LITERS OF SODA
24 people calls for 4 liters of lemon soda
18 people calls for x liters of lemon soda
24 people = 4 liters
18 people = x
cross multiply
24x = 72
Divide both-side of the equation by 24
x = 3
18 peoples calls for 3 liters of soda
PINT OF SHERBET
24 people calls for 2 pint of sherbet
18 people calls for x pint of sherbet
24 people = 2 pint
18 people = x
cross-multiply
24x = 36
Divide both-side of the equation by 24
x =1.5
18 peoples calls for 1.5 pint of sherbet
CUPS OF RICE
24 peoples calls for 6 cups of rice
18 people calls for x cups of rice
24 people = 6 cups of rice
18 people = x
cross multiply
24x = 108
Divide both-side of the equation by 24
x=4.5
18 people calls for 4.5 cups of rice
Hence, 18 people calls for; 3 liters of soda, 1.5 pint of sherbet and 4.5 cups of rice
Statistics: a professor recorded 10 exam grades but one of the grades is not readable. if the mean score on the exam was 82 and the mean of the 9 readable scores is 84 what is the value of the unreadable score?
To mean of a set is given by the sum of all values in the data-set divided by the number of values.
We have that the mean of the whole set is 82.
The mean of the 9 readable scores is 84.
So:
[tex]\begin{gathered} \frac{x}{9}=84 \\ x=84\cdot9 \\ x=756 \end{gathered}[/tex]So, we 9 readable scores add up to 801. If we add 756 to a number, y, and divide by 10, we'll have the mean score of the exam, 82.
[tex]\begin{gathered} \frac{756+y}{10}=82 \\ 756+y=820 \\ y=820-756 \\ y=64 \end{gathered}[/tex]So, the grade of the unreadable score was 64.
how would u decide if 3/5 or 59% is greater?
SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]If a cell disruptor is purchased with a frequency of 60Hz, what is the wavelength traveling through human tissue? (1540 m/s).
The wavelength traveling through human tissue when the velocity is 1540 m/s and frequency is 60Hz will be 25.67 m.
According to the question,
We have the following information:
Frequency of a cell disruptor = 60 Hz
Velocity of the cell disruptor = 1540 m/s
We know that the following formula is used to find the wavelength:
Wavelength = Velocity/frequency
Wavelength = 1540/60 m
(Note that when velocity is given m/s and frequency is given in Hz then the unit of wavelength is m. Every physical quantity has to be expressed with its units.)
Wavelength = 25.67 m
Hence, the wavelength traveling through human tissue is 25.67 m.
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The scale factor on a floor plan is 1 in8 ft. What is the actual distance represented by a 2.5 inches on the floor plan
Given:
Scale factor = 1 inch 8ft
Floor Plan measurement = 2.5 inches
Solution
We should re-write the scale factor in units of inches only.
Recall that:
[tex]1\text{ f}eet\text{ = 12 inches}[/tex]Then, the scale-factor in inch:
[tex]\begin{gathered} \text{Scale factor = 1 + 8 }\times\text{ 12} \\ =\text{ 1 + 96 } \\ =\text{ 97 inches} \end{gathered}[/tex]We can then find the actual distance by multiplying the represented distance (2.5 inches) by the scale factor.
So, we have:
[tex]\begin{gathered} \text{Actual distance = Represented distance }\times\text{ scale factor} \\ =2.5\text{ }\times\text{ 97} \\ =\text{ }242.5\text{ inches} \end{gathered}[/tex]Answer: Actual distance = 242.5 inches
General Mills is testing 12 new cereals for possible production. They are testing 3 oat cereals, 5 wheat cereals, and 4 rice cereals. If each of the 12 cereals has the same chance of being produced,
and 4 new cereals will be produced, determine the probability that of the 4 new cereals that will be produced, 2 are oat cereals, 1 is a wheat cereal, and 1 is a rice cereal.
The probabilis
(Type an integer or a simplified fraction.)
Using the combination formula, the probability that of the 4 new cereals that will be produced, 2 are oat cereals, 1 is a wheat cereal, and 1 is a rice cereal is of 4/33.
Combination Formula[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
This formula is used when the order in which the objects are chosen is not important, as is the case in this problem.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the total outcomes, 4 cereals are taken from a set of 12, hence:
[tex]T = C_{12,4} = \frac{12!}{4!8!} = 495[/tex]
For the desired outcomes, we have that:
2 oat are taken from a set of 3.1 wheat is taken from a set of 5.1 rice is taken from a set of 4.Hence the number is:
[tex]D = C_{3,2}C_{5,1}C_{4,1} = \frac{3!}{2!1!} \times \frac{5!}{1!4!} \times \frac{4!}{1!2!} = 3 \times 5 \times 4 = 60[/tex]
Hence the probability is:
p = 60/495.
Both numbers can be simplified by 5, hence:
p = 12/99.
They can also be simplified by 3, hence:
p = 4/33.
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How are the strategies the same and how are they different
Diagram 1.
Strategy 1.
[tex]A_{Total}=253\cdot31=(200+50+3)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]\begin{gathered} A_{Total}=A_1+A_2+A_3+A_4+A_5+A_6 \\ =(200\cdot30)+(50\cdot30)+(3\cdot30)+(200\cdot1)+(50\cdot1)+(3\cdot1) \\ =6000+1500+90+200+50+3 \\ =7843 \end{gathered}[/tex]Diagram 2.
Strategy 2.
[tex]A_{Total}=253\cdot31=(253)\cdot(30+1)[/tex]If we add all the areas together we get:
[tex]A_{Total}=A_1+A_2=253\cdot30+253\cdot1=7590+253=7843[/tex]We can see that we got the same answer: Total area = 7843 quare units
The strategies are similar because they are dividing the total area into smaller ones and then add them together.
However, they are different in that diagram 1 has more areas that are smaller compared to diagram 2. Also, the divisions in diagram 1 are designed to make multiplications easier compared to diagram 2.
use the half angle identity to find the exact value of the trigonomic expression. given 0
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
Tom said that the difference in length between the longest trail and the shortest trail is 2 5/8 miles. Does Tom's answer make sense? What mistake did he make? Answer in at least two complete sentences. Use the sentences below to get started: "Tom's answer (makes sense/does not make sense). His mistake was ________."
Solution:
Given:
From the trail lengths given,
[tex]\begin{gathered} The\text{ longest trail is }1\frac{7}{8} \\ The\text{ shortest trail is }\frac{3}{4} \end{gathered}[/tex]The difference in length between the longest trail and the shortest trail:
[tex]\begin{gathered} 1\frac{7}{8}-\frac{3}{4}=\frac{15}{8}-\frac{3}{4} \\ =\frac{15-6}{8} \\ =\frac{9}{8} \\ =1\frac{1}{8} \end{gathered}[/tex]
The sum of the longest trail and the shortest trail.
[tex]\begin{gathered} 1\frac{7}{8}+\frac{3}{4}=\frac{15}{8}+\frac{3}{4} \\ =\frac{15+6}{8} \\ =\frac{21}{8} \\ =2\frac{5}{8} \end{gathered}[/tex]From the calculations above, the conclusion can be reached that:
Tom's answer does not make sense. His mistake was he did the sum of the longest trail and the shortest trail.
hello I don't know if you can help me with this but I no am doing something wrong. because at the bottom its not spelling right
8. The difference of three and a number means x+3 or x-3 because in both equations you have three units plus or minus the number X.
10. '"4 times the sum of a number and three" means
[tex]4\cdot(x+3)=4x+12[/tex]Letter D
Identify the segments that are parallel, if any, if ∠ADH≅∠ECK.A. AD¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯B. AC¯¯¯¯¯¯¯¯ || CD¯¯¯¯¯¯¯¯C. AE¯¯¯¯¯¯¯¯ || CB¯¯¯¯¯¯¯¯D. none of these
Hi there. To solve this question, we have to remember some properties about similar triangle and congruency.
Given the triangles ADH and ECK,
We know that
[tex]\angle ADH\cong\angle ECK[/tex]That is, the angle at D is congruent to the angle at C in the respective triangles.
In this case, we can think of the congruency between the triangles in the following diagram:
Notice that ADCB is a parallelogram and the angles given show that the angles at D and at C are congruent, hence the other angles in the parallelogram must be congruent as well.
This means that opposite sides are parallel and have the same measure (length).
The opposite sides are AD and CB and DC and AB.
In this case, we find that only AD and CB are an option to this question, therefore the correct answer.
In fact, AC is the diagonal of the parallelogram and is not parallel to any segment of the figure.
AE isn't a segment drawn and hence not parallel to any other segment.
The correct answer is the option A).
Simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \sqrt[]{\frac{ \sqrt[3]{64}+\sqrt[4]{256}}{\sqrt[]{64}+\sqrt[]{256}}}
We are given the expression:
[tex]\sqrt[]{\frac{ \sqrt[3]{64}+\sqrt[4]{256}}{\sqrt[]{64}+\sqrt[]{256}}}[/tex]We will simplify this as shown below:
[tex]\begin{gathered} \sqrt[]{\frac{ \sqrt[3]{64}+\sqrt[4]{256}}{\sqrt[]{64}+\sqrt[]{256}}} \\ \text{Let's consider \& solve the terms one after the order, we have:} \\ \sqrt[3]{64}\Rightarrow\sqrt[3]{4\times4\times4}\Rightarrow4 \\ \sqrt[4]{256}\Rightarrow\sqrt[4]{4\times4\times4\times4}\Rightarrow4 \\ \sqrt[]{64}\Rightarrow\sqrt[]{8\times8}\Rightarrow8 \\ \sqrt[]{256}\Rightarrow\sqrt[]{16\times16}\Rightarrow16 \\ We\text{ will substitute each of these expressions back into the parent expression, we have:} \\ \sqrt[]{\frac{4+4}{8+16}} \\ =\sqrt[]{\frac{8}{24}} \\ =\sqrt[]{\frac{1}{3}} \\ =\frac{\sqrt[]{3}}{\sqrt[]{3}\times\sqrt[]{3}} \\ =\frac{\sqrt[]{3}}{3} \\ \Rightarrow\sqrt[]{\frac{\sqrt[3]{64}+\sqrt[4]{256}}{\sqrt[]{64}+\sqrt[]{256}}}=\frac{\sqrt[]{3}}{3} \\ \\ \therefore\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]If the line y-7=3(x+5) is dilated with a center at the origin and a scale factor of 4, which of the following equations would describe its image?
When we dilate a line with a scale factor of "a", we change its equation by changing the slope.
The slope gets multiplied by "a".
In the equation given, the slope is "3". After a dilation with a scale factor of 4, the slope would become:
3 * 4 = 12
The equation, after dilation, would be:
[tex]y-7=12(x+5)[/tex]Given the following confidence interval for a population mean compute the margin of error E
Given that the Confidence Interval for a population mean:
[tex]11.81<\mu<13.21[/tex]In this case, you can set up these two equations:
[tex]\bar{x}+E=13.21\text{ \lparen Equation 1\rparen}[/tex][tex]\bar{x}-E=11.81\text{ \lparen Equation 2\rparen}[/tex]Because by definition:
[tex]\bar{x}-E<\mu<\bar{x}+E[/tex]Where "ME" is the margin of error and this is the mean:
[tex]\bar{x}[/tex]In this case, in order to find the "ME", you need to follow these steps:
1. Add Equation 1 and Equation 2:
[tex]\begin{gathered} \bar{x}+E=13.21 \\ \bar{x}-E=11.81 \\ -------- \\ 2\bar{x}=25.02 \end{gathered}[/tex]2. Solve for the mean:
[tex]\begin{gathered} \bar{x}=\frac{25.02}{2} \\ \\ \bar{x}=12.51 \end{gathered}[/tex]3. Substitute the mean into Equation 1 and solve for "ME":
[tex]12.51+E=13.21[/tex][tex]\begin{gathered} E=13.21-12.51 \\ E=0.7 \end{gathered}[/tex]Hence, the answer is:
[tex]E=0.7[/tex]
3. Convert the angle 3π/4 to degrees.
Answer:
135°
Step-by-step explanation:
To convert an angle from radians to degrees, multiply by [tex]180/\pi[/tex].
[tex]\frac{3\pi}{4} \cdot \frac{180}{\pi}=135^{\circ}[/tex]
The stem-and-leaf plot shows the number of hours per semester that students in a certain school club watchtelevision. What is the greatest number of hours that were watched?
Answer:
45
Explanation:
The number on the left of the line represent the tens and the numbers on the right of the line represent the units, so data for the stem and leaf plot is:
20, 22, 22, 22, 23, 23
30, 31, 33, 35
40, 42, 42, 43, 43, 43, 45
It means that the greatest number of hours is 45.
Then, the answer is 45.
I need help answering the questions for person 2 on my group assignment
The equation for the relation of sides of triangle can be obtained by similar triangle property.
Consider triangle ABC and triangle DBE.
[tex]\begin{gathered} \angle CAB=\angle EDA\text{ (Each angle is right angle)} \\ \angle CBA=\angle EBD\text{ (common angle)} \\ \Delta CBA\cong\Delta EBD\text{ (By AA similarity condition)} \end{gathered}[/tex]Determine the ratio of corresponding sides of simillar triangle.
[tex]\frac{CB}{EB}=\frac{BA}{BD}=\frac{CA}{ED}[/tex]Thus similar triangle property is used to set up the equation.
use the listing method to represent the following set. picture attached
The correct option is A
{3, 4, 5, 6, ...}
Explanation:The condition given states that x is greater or equal to 3.
The only option that corresponds to this condition is:
{3, 4, 5, 6, ...}
a rectangular prisim has a volume of 80cm cubed it has a length of 2cm and a width of 5cm. What is the prisms height?
rectangular prism volume is ,
[tex]\begin{gathered} V=l\times b\times h \\ 80=2\times5\times h \\ h=\frac{80}{10} \\ h=8\text{ cm } \end{gathered}[/tex]I dont know the steps to solve this expression, help.
5
1) Let's solve that expression step by step
[tex]\frac{35}{2^3-1}[/tex]2) As we have an exponent, let's firstly solve this
[tex]\frac{35}{8^{}-1}[/tex]Now proceeding with the subtraction, and then divide it:
[tex]\frac{35}{7}=5[/tex]3) Hence, the answer is 5
I’m a parent and I’m not sure I’m understanding this question the practice test question says “How would you take apart 14 to solve 28 - 14? The choices are 7 and 710 and 4 12 and 220 and 8. I said 7 and 7
There are several ways of taking apart the number 14:
1 and 13
2 and 12
3 and 11
4 and 10
5 and 9
6 and 8
7 and 7
Nevertheless, as we can see by the note below that exercise,
"Have your child take apart 16 to make a ten to find 87 - 16",
we can conclude that the exercise is asking how to take apart 14 to make a ten. By doing so, the subtraction operation (28 - 14) gets simpler since you could subtract 4, and then subtract the ten:
14 = 10 + 4 (1 ten and 4 units)
So, when we do 28 - 14, we can do that in two steps:
• 28 - 4 = ,24
,• 24, - 10 = 14
Therefore, based on the note below exercise 6, the expected answer is
10 and 4
Please help I'm not sure what should I substitute the variable (x) by
From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
5-74.The number of girls at Middle SchoolCyber Summer Camp was six morethan twice the number of boys. Therewere a total of 156 middle schoolstudents at the camp. Use the 5-DProcess to find the number of boysand the number of girls at camp.
We have the following:
Describe/Draw
The statement tells us that the number of girls was 6 plus twice the number of boys and that in total there are 156 students.
Define
Number of girls: y, y = 6 + 2x
Number of boys: x
Number of students: 154
Do
[tex]\begin{gathered} x+y=156 \\ x+6+2x=156 \\ 3x=156-6 \\ x=\frac{150}{3} \\ x=50 \end{gathered}[/tex]for y:
[tex]y=6+2\cdot50=6+100=106[/tex]Decide
The answer is correct because the sum of both is equal to 156 students
Declare
In total there are 50 boys and 106 girls
A bicycle wheel is 63 centimeters from top to bottom . When the wheel goes all the way around one time , the bicycle travels 198 centimeters . How can this information be used to estimate the value of pi
Given :
A bicycle wheel is 63 centimeters from top to bottom .
So, the diameter of the wheel = 63 cm
When the wheel goes all the way around one time , the bicycle travels 198 centimeters .
So, the circumference of the circle = 198 cm
The circumference of the circle of diameter = d will be :
[tex]\pi\cdot d[/tex]So,
[tex]\begin{gathered} \pi\cdot63=198 \\ \\ \pi=\frac{198}{63}=\frac{22}{7} \end{gathered}[/tex]What is the slope of the line that passes through the points (2,8) and (12,20)?
The slope of the line with that passes through the coordinates (2,8) and (12,20) is 6/5.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8 )
x₁ = 2y₁ = 8Point 2( 12,20 )
x₂ = 12y₂ = 20Slope m = ?
To find the slope m, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 20 - 8 )/( 12 - 2 )
Slope m = ( 12 )/( 10 )
Slope m = 12/10
Slope m = 6/5
Therefore, the slope of the line is 6/5.
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Which number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
Use a sample mean to estimate a population mean with a certain specified OA certainty OB. accuracy OC. confidence OD. determination
SOLUTION
Given the question on the question tab;
Explanation:
When the sample mean is used as a point estimate of the population mean, some error can ... Lower levels of confidence lead to even more narrow intervals.
Final answer:
Which data sets should be displayed on a stem display instead of a dot plot? Select all that apply. A) 11, 23, 9, 24, 34, 18, 15, 11, 8, 14, 16B) -14, -15, -17, -15, -15, -15, -12, -14.-14C) 5,3, 8, 3, 7,5,6,3, 7, 3, 7, 6,5,6D) 1.1, 1.2, 1.1, 1.3, 1.4, 1.1, 1.2, 1.4, 1.2, 1.1E) 42.7, 39.8, 41.1, 39.7, 40.1, 39.8.42.3
In order to determine which data sets should be displayed on a stem display, you consider that the stem display is usefull in the cases in which you have data which can be grouped easily. For instance, for data set in which there are differents number with the same first digit(s).
According with the previous definition you can notice that the options E) and A) are the best options, because there are different number that can be grouped, for example, according to the first number.
For other options you have other situations, for option D) there is no way to group the data. For option C) there is only one number on each data, so, there wouldn't be leafs in the diagram, and the same applies to option B), the first number is the same in all data, then, there is no way to group.
In boot camp, a cadet must use a rope swing to cross an obstacle withoutfalling into the water hazard below. Unfortunately, they miss the platform onthe other side and swing back to where they started. If it takes the cadet 3.5seconds to swing from one side of the obstacle to the other and back, howlong is the rope swing? Use the formula:
Answer:
Choice C: 3.0 m
Explanation:
We are basically asked to solve for L using
Rierda Elwynn Garvey takes home $1250 each month. In addition to other expenses, she also makepayments to her debt of $230 per month. What is her Debt Payments to Income Ratio?
The debt payments to income ratio is the amount that Rierda spend paying her debt each mount divided by her monthly income:
[tex]\text{Ratio}=\frac{230}{1250}=\frac{23}{125}=0.184[/tex]You might need:CalculatorHiro painted his room. After 3 hours of painting at a rate of 8 square meters per hour, he had 28 squaremeters left to paint.Let y represent the area (in square meters) left to paint after chours.Which of the following information about the graph of the relationship is given?
The graph is that of area painted against the number of hours. Given that he painted 8 square meters per hour, the slope is 8 square meters per hour because slope is known as unit rate.
After 3 hours of painting, he would have painted 8*3 = 24 square meters.
Since he has 28 meters left to paint, it means that the total rea of the room that