Let
x -----> number of students that preferred vanilla cupcakes
y ----> number of students that preferred chocolate
we know that
x+y=750 -----> equation A
and
2/5=x/y
x=(2/5)y ------> equation B
substitute equation B in equation A
(2/5)y+y=750
solve for y
(7/5)y=750
y=750*5/7
y=536
find the value of x
x=(2/5)(736)
x=214
therefore
the answer is 214 students preferred vanilla cupcakesTranslate 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]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.
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"
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)
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]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?
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
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
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]At a certain hospital 39080 patients had their falls reported in the winter of 2004, thisrose to 42045 patients in the winter of 2014 (Lifespan, 2019). How would you calculatethe percentage rise in patients from 2004 to 2014?In a several sentences, how would you apply this to your life or job? If you had to teachsomeone who did not know how to this, what would be the steps from beginning to endthat you would use to teach them so that they would eventually do it accurately as youwould?Professor,I would calculate the percentage rise in patients from 2004 to 2014 by
Percentage rise in patients from 2004 to 2014 = 7.59%
Explanation:The number of patients in 2004 = 39080
The number of patients in 2014 = 42045
Increase in the number of patients = (The number of patients in 2014) - (The number of patients in 2004)
Rise in the number of patients = 42045 - 39080
Rise in the number of patients = 2965
[tex]\begin{gathered} \text{Percentage rise in patients = }\frac{\text{Rise in the number of patients}}{\text{Number of patients in 2004}}\times100 \\ Percentage\text{ rise in patients = }\frac{2965}{39080}\times100 \\ \text{Percentage rise in patients = }7.59\text{ \%} \end{gathered}[/tex]Percentage rise in patients from 2004 to 2014 = 7.59%
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]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
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.
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]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
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]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]Jack has an old scooter. He wants to sell it for 60% off the current price. The
market price is $130. What should his asking price be? Explain your reasoning.
For each value of v, determine whether it is a solution to v - 42 = 11
Given equation:
[tex]v\text{ - 42 = 11}[/tex]The first step is to solve the equation i.e. find the value of v
[tex]\begin{gathered} Collect\text{ like terms} \\ v\text{ = 11 + 42} \\ v\text{ = 53} \end{gathered}[/tex]The given options
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
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
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]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]6ft 3ft 8ft 16ft area of irregular figures
Solution.
From the figure given we will have to find the
(Area of A) + (The Area of B)
STEP 1 :
For figure B
b = 3
h = 6
[tex]\begin{gathered} \text{Area of A = }\frac{1}{2}\times b\times h \\ \text{ = }\frac{1}{2}\times3\times6 \\ \text{ = }\frac{18}{2}\text{ = 9} \end{gathered}[/tex]Step 2:
For Figure A
L = 16
b = 8ft
Area of B = L x B
= 16 x 8
= 128
STEP 3
Area of A + Area of B
128 + 9 = 137 square feet
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]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.
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.
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
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.