's goal is to walk more than 70,000 steps this week. The mean number of steps that Diego walked during the first 4 days of the week is 8,019.If the mean number of steps Diego walks during the last 3 days of the week is 12, 642, will Diego reach his goal of walking more than 70,000 steps this week? Explain your reasoning.
Solution
Diego goal was walk more than 70000 steoes
And in average in the first 4 days he walks 8019 steps
The expected mean number of steps for the next 3 days is 12642 then we can do this:
8019*4 + 12642*3= 32076 +37926 = 70002
then since 70002 > 70000
We can conclude that Diego can reach the goal for this case
On Monday, Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch. Let r represent the cost of a burger and y represent the cost of an order of fries. What linear equation would model this?
Let:
r = Cost of a burger
y = Cost of an order of fries
Freda spent $20 to buy 3 burgers and 4 orders of fries for her friends to share for lunch, therefore:
[tex]3r+4y=20[/tex]Listed below are amounts (in millions of dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service company's employees?The coefficient of variation for the amount collected by the security service company is __%.The coefficient of variation for the amount collected by other companies is __%.
The coefficient of variation of a dataset is given by the ratio between the standard deviation to the mean.
[tex]CV=\frac{\sigma}{\mu}[/tex]The mean and the standard deviation of a dataset with N elements are given by the following formulas:
[tex]\begin{gathered} \mu=\frac{\sum_i^Nx_i}{N} \\ \\ \sigma=\sqrt{\frac{1}{N-1}\sum_{n\mathop{=}0}^{\infty}(x_i-\mu)^2} \end{gathered}[/tex]Then, using those formula for the security service company, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.53 \\ \sigma=0.15670212364724... \\ CV=0.102419689...\approx10.2\% \end{gathered}[/tex]Then, using those formula for the other companies, we have the following coefficient of variation:
[tex]\begin{gathered} \mu=1.72 \\ \sigma=0.11352924243951... \\ CV=0.0660053735...\approx6.6\% \end{gathered}[/tex]1.Given triangle ABC shown, graph its image after a dilation centered at the origin with a scale factor of two. Give the coordinates of the images of the vertices below.2. List all pairs of parallel line segments from problem 1.
for the question 1: the image of the vertices will be A'=2(-4,4)=(-8,8); B'=2(-4,-3)=(-8,-6); C'=2(4,-3)=(8,-6)
for the question 2: there will be no pairs of parallel lines in the triangle
Study Surface Area and Volume of Pyramid and Cone1. How to find lateral area and total surface area of pyramid?
Explanation:
Lateral area of pyramid
Lateral area of squared pyramid is the sum of areas of its side faces.
[tex]\begin{gathered} L=2al \\ \text{a is base length} \\ l\text{ is slant height and it is given as,} \\ l=\sqrt[]{\frac{a^2}{4}+h^2} \\ \text{Here, h is height of pyramid.} \end{gathered}[/tex]Total surface area of pyramid
It is sum of the areas of its lateral faces and its base.
[tex]\begin{gathered} \text{Total surface area=}\frac{1}{2}pl+B \\ p\text{ is perimeter of base} \\ l\text{ is slant height} \\ B\text{ is base area} \end{gathered}[/tex]Geometric Probability: I don’t know how to do this please help quickly
Solution
From the question,
If buses arrive every 19 mins and each waited 3 mins before departing
Then we can say that each bus departed (19 + 3) = 22 mins.
if you arrived at the moment the bus left, you would need to wait for the next bus
The probability is
[tex]\frac{9}{22}=0.409[/tex]When 9 and 2/3 is written in simplest radical form, which value remains under the radical?36927
Given
[tex]9^{\frac{2}{3}}[/tex]To write it in the simplest form and to find which value remains under the radical.
Explanation:
It is given that,
[tex]9^{\frac{2}{3}}[/tex]It is known that,
[tex]x^{\frac{m}{n}}=\sqrt[n]{x^m}[/tex]That implies,
[tex]\begin{gathered} 9^{\frac{2}{3}}=\sqrt[3]{9^2} \\ =\sqrt[3]{3\times3\times3\times3} \\ =3\sqrt[3]{3} \end{gathered}[/tex]Therefore, the simplest form of the expression is,
[tex]3\sqrt[3]{3}[/tex]and the value that remains under the radical is 3.