In a certain Algebra 2 class of 26 students, 7 of them play basketballand 13 of them play baseball. There are 10 students who play neithersport. What is the probability that a student chosen randomly from theclass plays both basketball and baseball?
Answers
The situation can be represented by the above diagram
7 students play basketball, that is,
x + y = 7 (eq. 1)
13 students play baseball, that is,
y + z = 13 (eq. 2)
10 students who play neither sport.
x + y +z = 26 - 10
x + y +z = 16
Substituting with equation 2,
x + 13 = 16
x = 16 - 13
x = 3
Substituting with equation 1,
3 + y = 7
y = 7 - 3
y = 4
Then there are 4 students that play both sports. Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is: 4/26 = 2/13
Related Questions
Lamar received 7/8 of the 160 votes cast for class treasure how many votes did he receive
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160 is 1
x is 7/8
[tex]\frac{\frac{7}{8}\times160}{1}=\frac{7}{8}\times160=140[/tex]ANSWER
He received 140 votes
Need help with this one 3 tutors have canceled I been on it for 30 min
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Answer: We have to find the JK, the simple answer is as follows, it is calculated by first finding the angle M and then using a trigonometric ratio to calculate the JK.
The simple and brief steps are as follows:
[tex]\begin{gathered} \angle M=\theta_T=\sin^{-1}(\frac{LJ}{LM})=\sin^{-1}(\frac{12}{20})=36.869897646^{\circ} \\ \\ \theta=\frac{\theta_T}{2}=18.434948823^{\circ}\approx18.435^{\circ} \end{gathered}[/tex]Therefore the JK is:
[tex]\begin{gathered} \tan(\theta)=\frac{JK}{JM}\rightarrow\tan(18.435^{\circ})=\frac{JK}{16} \\ \\ \\ JK=16\tan(18.435^{\circ})=5.3333333\approx5.34 \\ \\ \\ JK\approx5.34 \end{gathered}[/tex]Therefore JK is 5.34.
labels the numbers as rational or irrational 1.5 13/3 .3333
Answers
1.5
13/3
.3333
A rational number is a number that can be express as the ratio of two integers. A number that cannot be expressed that way is irrational
Let's see
Step 1
1.5, this can be represented as
[tex]\frac{3}{2}[/tex]so, 1.5 is a rational number
Step 2
13/3, this is the ratio of 2 integers so it is a rational number
Step 3
0.3333
this number can be
[tex]0.3333=\frac{1}{3}[/tex]so, Again it is the ratio of 2 integers, then, 0.3333 is a rational number
I really hope this helps you
which of the following equations will produce the graph shown? (answers in photo)HELP PLEASE HELP PLEASE HELP PLEASEEEE!!! ASAPPP
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From the given graph,we find that the radius of the circle with center at the origin is r=4 units.
The equation of a circle with cter at the origin is
[tex]x^2+y^2=r^2[/tex]Here, r is the radius of the circle.
Put r=4 in the above equation.
[tex]\begin{gathered} x^2+y^2=4^2 \\ x^2+y^2=16 \end{gathered}[/tex]Multiply both sides of the above equation by 2.
[tex]\begin{gathered} 2x^2+2y^2=2\times16 \\ 2x^2+2y^2=32 \end{gathered}[/tex]Therefore, the equation representing the circle is,
[tex]\begin{gathered} \\ 2x^2+2y^2=32 \end{gathered}[/tex]The beachfront path was 5,907 feet long. A tropical storm caused waves that washed away 4,806 feet from the end. How long was the path after the storm?
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
5907 feet = beachfront path
4806 feet
Step 02:
beachfront path
Simplify the expression. e 2 In 4 16 e2 02 O 16
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To simplify this expression we need to remember the following properties:
[tex](b^x^{})^y=b^{xy}^{}[/tex]and
[tex]e^{lnx}=x^{}[/tex]Then, in our case
[tex]e^{-2ln4}=(e^{ln4})^{-2}^{}[/tex][tex]\begin{gathered} =(4)^{-2} \\ =\frac{1}{4^2} \\ =\frac{1}{16} \end{gathered}[/tex]Therefore
[tex]e^{-2ln4}=\frac{1}{16}^{}[/tex]simplify 38-87. I dont know
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To check if we can simplify the fraction 38/87, we need to decompose the numerator and the denominator in their prime factors:
[tex]\begin{gathered} 38=2\cdot19 \\ 87=3\cdot29 \end{gathered}[/tex]If the two numbers have any prime factor in common, we can divide both numbers by this prime factor. But in this case, the two numbers don't have prime factors in common, so we can't simplify the fraction further.
So the fraction 38/87 is already in the simplest fraction form.
Omar needs to read 5 novels each month. Let N be the number of novels Omar needs to read in M months. Write an equation relating N to M. Then graph your equation using the axes below
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If Omar needs to read 5 novels each month, then we can express it as 5M because M represents months, and this expression is equal to N because it represents the number of novels Omar needs to read.
Therefore, the equation that represents this situation is 5M = N.Now, to graph the expression, we have to evaluate it when M = 1 and M = 2.
[tex]\begin{gathered} 5\cdot1=N\Rightarrow N=5 \\ 5\cdot2=N\Rightarrow N=10 \end{gathered}[/tex]So, the ordered pairs are (1,5) and (2,10), let's graph them to then draw the line through those points.
Of the 100 people who tested three(3) sodas, 60 people preferred soda A. What fraction of the people preferred soda A? (Express As Fraction)
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please help!!!! the options for the select part are x or y
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We are given the graph of a function, which we are told that is polynomial of degree 4.
Recall that the domain of a function is the values of x for which the the function is defined. Using the graph, the domain is the set of x coordinates of the point s of the graph.
On the other side, recall that the range of a function is the set of values that the function takes. So, using the graph, the range is the set of y coordinates of the points of the graph.
Since we know that the graph is from a polynomial of degree 4, we recall that polynomials of any degree are defined for every value of x. Then, the domain of this graph is (-infinity, infinity).
On the other side, to determine the range. we take a look at the y coordinates of the graph. So the highest value from the graph is 7. Also, we see that the polynomial decreseases its value as x gets bigger or smaller. This behavior stays true globally, so, we can say that the range of the function is the interval (-infinity,7].
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 4 small boxes of oranges and 7 large boxes of oranges for a total of $169. Ming sold 4 small boxes of oranges and 2 large boxes of oranges for a total of $74. Find the cost of each of one small box of oranges and one large box of oranges.
Answers
Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 4 small boxes of oranges and 7 large boxes of oranges for a total of $169. Ming sold 4 small boxes of oranges and 2 large boxes of oranges for a total of $74. Find the cost of each of one small box of oranges and one large box of oranges
Let
x -----> the cost of each of one small box
y ----> the cost of each of one large box
we have that
Matt
4x+7y=169 -----> equation 1
Ming
4x+2y=74 -----> equation 2
Solve the system of equations
Solve by graphing
Remember that when solving by graphing the solution is the intersection point both lines
using a graphing tool
see the attached figure
the solution is the point (9,19)
therefore
the cost of each of one small box is $9the cost of each of one large box is $19Use graph paper Plot point Pot (2-4) Then plot the image of point P under a translation of 4 units to the left and 3 units down Upload a photo of your graph paper.
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We want to plot the point (2,-4) and apply a transformation to it. Then, we want to plot the resulting point after translating it.
The transformation is a translation of 4 units to the left and 3 units down. The x coordinate is related to the horizontal positions (and movements) and the y coordinate is related to the vertical positions (and movements).
So, a translation 4 units to the left means that we will subtract 4 to the x coordinate and a translation of 3 units down means that we will subtract 3 to the y coordinate.
So we have
[tex](2-4,-4-3)=(-2,-7)[/tex]So we want to plot points (2,-4) and (-2,-7).
Thus, we plot as follows
If the distance from point A to point C is approximately 7.2 units, then what is the approximate distance from point B to point C? 52 4 6 7.2
Answers
Answer
Using Pythagorean theorem
[tex]\begin{gathered} BC^2=DB^2+DC^2 \\ BC^2=4^2+6^2 \\ BC^2=16+36 \\ BC^2=52 \\ BC=\sqrt[]{52} \\ BC=7.211 \\ BC=7.2 \end{gathered}[/tex]The final answer
Option D
At a middle school, 74 students have freckles. There are 258students in the school. To the nearest tenth of a percent,what percent of the students have freckles?
Answers
The answer is 28.7% of the students have freckles (approximated to the nearest tenth of a percent).
Triangle L' is the image of triangle L under a dilation.
What is the center of the dilation?
Answers
Since triangle L' is the image of triangle L under a dilation, the center of the dilation is A.
What is dilation?In Geometry, dilation can be defined as a type of transformation which changes the size of a geometric figure, but not its shape. This ultimately implies that, the size of the geometric figure would be enlarged or reduced based on the scale factor that is applied.
What is the center of dilation?The center of dilation is also referred to as a point of dilation and it can be defined as a reference (fixed) point that is used to correctly scale the dilation of a geometric figure.
By critically observing the graph (see attachment) of triangles L and L', we can logically deduce that the point at which image of triangle L was dilated is point A because it is the reference (fixed) point.
Read more on dilation here: brainly.com/question/20482938
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show work!!What value of x makes the equation 33x=11 true33x=11
Answers
The value of x that makes the equation true is 1/3
Explanation:[tex]\text{33x = 11}[/tex]The value of x that will make the equation true will be a value when substituted will give same value on the right and left side of the equation.
To get x, we will divide both sides by the coefficient of x. The coefficient of x is 33. So we will divide both sides by 33:
[tex]\begin{gathered} \frac{33x}{33}\text{ = }\frac{11}{33} \\ x\text{ =}\frac{11}{33} \\ x\text{ = }\frac{1}{3} \end{gathered}[/tex]To determine if the value of x we got is right, we will substitute in the equation given:
[tex]\begin{gathered} 33x\text{ = 11} \\ 33(\frac{1}{3})\text{ = 11} \\ 11\text{ = 11} \\ left\text{ hand side = right hand side} \\ \\ Hence,\text{ the value of x that makes the equation true is }\frac{1}{3} \end{gathered}[/tex]what is the slope of (-3,7) and (2,-6)
Answers
The given points are (-3,7) and (2,-6)
we apply the slope formula:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} x_1=-3,y_1=7,x_2=2,y_2\text{ = }-6 \\ \text{slope = m}=\text{ }\frac{-6-7}{2-(-3)} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{-13}{2+3} \\ m\text{ = -13/5} \\ \text{slope = -2 }\frac{3}{5} \end{gathered}[/tex]Given IJK is congruent to LMN, find the length of all unbiased sides and the measure of all unlabeled angles. Round all answers to the nearest tenth.
Answers
Answer
IK = 6.9 cm
m < K = 30 degrees
NM =
Given that IJK is congruent to LMN
Therefore, IJ = ML
IK = LN
JK = MN
Where, IJ = 4cm
JK = 8cm
LN = 6.9cm
m < J = 60 degrees
m < N = 30 degrees
Since IK = LN
LN = 6.9cm
Therefore, IK = 6.9cm
m< K = m< N
m < N = 30 degrees
Therefore, m < K = 30 degrees
NM = JK
JK = 8cm
Therefore, NM = 8cm
ML = IJ
IJ = 4 cm
Therefore, ML is 4cm
m < M = m < J
m< J = 60 degrees
Therefore, m < M = 60 degrees
m < I = m < L
m < I = 90 degrees
Therefore, m < L = 90 degrees
K is the midpoint of JL. JK = 4x and KL= x + 3. Find JK, KL, and JL.
Answers
Answer:
JK = 4
KL = 4
JL = 8
Explanation:
Given that K is the midpoint of JL, we have:
See that JK = KL
So,
[tex]4x=x+3[/tex]We then solve for x
Subtract x from both sides
[tex]\begin{gathered} 4x-x=3 \\ \\ 3x=3 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ \\ x=1 \end{gathered}[/tex]Therefore
JK = 4x = 4(1) = 4
KL = x + 3 = 1 + 3 = 4
JL = JK + KL = 4 + 4 = 8
Drag each volume of a prism to match a rectangular prism on the left with the given dimensions.54 cu. in.72 cu. in.36 cu. in.80 cu. in.Dimensions of Rectangular PrismVolume of Rectangular Prism 4 in., 3 in., 6 in. 6 in., 3 in., 2 in. 4 in., 5 in., 4 in. 2 in., 9 in., 3 in.
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We need to determine the volume of each of the given rectangular prisms.
We know that the volume V of a rectangular prism with dimensions a, b, and c is given by:
[tex]V=a\cdot b\cdot c[/tex]Thus, to find the volume of each rectangular prism, we need to multiply its dimensions.
We obtain:
[tex]\begin{gathered} 4in,3in,6in\Rightarrow V=4in\cdot3in\cdot6in=(4\cdot3\cdot6)(in\cdot in\cdot in)=72in^{3} \\ \\ 6in,3in,2in\Rightarrow V=6in\cdot3in\cdot2in=(6\cdot3\cdot2)in^{3}=36in^{3} \\ \\ 4in,5in,4in\Rightarrow V=4in\cdot5in\cdot4in=(4\cdot5\cdot4)_{}in^{3}=80in^{3} \\ \\ 2in,9in,3in\Rightarrow V=2in\cdot9in\cdot3in=(2\cdot9\cdot3)in^{3}=54in^{3} \end{gathered}[/tex]Therefore, dragging each volume to its respective place, we obtain:
Which of the following measures is more accurate to 45 grams?O 44.45 grams?
Answers
Simplify: which measur eis more accurate to 45 grams
Explanation: for more accuracy of the number we try to find more closure value to the number.
so from the given options 44.85 is more closure to 45 . hence 44.85 grams is accurate to 45 grams
Final answer: 44.85 grams is more accurate to 45 grams.
Five times the sum of a number and three is the same as three times the difference of twice the number and 1.Find the number.
Answers
ANSWER
18
EXPLANATION
Let the number be x.
Fives times the sum of the number and three means:
5 * (x + 3)
=> 5(x + 3)
Three times the difference of twice the number and one means:
3 * [(2 * x) - 1]
=> 3(2x - 1)
Those two expressions are equal.
That is:
5(x + 3) = 3(2x - 1)
Expand the bracket:
=> 5x + 15 = 6x - 3
Collect like terms:
6x - 5x = 15 + 3
x = 18
The number is 18.
What angle (in racians) between 0 and 2(pi) has the same cosine as [tex] \binom{6\pi}{11} [/tex]
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180 degrees is equivalent to pi radians
[tex]\begin{gathered} \text{ }\pi\text{ = 180} \\ \\ \frac{6\text{ }\pi\text{ }}{11}\text{ = p} \end{gathered}[/tex]p = (6 x 180) / 11
[tex]98.18^0[/tex]Select the correct answer from each drop-down menu.What is the distance and midpoint between points D and E on the number line?
Answers
SOLUTION:
The points D and E are located at;
D is located -1.8
E is located at 2.4
Therefore, the distance from D to E is;
[tex]\begin{gathered} x_2-x_1=2.4-(-1.8)=2.4+1.8 \\ =4.2 \end{gathered}[/tex]The midpoint is given by;
[tex]\begin{gathered} \frac{x_2+x_1}{2} \\ =\frac{2.4+(-1.8)}{2} \\ =0.3 \end{gathered}[/tex]The point (7,-2) is a point on the graph of y=f(x) what point must lie on: A) y=2f(x-4) B) y=-f(x)-4 C) y=f(-x) D) write the function that would shift (7,-2) right 3 then up 4
Answers
Answer:
a) The point that must lie on the functions;
[tex](11,-4)[/tex]b) The point that must lie on the functions;
[tex](7,-2)[/tex]Explanation:
Given that the point (7,-2) is a point on the graph of y=f(x).
We want to find the point that must lie on the functions;
a)
[tex]y=2f(x-4)[/tex][tex]\begin{gathered} \frac{y}{2}=f(x-4) \\ \frac{y}{2}=-2 \\ y=-4 \\ x-4=7 \\ x=7+4=11 \\ x=11 \\ (11,-4) \end{gathered}[/tex]The point that must lie on the functions;
[tex](11,-4)[/tex]b)
[tex]y=-f(x)-4[/tex][tex]\begin{gathered} y+4=-f(x) \\ -(y+4)=f(x) \\ x=7 \\ -(y+4)=-2 \\ y+4=2 \\ y=2-4 \\ y=-2 \\ (7,-2) \end{gathered}[/tex]The point that must lie on the functions;
[tex](7,-2)[/tex]What are the calculations for the formula below? Tan-1 (5/401)
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Using a calculator, we have
[tex]\arctg(\frac{5}{401})=0.71437419575...^o[/tex]which of the following is not an ordered pair form the function f(x) = 5x - 6?
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the function is.
[tex]f(x)=5x-6[/tex]So to solve it we need to replace the order pair and see if the equation have sence so:
For (3,9)
[tex]\begin{gathered} 9=5\cdot3-6 \\ 9=15-6 \\ 9=9 \end{gathered}[/tex]So A is correct
For (1,-1)
[tex]undefined[/tex]Use the graph of the parabola to fill in the table .
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(a) We see that the parabola opens upward.
(b) The axis of symmetry is the axis that divides the parabola into two equal parts. We see that the axis of symmetry is a vertical line with x = 1.
(c) The vertex of a parabola is a point at which the parabola makes its sharpest turn. We see that the vertex of the parabola is the point (1, -4).
(d) The intercepts of a curve are the points where the curve intercepts the coordinate axis. We see that the intercepts of the parabola are:
• x-intercept (when y = 0): ,(-1, 0), (3, 0).
,• y-intercept (when x = 0): ,(0, -3).
Answers
(a) upward
(b) x = 1
(c) (1, -4)
(d)
• x-intercept: (-1, 0), (3, 0)
,• y-intercept: (0, -3)
Cost of Steak: Justin is purchasing two top sirloin steaks. The meat costs $4.00 per pound, and each steak weighs 6 lb 4 oz. What is the cost of the steak?The steak costs $.
Answers
Note thae 1 pound = 16 ounces
4 oz x 1/16 = 0.25 lb
The total weight of steak now is 6 lb + 0.25 lb = 6.25 lb
Multiply this weight by the cost per pound :
6.25 lb x $4 = $25
The answer is $25
If $2000 is invested at 8% compounded continuously, what is the amount after 2 years?
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Given:
P=$2000
r=8% = 0.08
t=2 years
Then, if the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:
[tex]A=P\cdot e^{rt}[/tex]Therefore:
[tex]A=2000\cdot e^{(0.08)(2)}=2000\cdot e^{0.16}=2347.02[/tex]Answer: $2347.02