Answer:
[tex]8.68,13.16[/tex]
Step-by-step explanation:
Hint- First we have to calculate the mean and standard deviation of the sample and then applying formula for confidence interval we can get the values.
Mean of the sample is,
[tex]\mu=\dfrac{\sum _{i=1}^{24}a_i}{24}=\dfrac{262}{24}=10.92[/tex]
Standard deviation of the sample is,
[tex]\sigma =\sqrt{\dfrac{\sum _{i=1}^{24}\left(x_i-10.92\right)^2}{24-1}}=5.6[/tex]
The confidence interval will be,
[tex]=\mu \pm Z\dfrac{\sigma}{\sqrt{n}}[/tex]
Here,
Z for 95% confidence interval is 1.96, and n is sample size which is 24.
Putting the values,
[tex]=10.92 \pm 1.96\cdot \dfrac{5.6}{\sqrt{24}}[/tex]
[tex]=10.92 \pm 2.24[/tex]
[tex]=8.68,13.16[/tex]
Confidence interval is used to express the degree of uncertainty associated with a sample.
95% confidence interval means that if we used the same sampling method to select different samples and calculate an interval, we would expect the true population parameter to fall within the interval for 95% of the time.
Final answer:
A 95 percent confidence interval is computed using the t-distribution and provides an estimated range where we can expect the population mean to lie. It reflects the level of certainty, but does not suggest that it contains 95 percent of the data.
Explanation:
To compute a 95 percent confidence interval for the number of hours students spent studying, we first need to calculate the mean and standard deviation of the given sample data. Then we can use the t-distribution because the sample size is small and we don't know the population standard deviation. The formula to calculate a confidence interval is: ± t× (s/√n), where t is the t-score associated with our confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.
Confidence intervals provide a range of values that we are a certain percentage sure (95% in this case) contains the population mean. It is not correct to think that a 95% confidence interval contains 95% of the data. Instead, it means that if we were to take many samples and build a confidence interval from each of them, 95% of those intervals would contain the true population mean. Therefore, the confidence interval gives an interval estimate for where the population mean lies, not a precise value.
combine like terms to simplify the expression. 2x+4y-7x+10y+8
Answer:
-5x + 14y + 8
Step-by-step explanation:
2x + 4y - 7x + 10y + 8
Combine 2x and -7x because they are both being multiplied by x.
-5x + 4y + 10y + 8
Combine 4y and 10y because they are both being multiplied by y.
-5x + 14y + 8
What is the total surface area
We have two right triangles and three different rectangles.
The formula of an area of a right triangle:
[tex]A_T=\dfrac{1}{2}l_1l_2[/tex]
l₁, l₂ - legs
We have l₁ = 20cm and l₂ = 21cm. Substitute:
[tex]A_T=\dfrac{1}{2}(20)(21)=(10)(21)=210\ cm^2[/tex]
The formula of an area of a rectangle:
[tex]A_R=lw[/tex]
l - length
w - width
We have:
rectangle #1: l = 22cm, w = 29cm
[tex]A_{R1}=(22)(29)=638\ cm^2[/tex]
rectangle #2: l = 22cm, w = 21cm
[tex]A_{R2}=(22)(21)=462\ cm^2[/tex]
rectangle #3: l = 22cm, w = 20cm
[tex]A_{R3}=(22)(20)=440\ cm^2[/tex]
The total Surface Area of the triangular prism:
[tex]S.A.=2A_T+A_{R1}+A_{R2}+A_{R3}\\\\S.A.=2\cdot210+638+462+440=1960\ cm^2[/tex]
a. 0.98 – 0.053 b. 0.67 – 0.4 c. 0.3 – 0.002 d. 3.2 – .789 e. 6.53 – 4.298 f. 6 – 4.32 g. 7 – 3.574 h. 4.83 – 1.8 i. 3.7 – 1.8 j. 16.17 – 11.632
a. 0.927
We have:
0.98 – 0.053
We can re-write it as:
0. 9 8 0 -
0. 0 5 3
Moving digits to the right:
0. 9 7 10 -
0. 0 5 3
Digit-per-digit subtraction:
0. 9 2 7
b. 0.27
We have:
0.67 – 0.4
We can re-write it as:
0. 6 7 -
0. 4 0
Digit-per-digit subtraction:
0. 2 7
c. 0.298
We have:
0.3 – 0.002
We can re-write it as:
0. 3 0 0 -
0. 0 0 2
Moving digits to the right:
0. 2 10 0 -
0. 0 0 2
Again:
0. 2 9 10 -
0. 0 0 2
Digit-per-digit subtraction:
0. 2 9 8
d. 2.411
We have:
3.2 – .789
We can re-write it as:
3. 2 0 0 -
0. 7 8 9
We need to rewrite the first term by moving digits to the right several times:
3. 2 0 0 = 2. 12 0 0 = 2. 11 10 0 = 2. 11 9 10
So now we have:
2. 11 9 10 -
0. 7 8 9
Digit-per-digit subtraction:
2. 4 1 1
e. 2.232
We have:
6.53 – 4.298
We can re-write it as:
6. 5 3 0 -
4. 2 9 8
We need to rewrite the first term by moving digits to the right several times:
6. 5 3 0 = 6. 5 2 10 = 6. 4 12 10
So now we have:
6. 4 12 10 -
4. 2 9 8
Digit-per-digit subtraction:
2. 2 3 2
f. 1.68
We have:
6 – 4.32
We can re-write it as:
6. 0 0 -
4. 3 2
We need to rewrite the first term by moving digits to the right several times:
6. 0 0 = 5. 10 0 = 5. 9 10
So now we have:
5. 9 10 -
4. 3 2
Digit-per-digit subtraction:
1. 6 8
g. 4.426
We have:
7 – 3.574
We can re-write it as:
7. 0 0 0 -
3. 5 7 4
We need to rewrite the first term by moving digits to the right several times:
7. 0 0 0 = 6. 10 0 0 = 6. 9 10 0 = 6. 9 9 10
So now we have:
6. 9 9 10 -
3. 5 7 4 =
Digit-per-digit subtraction:
3. 4 2 6
h. 3.03
We have:
4.83 – 1.8
We can re-write it as:
4. 8 3 -
1. 8 0
We can immediately do the digit-per-digit subtraction:
3. 0 3
i. 2.9
We have:
3.7 – 1.8
We can re-write it as:
3. 7 -
1. 8
We need to rewrite the first term by moving digits to the right:
3. 7 = 2. 17
So now we have:
2. 17 -
1. 8 =
Digit-per-digit subtraction:
2. 9
j. 4.538
We have:
16.17 – 11.632
We can re-write it as:
1 6 . 1 7 0 -
1 1 . 6 3 2
We need to rewrite the first term by moving digits to the right:
1 6. 1 7 0 = 1 6. 1 6 10 = 1 5. 11 6 10
So now we have:
1 5. 11 6 10 -
1 1. 6 3 2 =
Digit-per-digit subtraction:
0 4. 5 3 8
please help!! Which shape is a continuous line of equal distance from its center?
Answer: I know it’s a circle but I forget why actually sorry that doesn’t help much
Step-by-step explanation:
Need help please help me
y = mx + b - it's the equation of a straight line. We need only two points to the plotting the graph of that function.
Select any two x values and calculate y values:
[tex]y=\dfrac{1}{2}x+2\\\\for\ x=0\to y=\dfrac{1}{2}(0)+2=0+2=0\to(0,\ 2)\\\\for\ x=-4\to y=\dfrac{1}{2}(-4)=-2+2=0\to(-4,\ 0)[/tex]
[tex]y=x+5\\\\for\ x=0\to y=0+5=5\to(0,\ 5)\\\\for\ x=-5\to y=-5+5=0\to(-5,\ 0)[/tex]
Look at the picture.
The solution of the system of equations is the intersection point of the line.
Answer: (-6, -1) → x = -6 and y = -1f(x)=-x^2+1 find f(-3)
Answer:
-8
Step-by-step explanation:
All you have to do to solve this equation is plug "-3" into the equation where you see "x"
[tex]f(x)=-x^2+1\\f(-3)=-(-3)^2+1\\f(-3)=-(9)+1\\f(-3)=-9+1\\f(-3)=-8[/tex]
Find the missing lengths of the sides
Answer: A
Step-by-step explanation: sin45(9 radical 2)
Item 1 Solve the system of linear equations by graphing. 5x+5y=15 2x−2y=10
After graphing both lines, we're able to tell the solution by looking at the point where the lines cross. In this case, it's at (4, -1). And so that is the solution set.
Mr. Mateo ordered several copies of a book that weighs 3/5 of a pound each along with some other school supplies for his classroom. If the total weight of the box that contains the supplies was 10 pounds, what is the maximum number of copies of the bookthat Mr. Mateo could have ordered
Answer:
It's 16 I just did the same question on a quiz
If the total weight of the box that contains the supplies was 10 pound.
The maximum number of copies of the book that Mr. Mateo could have ordered is 16.
Given:
The number of copies of a book = [tex]\frac{3}{5}[/tex] pound
The total weight of the box = 10 pounds
According to question,
[tex]\frac{3}{5} x<10\\3x<50\\x<\frac{50}{3}\\x<16.66[/tex]
let: x = 16
Therefore, the maximum number of copies of the book that Mr. Mateo could have ordered is 16.
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Find the measure of angle x in the diagram below.
A. 25°
B. 45°
C. 105°
D. 145°
Answer:
C. 105°
Step-by-step explanation:
To find the answer, we can use the method of exterior angle of triangles, which would be <A + <B = <C, in which A and B is any interior angles of triangles and C would be the exterior angle for the remaining angle.
In this case:
45°+60° = 105°
Therefore the answer is C. 105°
Hope it helps!
The measure of the angle x is 105 degrees option (C) is correct.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have a triangle shown in the picture.
As we know,
The sum of two interior angles is equal to the exterior angle;
The measure of the angle x:
x = 60 + 45
x = 105 degrees
Thus, the measure of the angle x is 105 degrees option (C) is correct.
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I need help could you please help me
properties of isoceles trapezoids??
Answer:
Parallel bases.
The legs are congruent by definition.
The lower base angles are congruent.
The upper base angles are congruent.
Any lower base angle is supplementary to any upper base angle.
The diagonals are congruent.
Step-by-step explanation:
which of the following is equal to the fraction below (5/9)^8
Answer:
the answer is D because both are to the power of 8
Step-by-step explanation:
Answer:
Option D is correct
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Step-by-step explanation:
[tex]\text{Given the fraction }(\frac{5}{9})^8[/tex]
we have to choose the correct option which is equivalent to above.
As we know
[tex](\frac{a}{b})^x=\frac{a^x}{b^x}[/tex]
Put a=5, b=9, x=8
[tex](\frac{5}{9})^8=\frac{5^8}{9^8}[/tex]
Therefore, option D is correct
A jar contains 133 pennies. A bigger jar contains 1 2/7 times as many pennies. What is 5he value of the pennies in the bigger jar
Answer:
The Jar contained 5^67 pennis of nickels and quaters. Making a lot of money in 1/4 of a month. The 5he value of the pennies in the bigger than the amount of the total fitting of itself. The Largest pennies in the jar depended on the nickels and quaers inside. The 133 pennies wer the jar that contained the lesser amount of pennies, therfore the bigger jar standes with a larger value
Step-by-step explanation:
write the slope-intercept form of the equation of the line described.
through:(-2,-4), perpendicular to y=2x+5
Answer:
Find the negative reciprocal of the slope of the original line and use the slope-intercept form
y=mx+b to find the line perpendicular to [tex]y=2x+5[/tex].
[tex]y=−12x−5[/tex]
Hope this helps!!
[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\\text{We have}\ k:y=2x+5\to m_1=2.\\\\l:y=mx+b\to m=-\dfrac{1}{2}\to y=-\dfrac{1}{2}x+b.\\\\\text{The line passes through the point (-2, -4).}\ \text{Put the coordinates to the equation:}\\\\-4=-\dfrac{1}{2}(-2)+b\\\\-4=1+b\qquad\text{subtract 1 from both sides}\\\\-5=b\to b=-5\\\\Answer:\ \boxed{y=-\dfrac{1}{2}x-5}[/tex]
A proportional relationship between the number of pounds of carrots (x) and the price in dollars (y) is graphed, and the ordered pair (8, 6) is on the graphed line. Part A: What is the price of 1 pound of carrots? Show your work. (8 points)
Answer:
$0.75
Step-by-step explanation:
We have been given that a proportional relationship between the number of pounds of carrots (x) and the price in dollars (y).
We can represent this information as: [tex]y=kx[/tex].
We are also told that the ordered pair (8, 6) is on the graphed line. Let us substitute x= 8 and y= 6 in our proportional equation to find the constant of proportionality.
[tex]6=k*8[/tex]
[tex]k=\frac{6}{8}[/tex]
[tex]k=\frac{3}{4}[/tex]
Now let us substitute k=3/4 and x=1 in our proportionality equation.
[tex]y=\frac{3}{4}*1[/tex]
[tex]y=\frac{3}{4}[/tex]
[tex]y=0.75[/tex]
Therefore, the price of 1 pound of carrots will be $0.75.
what is the volume of this cuboid?
Please help me!!!?!
The formula of a volume of a cuboid:
[tex]V=lwh[/tex]
l - length
w - width
h - height
We have:
l = (x + 4) cm
w = (x + 1) cm
h = 3 cm
Substitute:
[tex]V=(x+4)(x+1)(3)[/tex] use distributive property
[tex]V=(x+4)(3x+3)[/tex]
[tex]V=(x)(3x)+(x)(3)+(4)(3x)+(4)(3)[/tex]
[tex]V=3x^2+3x+12x+12[/tex] combine like terms
[tex]\boxed{V=3x^2+15x+12}[/tex]
A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 ft/s against the walkway and 5 ft divided by s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Answer: The traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
Step-by-step explanation:
Given: A traveler is walking on a moving walkway in an airport.
Let 't' be the traveler's speed off the walkway and 'w' be the speed of walkway.
Then the traveler's ground speed against the walkway (t-w)= 1 ft/s
And the traveler's ground speed with the walkway (t+w)= 5 ft/s
thus we get the following equations [tex]t-w=1..........(1)\\t+w=5.............(2)[/tex]
Adding (1) and (2), we get
[tex]2t=6\\\Rightarrow\ t=3[/tex]
Subtract (2) from (1), we get
[tex]2w=4\\\Rightarrow\ w=2[/tex]
Therefore, the traveler's speed off the walkway= 3 ft/s
The speed of the moving walkway= 2 ft/s
What is the equation of the line that passes through the points (-3,2) and (-5,8)
Answer:
y = -3x - 7
Step-by-step explanation:
Slope = (8 - 2)/(-5 + 3) = 6/-2 = -3
Equation
y - 2 = - 3(x + 3)
y - 2 = -3x - 9
y = -3x - 7
Answer
y=-3x-7
is the equation of line that passes through the points (-3,2) and (-5,8)
step by step explanation:
we are given
(x1,y1)=(-3,2)
(x2,y2)=(-5,8)
formula of slope
m=(y2-y1 )/ (x2-x1)
putting value in formula
m=(8-2) /-5-(-3)
m=6/-5+3
m=6/-2
m=-3
Formula of line slop form of equation is
y-y1=m(x-x1)
putting the values in the formula
y-2= -3(x-(-3))
y-2= -3(x+3)
y-2=-3x-9
y=-3x-9+2
y=-3x-7
is the equation of line that passes through the points (-3,2) and (-5,8)
Analyze the reflectional symmetry of the regular polygons. The square has -fold reflectional symmetry. The regular octagon has -fold reflectional symmetry.
Answer:
The square has 4-fold reflectional symmetry. The regular octagon has 8-fold symmetry.
Step-by-step explanation:
For a square,
There are two lines of symmetry along two diagonals and
two lines of symmetry along midpoints of two pairs of opposite sides.
Therefore, there are 4 lines of reflectional symmetry in total.
For a regular octagon,
There are four lines of symmetry along four diagonals and
four lines of symmetry along midpoints of four pairs of opposite sides.
Therefore, there are 8 lines of reflectional symmetry in total.
Final answer:
A square has 4-fold reflectional symmetry, while a regular octagon has 8-fold reflectional symmetry.
Explanation:
Reflectional symmetry refers to a property of a shape where it can be divided into two mirror-image halves. The -fold reflectional symmetry of a regular polygon refers to the number of lines of symmetry it possesses. A line of symmetry is an imaginary line that divides the shape into two equal halves that are mirror images of each other.
For example, a square has 4-fold reflectional symmetry because it has 4 lines of symmetry, dividing it into 4 equal halves. Each line of symmetry passes through the midpoints of opposite sides.
On the other hand, a regular octagon has 8-fold reflectional symmetry because it has 8 lines of symmetry, dividing it into 8 equal halves. Each line of symmetry passes through the midpoints of opposite sides or vertices.
Is 42 and 105 relatively
prime
Answer:
No.
Step-by-step explanation:
42 has the following prime factors: 2, 3, 7
105 has prime factors: 3, 5, 7
Both prime factors 3 and 7 divide 42 and 105. If 42 and 105 were relatively prime (co-prime), the set of prime factors that divide both would be empty.
the sum of two numbers is 17 and their difference is 29 what are the two numbers
Answer:
According to the question,
Numbers are : 23 and -6
The two numbers are -6 and 23.
To find the two numbers, we can set up a system of equations based on the given information. Let the two numbers be [tex]\( x \) and \( y \), where \( x > y \)[/tex]. According to the problem, we have:
1. The sum of the two numbers is 17:
[tex]\[ x + y = 17 \][/tex]
2. The difference between the two numbers is 29:
[tex]\[ x - y = 29 \][/tex]
Now, we can solve this system of equations. We can add the two equations together to eliminate [tex]\( y \)[/tex] :
[tex]\[ (x + y) + (x - y) = 17 + 29 \] \[ 2x = 46 \] \[ x = \frac{46}{2} \] \[ x = 23 \][/tex]
Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into one of the original equations to find [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[ 23 + y = 17 \] \[ y = 17 - 23 \] \[ y = -6 \][/tex]
Therefore, the two numbers are 23 and -6.
Which is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)
Simplify 7/5x to 7x/5
3(7x/5 + 4) -2(3/2 - 5/4x)
Simplify 5/4x to 5x/4
3(7x/5 + 4) -2(3/2 - 5x/4)
Expand
21x/5 + 12 - 3 + 5x/2
Collect like terms
(21x/5 + 5x/2) + (12 - 3)
Simplify
67x/10 + 9
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
What is an Expression ?Expression is a mathematical statement which consists of variables , constant and mathematical operators all together simultaneously.
The given expression is 3(7/5x+4)-2(3/2-5/4x)
[tex]\rm 3 ( \dfrac{7}{5} x+4) -2 ( \dfrac{3}{2}-\dfrac{5}{4}x)[/tex]
(21/5)x +12 - 3 + (5/2)x
((42+25)/10)x + 9
(67x + 90)/10
The simplified form of the expression 3(7/5x+4)-2(3/2-5/4x) is (67x + 90)/10
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What monomial do you have to raise to the power of 2 to get the given monomial? What monomial do you have to raise to the power of 3 for this? a x6y12
When raising a monomial to a power, you multiply the exponents of each variable by that power.
Explanation:When you raise a monomial to the power of 2, you multiply the exponents of each variable by 2. So in the given monomial ax6y12, you would raise each exponent to the power of 2 to get a2x12y24.
Similarly, when you raise a monomial to the power of 3, you multiply the exponents of each variable by 3. So in the given monomial ax6y12, you would raise each exponent to the power of 3 to get a3x18y36.
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1. find the difference 7 1/4 - 3 1/2 =
a. 3 3/4
b. 4 3/4
c. 3 1/2
d. 4 1/2
2. find the product and write it in simplest form 3/8 x 2/3
a. 9/16
b. 6/24
c. 2/8
d. 1/4
3. find the product and write it in simplest form 2 3/8 x 1 2/3
a. 2 6/24
b. 3 23/24
c. 3 3/4
d. 95/8
4. perform the division and write it in simplest form 7/10 ÷ 3/5
a. 35/30
b. 6/7
c. 21/60
d. 1 1/6
Answer:
1. a
2. d
3. b
4. it would be 7/6 NOT 6/7
Step-by-step explanation:
Threeangles of a quadrilateral are equal and its fourth angel is 120° . Find all the angels
Answer:
80°
Step-by-step explanation:
Three angles are equal
Let the equal angle be x
3x+120=360
3x=240
x=240/3
=80
Hence the three angles are 80∘
Answer:
Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
Step-by-step explanation:
The sum of the measures of the angles of an n-sided polygon is (n - 2)180.
A quadrilateral has 4 sides, so n = 4 in the formula above.
(n - 2)180 = (4 - 2)180 = 2(180) = 360
The sum of the measures of the angles of a quadrilateral is 360 degrees.
Three angles are congruent. Let the measures of the three congruent angles be x. The sum of the measures of the 3 angles is x + x + x = 3x.
The sum of the measures of the angles is 360 deg.
3x + 120 = 360
Subtract 120 from both sides.
3x = 240
Divide both sides by 3.
x = 80
Answer: Each of the three congruent angles has measure 80 deg. The fourth angle has measure 120 deg.
How do you graph square roots
Answer: Simplify the number in the square root.
Step-by-step explanation: For example, √25 can be simplified to 5 because half of 25 is 5. If x=5, graph this on the x-axis or horizontal line on the graph. Another example, √2 can be simplified to approximately 1.414. To graph this, you can use a graphing tool for accurate representation, or create a graph and place a dot right before 1.5 (in between 1 and 2).
identify the slope x + y= -3 solve for b
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
x + y = -3 subtract x from both sides
y = -x - 3
slope = -1A line passes through (3, -2) and (6, 2). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Answer:
(a)
Given: A line passes through the points (3, -2) and (6, 2)
Point slope form: An equation of line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]y -y_1=m(x-x_1`)[/tex] .....[1] where m is the slope of the line.
Calculate first the slope of the line:
Slope(m) = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points;
[tex]m = \frac{2-(-2)}{6-3}=\frac{2+2}{3} =\frac{4}{3}[/tex]
Substitute the value of m in [1] ;
[tex]y - (-2) = \frac{4}{3}(x-3)[/tex]
[tex]y+2=\frac{4}{3}(x-3)[/tex] ......[1]
therefore, the equation of line in point slope form is, [tex]y+2=\frac{4}{3}(x-3)[/tex]
(b)
to find the standard form of the equation [1]
Multiply both sides by 3 in [1] we get;
[tex]3(y+2) = 4(x-3)[/tex]
using distributive property; [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
3y + 6 = 4x -12
Subtract 3y to both sides we get;
3y + 6 -3y = 4x - 12 - 3y
Simplify:
6 = 4x - 3y -12
Subtract 6 from both sides we get;
0 = 4x - 3y -12-6
Simplify:
4x - 3y - 18 =0
Therefore, the standard form of the equation is; 4x - 3y - 18 =0
sarahs volleyball team won 12 games of their first 18 games. if the continue to win at this rate, how many games will they lose if they play 36 games
Answer:
They lost 12 games.
Step-by-step explanation:
Set up a proportion.
12/18 = x/36
36 x 12 = 432
432/18 = 24
Because 18 represents how many games they won, the 24 also represents how many games they won. Therefore, you must subtract to find the amount of times that they lost.
36 - 24 = 12
Answer:
they lost 12 games
Step-by-step explanation:
they lost 12 games