the ratio is 6:25, because for every 25 students that dont wear glesses there are 6 that do.
Answer:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
Step-by-step explanation:
The ratio of students that wear glasses to the total number of students is: (12:62) or, when simplified (6:31)
The total number of students is 62, and 12 of them wear glasses.
The ratio of students that do not wear glasses to the total number of students is:
(50:62) or when simplified (25:31)
The total number of students is 62, and 50 of them do not wear glasses.
The ratio of students that do not wear glasses to the students that do wear glasses is:
(50:12) or when simplified (25:6)
The 50 students do not wear glasses, while 12 students wear glasses.
The ratio of students that do wear glasses to the students that wear glasses is:
(12:50) or when simplified (6:25)
There are 12 students who wear glasses and 50 who do not.
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4)-1 and 3 + 2i A) (x)= x3 + 5x2 +7x + 13 B)(x) = x3 - 5x2 + 7x - 13 C)(x)= x3 - 5x2 + 7x + 13 D) f() = x3 - 5x2 + 7x + 14
trey is draining an aquarium. the graph shows the amount of water (in liters) in the aquarium versus time (in minutes)
Given the graph represents the amount of water in the aquarium versus time.
A) As shown in the graph :
as the time increases the amount of water in the aquarium decreases
The rate of water decreasing =
[tex]\frac{480}{8}=60[/tex]so, the rate = 60 litres per minute
A sample was done, collecting the data below. Calculate the standard deviation, to one decimalplace.х24726573
We have the following data
[tex]24,7,26,5,13[/tex]The standard deviation is given by
[tex]\sigma=\sqrt[]{\frac{\sum(x_i-\mu)^2}{N}}[/tex]Where μ is the mean and N is the number of data points
Let us first find the mean of the data.
[tex]\mu=\frac{\text{sum}}{number\text{ of data points}}=\frac{24+7+26+5+13}{5}=\frac{75}{5}=15[/tex]Finally, the standard deviation is
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{(24-15)^2+(7-15)^2+(26-15)^2+(5-15)^2+(13-15)^2}{5}} \\ \sigma=\sqrt[]{\frac{(9)^2+(-8)^2+(11)^2+(-10)^2+(-2)^2}{5}} \\ \sigma=\sqrt[]{\frac{81^{}+64^{}+110^{}+100^{}+4^{}}{5}} \\ \sigma=\sqrt[]{\frac{359}{5}} \\ \sigma=\sqrt[]{71.8} \\ \sigma=8.5 \end{gathered}[/tex]Therefore, the standard deviation of the data set is 8.5
Given two vectors,find y so that a and b are orthogonal,
In they are orthogonal the their scarlar product will be zero.
So
[tex]a\cdot b=0[/tex][tex]\begin{gathered} (9,-7,-7)\cdot(6,y,-4)=0 \\ 54-7y+28=0 \\ -7y=-82 \\ y=11.714 \end{gathered}[/tex]Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
What is the vectors?
Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point.
Various operations can be applied to vectors such as addition, subtraction, and multiplication.
Here given that,
[tex]a=(9,-7,-7)\\b=(6,y,-4)[/tex]
If they are orthogonal the their scarlar product will be zero.
So,
[tex](9,-7,-7).(6,y,-4)=0\\54-7y+28=0\\-7y=-82\\As,\\a.b=0\\y=\frac{82}{7}\\y=11.714[/tex]
Hence, [tex]y=11.714[/tex] when the [tex]a[/tex] and [tex]b[/tex] are orthogonal.
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What is the solution to the linear equation 2/5+p=4/5+3/5p
Ok ,we need to find p in the following equation: 2/5+p=4/5+3/5p, lets
A standard pair of six sided dice is rolled what is the probability of rolling a sum greater than or equal to 11
The diagram below shows all the possible outcomes from rolling a pair of six sided dice.
The first row and first columns represents the numbers on each die. The numbers in the other rows and columns are outcomes for each roll. Thus, the total number of outcomes is the total number of pairs in the other rows and columns.
Total number of outcomes = 36
Number of outcomes with sum greater than or equal to 11 are the circled pairs. They are 3
Thus, the probability of rolling a sum greater than or equal to 11 is
3/36 = 1/12
Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle ABC and triangle PQR .
Consider the triangle ABC and triangle PQR .
we can see that
(i) angle C = angle R .....given in the figure
(iii) angle B = angle Q .... given in the figure
(ii) side BC = side QR ....given in the figure
From the above three statements we conclude that
ΔABC ≅ ΔPQR
both the triangles KLM and PQR are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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i need to know which one is the answer , i’m having a hard time figuring it out
Answer:
Explanation:
Here, we want to know the table that represents a function
For a relationship to represent a function, no two y values can have a single x value but two x values can have a single y value.
What this means is that two independent variable values can take a single dependent variable value but no two dependent variable values can take a single independent variable value
Now, looking at the table given:
what does translation mean?
translation means moving a geometric object in the cartesian plane without rotating it.
Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?
We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.
We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:
[tex]v=\frac{d}{t}[/tex]where v is speed, d is distance and t is time, we know that for the first jet:
[tex]x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1[/tex]Where d₁ represents the distance of the first jet from the starting point. For the second jet:
[tex]x=\frac{d_2}{4}\Rightarrow4x=d_2[/tex]Where d₂ represents the distance of the second jet from the starting point.
We also know that:
[tex]d_1+d_2=6000[/tex]As:
Thus, we have that:
[tex]\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}[/tex]This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).
Question #10: Given triangle A is the pre image and B is the image, state the scale factor of the dilation from A to B. * 4 B 10 18 А 7.2 15
To find the acale factor we need to solve the following equation:
[tex]\begin{gathered} 18k=7.2 \\ k=\frac{7.2}{18} \\ k=0.4 \end{gathered}[/tex]This comes from the fact that the biggest sides of both triangles have to be realted.
Therefore the dilation factor is 0.4.
What is the slope for this equation y = -2.5x + 92
EXPLANATION
Given the equation y = -2.5x + 92
The slope is equal to -2.5
The volume of gas kept at a constant pressure varies inversely with the temperature T. If the temperature is 50 degrees, the volume is 20 quick feet. What will the volume be when the temperature is 100 degrees. V= , Temperature=. . Solution
Given that the volume of gas kept at constant pressure varies inversely with the temperature T and when the temperature is 50 degrees, the volume is 20 cubic feet.
We have to find the volume of gas when the temperature is 100 degrees.
Since it is given that volume varies inversely with the temperature. It means
[tex]T_1V_1=T_2V_2[/tex]Substitute T1 = 50, V1 = 20, T2 = 100.
[tex]\begin{gathered} 50\times20=100\times V_2 \\ 1000=100\times V_2 \\ \frac{1000}{100}=V_2 \\ 10=V_2 \end{gathered}[/tex]Thus, the volume of gas when the temperature is 100 degrees is 10 cubic feet.
Find anequation for the perpendicular bisector of the line segment whose endpointsare (5,-4) and (-9, -8).
First, we need to find the slope of the line:
Let:
(5, -4) = (x1,y1)
(-9, -8) = (x2,y2)
m = (y2-y1)/(x2-x1) = (-8-(-4))/(-9-5) = -4/-14 = 2/7
Also, we need to find the midpoint:
let:
MP = (xp,yp)
xp= (x1+x2)/2 = (5-9)/2 = -2
yp = (y1+y2)/2 = (-4-8)/2 = -6
MP = (-2, -6)
Now, the slope for the perpendicular bisector is -m = -7/2
y = -mx + b
Using the midpoint
-6 = -7/2(-2) + b
-6 = 7 + b
Solving for b:
b = -13
Therefore, the equation for the perpendicular bisector is:
y = -7x/2 - 13
Find the equation for the line that passes through the point (3.-5), and that is perpendicular to the line with the equation x = -2
• Line x = -2 is a vertical line that passes through point x = -2
Given the point ( 3;-5)
• We know that perpendicular lines have opposite reciprocal slopes , so the slope of the line will be
,• m = 1/2
• so , the standard formula for a line : y = mx +c
at point ( 3-5) , we will have :
-5 = 1/2(3) + c
Therefore c = -5 -3/2
= -13/2
• Our y- intercept will be -13/2
• Finally , our equation of the line will be :
y = 1/2x -13/2
Write the point-slope form of the equation of the line through the points (-1, -1) and (2, 4)
The point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1) - 1.
The point-slope form is simply writing an equation of a line so that the slope or steepness and x-intercept i.e. where the line crosses the vertical x-axis are immediately apparent.
The slope-intercept equation is y - y1 = m(x - x1), where x and y are two variables, and m is the slope.
Slope m = (y2-y1) / (x2-x1)
Let,
(x1, y1) = (-1, -1)
(x2, y2) = (2, 4)
Slope (m) = ((4) - (-1)) / ((2) - (-1))
= 5/3
y - y1 = m(x - x1) => (y - (-1)) = 5/3(x - (-1))
=> y+1 = 5/3(x + 1)
=>y = 5/3(x+1)-1
Therefore, the point-slope form of (-1, -1) and (2, 4) is y = 5/3(x+1)-1.
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The population of Boom town is 775,000 and is increasing at a rate of 6.75% each year. How many years will it take to reach a population of 1,395,000?
To study population growth, we use the following formula
[tex]P=P_0\cdot e^{rt}[/tex]Where,
[tex]\begin{gathered} P=1,395,000 \\ P_0=775,000 \\ r=0.0675 \end{gathered}[/tex]Let's replace the values above, and solve for t.
[tex]\begin{gathered} 1,395,000=775,000\cdot e^{0.0675t} \\ e^{0.0675t}=\frac{1,395,000}{775,000} \\ e^{0.0675t}=1.8 \\ \ln (e^{0.0675t})=\ln (1.8) \\ 0.0675t=\ln (1.8) \\ t=\frac{\ln (1.8)}{0.0675} \\ t\approx8.7 \end{gathered}[/tex]Hence, it would take 8.7 years to reach a population of 1,395,000.A 3 dimensional shape is created when the shape isrotated around the y-axisFind the volumen of shape
By rotating the shape of the graph, we get the following cylinder:
So we have a cylinder with:
• radius r = 4,
,• height h = 6.
The volume of the cylinder using π = 3.14 is given by:
[tex]V=\pi *r^2*h=3.14*4^2*6=301.44.[/tex]AnswerThe solid obtained is a cylinder of volume 301.44.
If the rate of inflation is 2.5% per year, the future price P(T) in dollars of a certain item can be modeled by the following exponential function, where T is the number of years from today
Solution:
The future price p(t), in dollars, can be modelled by the exponential function;
[tex]p(t)=800(1.025)^t[/tex](a) The current price is;
[tex]\begin{gathered} t=0; \\ \\ p(0)=800(1.025)^0 \\ \\ p(0)=800(1) \\ \\ p(0)=800 \end{gathered}[/tex]ANSWER: $800
(b) The price 8 years from today;
[tex]\begin{gathered} t=8 \\ \\ p(8)=800(1.025)^8 \\ \\ p(8)=800(1.2184) \\ \\ p(8)=974.72 \\ \\ p(8)\approx975 \end{gathered}[/tex]ANSWER: $975
Write the slope-intercept (y = mx + b) form of an equation for a line with y-intercept-5 and slope 2.
The slope-intercept form of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
so we only need to substitute the values into the equation
m=2
b= -5
the equation is
[tex]y=2x-5[/tex]f(×) = 3× + 7 f(1) =
f(1) = 10
Explanation:Given f(x) = 3x + 7
To find f(1), replace x by 1 in the equation above
f(1) = 3(1) + 7
= 3 + 7
= 10
points a,b, and are b lies between a and c. if ac=48,ab =2x+2and bc =3x+6, what is bc?
Given that A, B, and C are collinear and B lies between A and C, then:
AB + BC = AC
Replacing with data:
(2x + 2) + (3x + 6) = 48
(2x + 3x) + (2 + 6) = 48
5x + 8 = 48
5x = 48 - 8
5x = 40
x = 40/5
x = 8
Then,
BC = 3x + 6
BC = 3(8) + 6
BC = 24 + 6
BC = 30
I need help with fractions and word problem can you help me
Grace wants to bring a small wedge of cheese for the next 12 days, but there are three small rounds of cheddar cheese in Grace's refrigerator, That is to say, that Grace needs to buy cheese to fulfill this purpose, the small wedge of cheese that Grace needs are:
[tex]12-3=9[/tex]but we must represent this infraction, for this, we will take the 12 small wedges of cheese as a unit, which is formed by having the 12 portions.
That is, out of 12/12 portions, we only have 3/12, To do this we do subtraction and see how many we need in fractional form.
[tex]\begin{gathered} \frac{12}{12}=1 \\ \frac{12}{12}-\frac{3}{12}=\frac{9}{12} \end{gathered}[/tex]In conclusion, Grace need 9 portions i.e. 9/12
Now, that we know this fraction, this is a correct answer, however, we can simplify this fraction.
[tex]\frac{9}{12}=\frac{3}{4}[/tex]In conclusion, Grace needs 3/4 small wedge of cheese.
Note: the answer can be 9/12, but also its simplified form which corresponds to the same, this simplified form is 3/4.
4x + 8 = 28Describe a real-world situation the equation could represent.
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
The equation 4x +8=28 could be used to describe a scenario like this below:
In a club, the entrance ticket is $8. And every time you order a soda you have to pay $4 per can. Since you only have $28 in your pocket, how many sodas can you afford?
Notice the fixed amount (8) and the variable (4x) and the total of money you have (28). So the sum above describes the amount of money for that club.
With that equation you can find that:
4x +8=28
4x+8 -8 =28-8
4x=20
x=5
5 cans of soda.
Determine if the triangles, △YPQ and △NPD, are similar. if so, Identify criterion.
Answer:
Yes, they are similar.
Criterion: AA Similarity
Explanation:
Looking at triangles YPQ and NPD, we can see that angles NPD and YPQ are vertically opposite angles and are congruent since vertically opposite angles are always congruent;
[tex]\angle YPQ\cong\angle NPD\text{ (vertically opposite angles)}[/tex]We can also observe that angles N and Y are congruent since they are alternate angles;
[tex]\angle N\cong\angle Y\text{ (alternate angles)}[/tex]From the AA similarity rule, we know that two triangles are said to be similar if two angles in one triangle are equal to two triangles in the other triangle.
Therefore, from the AA rule, we can say that triangles YPQ and NPD are similar.
Mia made a pencil box in the shape of a right rectangular prism what's the surface area of the box 20cm,6cm,7cm
1) Let's visualize it to better understand:
A right rectangular prism is made from
2 faces 6 x 7
4 faces 20 x 6
Since we have rectangles, we can write calculating the area of each rectangle.
S base = 2 (6x 7) ⇒ S base = 84 cm²
S faces = 2 (20 x 6) ⇒ S faces = 240 cm²
S faces = 2 (20 x 7) ⇒ S faces = 280 cm²
2) Then the total surface area
84+240+280=604 cm²
A randomly generated list of integers from O to 4 is being used to simulate anevent, with the number 3 representing a success. What is the estimatedprobability of a success?
We have that:
• A randomly generated list of, integers from 0 to 4 i,s being used to simulate an event.
• The number 3 represents a success.
And we need to find the estimated probability of success.
We can achieve that if we know that:
1. We have the following sample space for the experiment - we have a list of integers from 0 to 4:
[tex]\Omega=\lbrace0,1,2,3,4\rbrace[/tex]2. Then the probability of having a 3 is:
[tex]P(3)=\frac{1}{5}=0.2\Rightarrow20\%[/tex]We have one possibility of getting a 3 (one possibility) out of 5 possibilities (0, 1, 2, 3, 4).
Therefore, the estimated probability of success is 20% (option D.)
I have 3 more questions but it didn’t fir here
Probability = number of required outcome/number of the possible outcome
(a) To determine the theoretical probability for mary
[tex]\begin{gathered} \text{ Probability of spinner landing on grey = }\frac{\text{ number of grey}}{Total\text{ colour}} \\ \text{Probability of spinner landing on grey = }\frac{593}{1000} \\ \text{Probability of spinner landing on grey = 0.}593 \end{gathered}[/tex](b) To determine the experimental probabiity for mary's result
[tex]\begin{gathered} \text{Experimental probabil}ity\text{ = }\frac{\text{ number of grey}}{Total\text{ number}} \\ \text{Experimental probabil}ity\text{ = }\frac{3}{5\text{ }} \\ \text{Experimental probabil}ity=\text{ 0}.600 \end{gathered}[/tex](c) Assuming the spinner is fair, with a large number of spins there might be a difference between the experimental and theoretical probability but the difference will be small.
the density of aluminum is 2700 kg/m3. what is the mass of a solid cube of aluminum with side lengths of 0.5 meters?
SOLUTION
Density is calculated as
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ \end{gathered}[/tex]The side lengths of the aluminium cube has been given as 0.5 m
The volume becomes
[tex]\begin{gathered} volume=length\times length\times length \\ V=L\times L\times L \\ V=0.5\times0.5\times0.5=0.125m^3 \end{gathered}[/tex]so the volume is 0.125 cubic-meters.
The mass becomes
[tex]\begin{gathered} Density=\frac{mass}{volume} \\ mass=density\times volume \\ mass=2700\times0.125 \\ =337.5 \end{gathered}[/tex]Hence the answer is 337.5 kg
I am having a hard time finding the apt for this question pls help me?
The APR, that is Annual Percentage Rate, is calculated using the formula below;
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