ANSWER
cos(bº) = 4/5
EXPLANATION
When a triangle is dilated, the resulting triangle is similar to the original triangle. Therefore, the interior angles of the dilated triangle are congruent to the interior angles of the original triangle. This means that cos(bº) is the same for both triangles.
Using the relationship between these three trigonometric ratios:
[tex]\tan (bº)=\frac{\sin (bº)}{\cos (bº)}[/tex]We can find the cosine:
[tex]\cos (bº)=\frac{\sin (bº)}{\tan (bº)}[/tex][tex]\cos (bº)=\frac{\frac{3}{5}}{\frac{3}{4}}=\frac{3}{5}\colon\frac{3}{4}=\frac{3}{5}\times\frac{4}{3}=\frac{4}{5}[/tex]Data collected on types of fruit is given below.R = Red Fruit. B = Berries Given that:r1 =49r2 =10r3 =5r4 = 8A) how many types of fruit are not red?B) how many types of fruit are berries?C) how many types of fruit are red berries D) how many types of fruit are not red and not berries
You have the next diagram:
R=10+5=15
B=5+8=13
R∩B=5
U=49+5+8+10=72
A) how many types of fruit are not red?The number of fruits that are not reds is those that are outside of the set R: 57
[tex]\begin{gathered} R^{\prime}=U-R=72-15 \\ R^{\prime}=57 \end{gathered}[/tex]B) how many types of fruit are berries?The number of fruits that are berries is those that are in the set B: 13
[tex]B=13[/tex]C) how many types of fruit are red berriesThe number of fruits that are red berries is those that are in set R and in set B: 5
[tex]R\cap B=5[/tex]D) how many types of fruit are not red and not berriesThe number of fruits that are not red and not berries is those that are outside the sets R and outside the set B: 49
Which inequality is represented by the graph?
Answer:
[tex]y < \frac{5}{3} x - 3 \\ [/tex]
Step-by-step explanation:
- General linear equation of a line passing through point (x, y) with a gradient m and y-intercept (0, c) is ;
[tex]{ \rm{y = mx + c}}[/tex]
- As finding gradient, m; consider points (0, -3) and (3, 2) from the graph;
[tex]{ \rm{slope \: m = \frac{2 - ( - 3)}{3 - 0} }} \\ \\ { \rm{m = \frac{5}{3} }}[/tex]
- Then our equation becomes y = 5/3x + c
- Consider point (0, -3), relate it with (0, c) hence c is -3;
[tex]{ \rm{y = \frac{5}{3}x - 3 }}[/tex]
- If you see the format of the coordinates, x coordinates are greater than y coordinates, hence y < x
[tex]{ \rm{y < \frac{5}{3}x - 3 }} \\ [/tex]
Answer:
[tex]y < \dfrac{5}{3}x-3[/tex]
Step-by-step explanation:
All given answer options have the same linear equation:
[tex]y=\dfrac{5}{3}x-3[/tex]
Therefore, there is no need to work out the equation of the line for this question as it is already given.
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.From inspection of the graph there is:
A dashed line.Shading under the line.Therefore, the inequality that is represented by the graph is:
[tex]y < \dfrac{5}{3}x-3[/tex]
what percentage of the eggs were not at room temperature? do not include (%) in the answer round the answer to the nearest whole number .
Given a table represents the number of eggs that hatched at 3 different temperature:
The total number of eggs = 14 + 11 = 25
There are just 25 eggs in each time to make the experiment
The number of eggs was not hatched at room temperature = 11
so, the percentage will be =
[tex]\frac{11}{25}\cdot100=44[/tex]So, the answer will be = 44
Which of the following is an x-intercept of the graph of the function shown below? f(x) = x2 + 6x + 9 O A. x = 6 O B. x=9 O C. X=-3 O D. x = 3 PREVIOUS Type here to search
Given:
The function is,
[tex]f(x)=x^2+6x+9[/tex]Explanation:
For x-intercept of the function f(x) = 0. So
[tex]0=x^2+6x+9[/tex]Solve the equation for x.
[tex]\begin{gathered} x^2+6x+9=0 \\ x^2+3x+3x+9=0 \\ x(x+3)+3(x+3)=0 \\ (x+3)(x+3)=0 \\ x=-3,-3 \end{gathered}[/tex]So x-intercept of the function is x = -3.
Answer: x = -3
Option C is correct
The number of boots that 25 students had in their homes in Florida were recorded below:
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 9
a) What value would you predict to be an outlier?
b) How does the outlier affect the median?
c) How does the outlier affect the mean?
d) Which measure of center would best describe the data?
e) How does the outlier affect the standard deviation?
f) How does the outlier affect the interquartile range?
g) Which measure of spread would best describe the data?
PLEASE ANSWER, WILL MARK BRAINLIEST
1.The outlier affect the Min = 0 for the minimum
2. the outlier affect the median is 2
Q₁ = 0 Q₃ = 3 Maximum Max = 8
The middle value in a sorted data set is known as the median.
what is more about?
Think of your sorted data as being
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 5, 8
1.Min = 0 for the minimum
The median
The middle value in a sorted data set is known as the median.
2.Since there are 25 items,
the 13th item is the median.
median is 2
3. The median of the data set's lower half is the first quartile, or Q1.
Between 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, the median is 0.
Q₁ = 0
Pretend that your s
4.Third quartile
The top half of the data set's median is Q3.
2, 2, 2, 2, 2, 3, 3, 3, 4, 5, and 8 have a median value of 3 each.
Q₃ = 3
5. Maximum Max = 8
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What’s -4(x-2)
show step by step !
Normally, by order of operations, we simplify what's in the parenthesis first. However, since we don't know the value of x, it is already simplified. So we use the distributive property to distribute -4 to the binomial.
-4(x - 2)
(-4 × x) + (-4 x -2)
-4x + 8
Answer:
-4x+8
Step-by-step explanation:
-4×(x)=-4x
-4×-2=8
What can you observe about the
segments that connect
corresponding
vertices?
It is observed about the segments that the two triangles are congruent, the corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
What is segment?
In mathematics, the line segment is one of the part of the straight line. It has two endpoints which can be used to calculate the length of the respective segment. It is measured in different units called as meter, centimeter, etc.
According to the question, the given data for the line segment is as follows:
DD' = 58.4 cm; EE' = 58.4 cm; FF' = 58.4 cm
All three segments are equal in length.
In this, the ΔDEF and ΔD'E'F' are equal from angle as well as length sides. And the relationship between two triangles and their vertex state that they are forming two congruent Polygon shapes as well as generating a segment between them. Thus, if there is congruence among the pentagons, it will exist between the formed triangles.
Therefore, it is observed about the segments that connect corresponding vertices that the two triangles are congruent and its corresponding angle pair is congruent. also the two corresponding side pairs are also congruent.
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Sum of two rational numbers are 2/15 , if one rational number is 2/3 . Find the other rational number
Step-by-step explanation:
the answers is attached
hope it helps
An archer releases an arrow with an initial velocity of 24 feet per second at a height of 16 feet. The path the arrow takes can be modeled using the function f(x)=−16x2+24x+16, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. How many seconds until the arrow hits the ground? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.
Answer:
18.25
Step-by-step explanation:
From the quadratic equation given, the time it will take till the arrow hits the ground is 22.75 seconds
How many seconds until the arrow hits the ground?To determine when the arrow hits the ground, we need to find the value of x when the height, f(x), is equal to 0. In other words, we need to solve the equation:
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a),
where a, b, and c are the coefficients of the quadratic equation
In this case, a = -16, b = 24, and c = 16. Substituting these values into the quadratic formula:
x = (-(24) ± √((24)² - 4(-16)(16))) / (2(-16)).
Simplifying further:
x = (-24 ± √(576 + 1024)) / (-32),
x = (-24 ± √(1600)) / (-32),
x = (-24 ± 40) / (-32).
x = -101/4 or x = 101/4
Since x≠ negative;
x = 101/4 = 22.75 seconds
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Add/Subtract. Express your answer as a polynomial in standard formMultiply/Dividea) (5^3)(6^4)b) (6^7)(1/2^8)c) (1/2 ^5)(1/3 ^9)d) 14^5 7^2
To multiply them, we will multiply the coefficient 5 and 6
5 * 6 = 30
for x we will add their power to multiply them
[tex](5x^3)(6x^4)=(5\times6)(x^{3+4})=30x^7[/tex][tex](6x^7)(\frac{1}{2}x^8)[/tex]We will multiply 6 by 1/2
6 * 1/2 = 3
Then add the power of x
[tex](6x^7)(\frac{1}{2}x^8)=(6\times\frac{1}{2})(x^{7+8})=3x^{15}[/tex]Kelly bought a soda for three dollars and 7 candy barswent to the movies. She spent a total of $21. How much did eachcandy bar cost?Write equation and solve. Show work
She spent a total of $21 dollars.
The soda cost $3
Then, she bought 7 candy bars for x dollars
We set x because we don't know the price
3 + 7x = 21
Solve the equation for x
Subtract both sides by 3
3-3 + 7x = 21 -3
7x = 18
Divide both sides by 7
7x/7 = 18/7
x= 2.571
Each candy bar cost 2.57 aprox
resume the line between (4 -4) and (-4 -4)for was the form inside of the right time of (-4,4) is reflect over both axes to create the triangles third vertex how long will the resultant base be
For this case we have two points given:
(-4, -4) and (-4,4)
The third vertex for this case would be:
(4,-4)
And then the resulting base would be:
d= 4+4 = 8
correct answer:
8 units
Which of the following ratios does NOT represent a proportional relationship?
ANSWER
D 3/4 = 8/6
EXPLANATION
For the ratios to be proportional, the fraction on the left hand side must be equivalent to the one on the right hand side.
So, for each of them, we will check if the values are the same.
a) 3/4 = 6/8
Simplifying 6/8 by dividing numerator and denominator by 2 yields:
3/4 = 3/4
The ratio is proportional.
b) 3/6 = 4/8
Simplifying both sides yields:
1/2 = 1/2
The ratio is proportional.
c) 4/3 = 8/6
Simplifying 8/6 by dividing numerator and denominator by 2 yields:
4/3 = 4/3
The ratio is proportional.
d) 3/4 = 8/6
Simplifying 8/6 by dividing numerator and denominator by 2 yields:
3/4 = 4/3
Because the two fractions are not equal, the ratio is not proportional.
The answer is D.
Sheldon thought of a natural number, and then he added the next natural number to it.
He got the sum of 75. What was Sheldon's number?
Using a system of equations, it is found that Sheldon's number is of 37.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.
For this problem, we have to consider that:
The natural number is of x.The next natural number is the successor of x, represented by x + 1.The sum of these numbers is given by:
x + x + 1 = 2x + 1 (combining the like terms).
The sum is equals to 75, hence we can solve for the natural number x as follows:
2x + 1 = 75
2x = 74
x =74/2
x = 37. (which is Sheldon's natural number).
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Find the slope of the line shown in the graph below enter your answer as a simplified improper fraction if necessary
The slope is 1
Explanation:Choose the points (2, -3) and (4, -1)
The slope is:
[tex]\begin{gathered} y=\frac{-1-(-3)}{4-2}=\frac{-1+3}{4-2} \\ \\ =\frac{2}{2}=1 \end{gathered}[/tex]what % less 60 is 51
To find the percent we are looking for we can use the rule of three:
[tex]\begin{gathered} 60\rightarrow100 \\ 51\rightarrow x \end{gathered}[/tex]then:
[tex]\begin{gathered} x=\frac{51\cdot100}{60} \\ x=85 \end{gathered}[/tex]This means that 51 is 85% of 60.
Therefore 51 is 15% less than 60.
Write 10x – 5y = –30 in slope-intercept form.
Answer:
the answer of the question is
y= 2x+6
Angles A and B are supplementary angles. If m
Answer:
138 degrees
Explanation:
Two angles are said to be Supplementary if they add up to 180 degrees.
Given that Angles A and B are supplementary and:
[tex]\begin{gathered} m\angle A=(2x-24)^0 \\ m\angle B=(5x-27)^0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} m\angle A+m\angle B=180^0 \\ 2x-24+5x-27=180 \\ 7x=180+27+24 \\ 7x=231 \\ x=\frac{231}{7} \\ x=33^0 \end{gathered}[/tex]Therefore, the measure of angle B will be:
[tex]\begin{gathered} m\angle B=(5x-27)^0 \\ =5(33)-27 \\ =165^0-27^0 \\ =138^0 \end{gathered}[/tex]The measure of angle B is 138 degrees.
100 POINTS!!! And BRAINLIEST
Select the correct option for each
cos(-25°) = _____.
cos 115°
cos 25°
sin 25°
-cos 335°
sin(-136°) = _____.
sin (-316)°
-sin 44°
-sin 316°
-cos 44°
tan(-212°) = _____.
-cot 32°
tan 32°
cot 32°
-tan 32°
cot(-315°) = _____.
cot (-45)°
cot 135°
cot 45°
-cot 45°
Using equivalent angles, the correct options are given as follows:
cos(-25°) = cos(25º).sin(-136º) = -sin(44º).tan(-212º) = -tan(32º).cot(-315º) = cot(45º).Cos(-25º)Negative 25 degrees is on the fourth quadrant, with the positive angle measure being given by:
360 - 25 = 335º.
The equivalent angle on the first quadrant is of 360º - 335º = 25º, and the cosine on the first quadrant is positive, just like in the fourth, hence:
cos(-25°) = cos(25º).
Sin(-136º)The positive angle measure is given as follows:
360 - 136 = 224º.
Which is on the third quadrant, in which both the sine and the cosine are negative.
The equivalent angle on the first quadrant is given as follows:
224º - 180º = 44º.
Hence the expression is:
sin(-136º) = -sin(44º).
Tan(-212º)The positive angle measure is given as follows:
360 - 212 = 148º.
Which is on the second quadrant, in which the tangent is negative.
The equivalent angle on the first quadrant is given as follows:
180º - 148º = 32º.
Hence the expression is:
tan(-212º) = -tan(32º).
Cot (-315º)The positive angle is given as follows:
360 - 315 = 45º.
Which is already on the first quadrant, hence the expression is given as follows:
cot(-315º) = cot(45º).
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4/5(720-240)-180 step by step
To solve, we use the order of operations PEMDAS, where
P = Parenthesis
E = Exponets
M = Multiplication
D = Division
A = Addition
S = Subtraction
State the expression to be simplified:
Possibility 1
[tex]\frac{4}{5}(720-240)-180[/tex]Expanding the parenthesis:
[tex]\frac{4}{5}\times480-180[/tex]Multiplying then subtracting,
[tex]384-180[/tex]Therefore, the answer is 204.
Possibility 2
[tex]\frac{4}{5(720-240)}-180[/tex]Expanding parenthesis:
[tex]\frac{4}{5\times480}-180[/tex]Multiplying:
[tex]\frac{4}{2400}-180[/tex]Dividing then subtracting:
[tex]\begin{gathered} \frac{1}{600}-180 \\ =-179.998 \end{gathered}[/tex]Therefore, the answer is -179.998.
Possibility 3
[tex]\frac{4}{5(720-240)-180}[/tex]
Expanding parenthesis:
[tex]\frac{4}{5\times480-180}[/tex]Multiplying:
[tex]\frac{4}{(2400-180)}[/tex]Further expanding the parenthesis then dividing:
[tex]\begin{gathered} \frac{4}{2220} \\ =0.0018 \end{gathered}[/tex]Therefore, the answer is 0.0018.
Which is bigger 978cm or 12m?
It is given that there are two quantities 978cm and 12 m.
The units are different so convert in same units.
It is known that 1m=100cm
So 12m=1200cm.
Since 1200>978 so it follows
1200cm>978cm.
so 12m>978cm.
Hence 12 meters is greater than 978cm.
According to a study of the power quality (sags and swells) of a transformer, for transformers built for heavy industry, the distribution of the number of sags per work has a mean of 346 with a standard deviation of72. Of interest is x, the sample mean number of sags per week for a random sample of 216 transformers. Completo parts a through d below.a. Find E(%) and interpret its valueE() -(Type an integer or a decimal. Do not round.)Interpret the value of E(). Select the correct choice below and fill in the answer box to complete your choice(Type an integer or a decimal. Do not round.)O A. For any random sample of 216 transformers, the mean number of sags por wook is always. B. 1 many random samples of 216 transformers are taken, then the mean of the sample variances is sags por wookOC. If many random samples of 218 transformers are taken, then the mean of the sample mean numbers of sags per week isOD. I many random samples of 216 transformers are taken, then the mean of the sample standard deviations is sags por wookb. Find Var()Var) -(Type an integer or a decimal Round to three decimal places as needed.)c. Describe the shape of the sampling distribution of Xwith mean - and standard deviation -(Type intogors or decimal Round to three decimal places as needed)The sampling distribution of xd. Howey is it to observe a sample mean number of sags por wook that exceeds 3007C
Given data:
Population Mean = 346
Standard Deviation = 72
Expected Value of e(x) = population mean = 346
Sample Size = 216
In this case, if many random samples of 216 are taken, then the mean of the sample mean numbers per week is 346. (Option C)
To solve for the variance of x or var(x), we follow the formula below:
[tex]var(x)=\frac{\sigma^2}{n}=\frac{(s\tan darddeviation)^2}{\text{sample size}}[/tex]In this case, the given standard deviation is 72 and the sample size is 216. Therefore, we have:
[tex]var(x)=\frac{72^2}{216}=\frac{5184}{216}=24[/tex]One of the properties of the Sampling Distribution of the Mean is that the sampling distribution of the mean is approximately normally distributed so long as the sample size is 30 or higher. Our sample mean here is 346 with a sample standard deviation of √24 or 4.899.
How likely is it to observe a sample mean number of sags per week that exceeds 390?
For this one, we have this formula to use:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Our bar "x" is 390. The "myu" symbol is our population mean which is 346. This σ symbol is the population standard deviation 72 and n is our sample size = 216.
[tex]z=\frac{390-346}{\frac{72}{\sqrt[]{216}}}=\frac{44}{2\sqrt[]{6}}=8.98[/tex]Under a normal curve, the areas defined are between z = -3.5 to z = +3.5. Since our z should exceed > 8.98 and thus far greater than +3.5, then we can say that the probability of having a sample mean that exceeds 390 is zero.
in the diagram the perpendicular bisectors of triangle MNP meet at point O the circumcenter find the measure of PO
The circumcenter must have equal distance between center and veriter
8.062,8.26,0.026,8.6 least togreatest
Answer:
0.026, 8.062, 8.26, 8.6
Step-by-step explanation:
Hope this helps!
Btw, pls give brainliest, thanks!
Answer:
0.026, 8.062, 8.26, 8.6
Sam ran 63,756 feet in 70 minutes. What is Sam's rate in
miles per hour? (There are 5,280 feet in one mile.)
Step 1: What is Sam's rate as stated?
The Sam's rate is 10.35 miles per hours.
What is miles per hour?
In mathematics, miles per hour is the unit for the speed measurement. It is used for the calculation of the speed of the train or people or any another objects. It can be calculated by dividing the distance with time.
According to the question, the given data states that the Sam ran 63,756 feet in 70 minutes.
Distance = 63,756 feet and Time = 70 minutes
And the given conversion is: 5280 feet = 1 miles
Therefore, Sam's rate or speed in miles per hour is as written below:
Speed = Distance/Time
Speed = (63,756/70) x (1/5280) x 60 = 10.35 miles per hours
Hence, the Sam's rate is 10.35 miles per hours.
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Jordan wants to solve the following system using the elimination method:2x + 3y = 10x + y = 7what numbers should the equation x + y = 7 be multiplied by to eliminate ya. -2b. 2c. -3d. 3
In elimination method one equation is multiplied by the negative coefficient of the other
so then in this case y have coefficient 3, the other equation have coefficient y is 1 . Then divide 3/1 = 3 and change sign ,gives -3.
Then the final answer is -3, option c)
HELP ASAP WILL GIVE THE BRAINLIEST TO ANYONE WHO ANSWERS THIS CORRECTLY HELP ASAP
Answer: the answer is B or the second option /note b and the second option are the same thing
Step-by-step explanation:
n/a
Answer: The second one
Step-by-step explanation:
You have to go down 3 boxes, and go 6 boxes to the right in order to correlate with the same letter
i need help with subtracting,multiplying,dividing,and adding fractions.
Adding fractions
To add two fractions, you have to make sure that the numbers in the denominator are the same.
For the fractions
[tex]\frac{1}{2}+\frac{2}{5}[/tex]The denominators are different, you have to look for a common factor between 2 and 5, the quickest way is to multiply them, you know that 10 is both a multiple of 2 and of 5.
Multiply 1/2 by 5 to obtain the equivalent expressed in tenths and multiply 2/5 by 2 to obtain the equivalent fraction in tenths
[tex]\frac{1}{2}\cdot5=\frac{5}{10}[/tex][tex]\frac{2}{5}\cdot2=\frac{4}{10}[/tex]Now that both fractions have the same denominator you can add them
[tex]\frac{5}{10}+\frac{4}{10}=\frac{5+4}{10}=\frac{9}{10}[/tex]Subtracting Fractions
You must apply the same procedure when subtracting two different fractions. First find a common factor so that the denominator is the same for both fractions:
[tex]\frac{1}{2}-\frac{1}{5}[/tex]As before, the common factor is 10, so the equivalent fractions will be:
[tex]\frac{5}{10}-\frac{4}{10}=\frac{5-4}{10}=\frac{1}{10}[/tex]Dividing fractions
To divide two fractions you have to do the following steps.
1- Invert the fraction that corresponds to the denominator of the division, i.e. the one you want to divide for (the second one).
This is called a reciprocal fraction.
2-Multiply the first fraction, the one you want to divide by the reciprocal fraction.
3-If possible, simplify the result.
1-Invert the denominator of the division
[tex]\frac{2}{5}=\frac{5}{2}[/tex]2-Multiply the denominator by the reciprocal fraction
[tex]\frac{1}{2}\cdot\frac{5}{2}=\text{ }\frac{1\cdot5}{2\cdot2}=\frac{5}{4}[/tex]1/2 divided by 2/5 equals 5/4
A microwave is placed on top of two boxes. One box is 3 feet 5 inches tall, the other box is 2 feet 8 inches tall, and the microwave is 3 feet 10 inches tall. How tall are they combined? Write your answer in feet and inches. Use a number less than 12 for inches.
The combined length is 9 feet 11 inches
What is length?
Distance is measured by length. Length is a quantity having the dimension distance in the International System of Quantities. Most measuring systems use a base unit for length from which all other units are derived. The metre is the basic unit of length in the International System of Units (SI). The greatest extended dimension of a stationary item is typically believed to be its length. This is not always the case, as it may depend on the location of the item. Height, sometimes known as vertical length or vertical extent, and width, breadth, or depth are all words used to describe the length of a stationary object. When length is the greatest dimension, width or breadth generally relate to a lesser dimension.
Given, length of a box = 3 feet 5 inches
length of another box = 2 feet 8 inches
length of microwave = 3 feet 10 inches
Total length = 3 feet 5 inches + 2 feet 8 inches + 3 feet 10 inches
= 9 feet 11 inches
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The table below shows the students in an Algebra class.GirlsBoysTotalOwn a graphing Do not own a graphingcalculatorcalculator125176713Total181230What is the probability that a randomly chosen student will be a girl and own a graphingcalculator?
Explanation:
The total number of students in the algebra class is given below as
[tex]n(S)=30[/tex]The number of girsl who won a graphing calculator is given below as
[tex]\begin{gathered} n(G_h\cap G_n)=12 \\ where, \\ G_h=have\text{ }graphing\text{ }calculator \\ G_n=does\text{ }not\text{ }have\text{ }graphing \end{gathered}[/tex]Concept:
To figure out the probabaility that a randomly chosen student will be a girl and own a graphing calculator, we will use the formula below
[tex]Pr(G_h\cap G_n)=\frac{n(G_h\cap G_n)}{n(S)}[/tex]By substituting the values, we will have
[tex]\begin{gathered} Pr(G_{h}\operatorname{\cap}G_{n})=\frac{n(G_{h}\operatorname{\cap}G_{n})}{n(S)} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{12}{30} \\ Pr(G_h\operatorname{\cap}G_n)=\frac{2}{5} \end{gathered}[/tex]Hence,
The final answer is
[tex]\frac{2}{5}[/tex]The FOUTH OPTION is the correct answer