To get the probability of an event to occur, we have the following formula:
[tex]P=\frac{no.\text{ of favorable outcomes}}{\text{total no. of possible outcomes}}[/tex]According to the problem, the sample space is (1, 6, 9, 11, 12, 14, 17, 18, 19, 20) therefore, the total no. of possible outcomes is 10.
For Set B, the sample is (9, 12, 14, 17, 18), therefore, there are 5 possible outcomes that belong to set B.
Starting with the first question, what is the probability of Set B to occur?
[tex]P=\frac{no.\text{ of outcomes from B}}{\text{total no. of possible outcomes}}=\frac{5}{10}=\frac{1}{2}=0.50=50\text{ percent}[/tex]For Set C, the sample is (6,9,11, 12, 18, 19) therefore, there are 5 possible outcomes that belong to set C as well.
On the next question, what is the probability of Set C to occur?
[tex]P=\frac{no.\text{ of outcomes from C}}{\text{total no. of possible outcomes}}=\frac{5}{10}=\frac{1}{2}=0.50=50\text{ percent}[/tex]For the third question, what is the probability of Set B or C to occur?
Since the outcomes under B or C are (6, 9, 11, 12, 14, 17, 18, 19), the probability of the union of B and C is:
[tex]P=\frac{no.\text{ of outcomes from B or C}}{\text{total no. of possible outcomes}}=\frac{8}{10}=\frac{4}{5}=0.80=80\text{ percent}[/tex]On to the last question, what is the probability of the intersection of B and C to occur?
Since the outcomes that are found on both B and C are (9,12,18), the probability of the intersection of B and C is:
[tex]P=\frac{no.\text{ of outcomes found on both B and C}}{\text{total no. of possible outcomes}}=\frac{3}{10}=0.30=30\text{ percent}[/tex]what is the value of the expression when m=2 and n=-3. (4m^-3n^2)^2
Giving the funtion
[tex](4m^{-3}n^2)^2[/tex]m=2
n=-3
[tex](4(2)^{-3}(-3)^2)^2[/tex][tex](\frac{4}{2^3}(9))^2[/tex][tex](\frac{36}{2^3})^2[/tex][tex](\frac{36^2}{2^6})[/tex][tex](\frac{2^49^2}{2^2*2^4})=\frac{9^2}{2^2}[/tex][tex]\frac{81}{4}[/tex]then the evaluated function in m=2 n=-3
has a value of 81/4
write the equation for this line in slope intercept form.y= ? × + __ a) -4 b) 2c) -2 d) -1/2
we know that
the equation in slope intercept form is equal to
y=mx+b
In this problem
we have
b=-4 ------> because the y-intercept is (0,-4)
Find the slope
we need two points
we take
(-2,0) and (0,-4)
so
m=(-4-0)/(0+2)
m=-4/2
m=-2
therefore
y=-2x-4-What is the product of (a - 1) and (2a + 2)?A 2(a2 - 2)B 2(a2 - 1)C a2 + 4a - 2D2a2 - 4a - 2-
The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B
$480 invested at 15% compounded quarterly after a period of six years
Answer: $1161
Step-by-step explanation: The equation for compound interest is A=P(1+r/n)^n*t. P is the principal, in this case, being $480 originally invested, r is the rate, in this case being 15% or 0.15, and n is 4 because it is compounded quarterly. t is 6 because the period invested is 6 years. A=480(1+0.15/4)^4*6. This can simplify to 480(1.0375)^24, which equals approximately $1161 dollars. If the question requires to the tenths, it is $1161.3, and for the hundredths, $1161.33.
How are these functions related? How are their graphs related
Notice that the difference between the two equations is the +5 on the right side of the second equation.
The graph of the following equations are as folllows:
For y=x:
For y=x+5:
Thus, the graph of y = x was shifted 5 units upward to obtain the graph of y=x+5.
Therefore, each value or output of y=x+5 is 5 more than the corresponding output of y=x. Consequently, the graph of y=x+5 is the graph of y=x translated up by 5 units.
Thus, the correct answer is option C.
The mean per capita income is 24,653 dollars per annum with the standard deviation of 778 dollars per annum. What is the probability that the sample mean would be less than $24,745 if a sample of 441 persons is randomly selected? Round your answer to four decimal places
Remember that
[tex]z=\frac{x-μ}{\frac{σ}{\sqrt{n}}}[/tex]where
μ=24,653
σ=778
n=441
X=24,745
substitute
[tex]\begin{gathered} z=\frac{24,745-24,653}{\frac{778}{\sqrt{441}}} \\ \\ z=2.4833 \end{gathered}[/tex]using the values of the z-score table
we have that
P(x>2.4833) = 0.0065086
therefore
The answer is 0.0065i need help with math
Answer:
7
Step-by-step explanation:
opposite angles are the same
8z+18=74
8z=56
z=7
Answer:
7 is my final answer thank you
Step-by-step explanation:
set as brainliest
2 5/6 divided by 1 3/4
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
The quotient is 113/21.
What is a mixed number?It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.
2 5/6 = (2·6 +5)/6 = 17/6
1 3/4 = (1·4 +3)/4 = 7/4
Here 17/6 is dived by 7/4,we get
(17/6) ÷ (7/4) = (17/6) × (4/7) = (17×4)/(6×7) = (17×2)/(3×7) = 34/21
Here 34/21 is converted into a mixed number.
34/21 = (21 +13)/21 = 1 13/21
Therefore, the quotient is 113/21
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Select the correct anawer Which of the following represents a function?
A function relates input to output. Functions can be one to one or many to one. The x values represent the input while the y values represent the output. In the case of one to one, it means that the output has only one corresponding input. Many to one means that there are many input values for one output value. An input value cannot have more than 1 output value. If this happens, then it is not a function. Looking at the options given,
Option A is a function since no input value has more than one output value
Option B is not a function since the output values of 7 and 1 has the same input value of - 1
For option C, the values are (- 3, - 2)' (- 1, 1), (- 1, - 5), (1, 4). It is not a function since the output values of 1 and - 5 has the same input value of - 1
Option D is not a function since the output values of 7 and 1 has the same input value of - 1
The correct option is A
Choose the median for the set of data. 99 95 93 92 97 95 97 97 93 97 a. 7b. 95.5 c. 96d. 97
The median is the middle of a sorted list of number. So, we need to place the number in value order, that is,
[tex]92,93,93,95,95,97,97,97,97,99[/tex]then, the middle is between the 5th and 6th number:
then, we need to find the mean value of these numbers. So, the median is
[tex]\text{ median=}\frac{95+97}{2}=96[/tex]Therefore, the answer is option C.
Evaluate ( (dx-4) dx 16 S (WX - 4) dx = ( (Type an exact answer in simplified form) 9
Which inequality represents all values of x for which the quotient below is defined? (Division)
We want to calculate the following quotient
[tex]\frac{\sqrt[]{28(x-1)}}{\sqrt[]{8x^2}}[/tex]Note that using properties of radicals, given non zero numbers a,b we have that
[tex]\frac{\sqrt[]{a}}{\sqrt[]{b}}=\sqrt[]{\frac{a}{b}}[/tex]So, using this fact, our quotient becomes
[tex]\sqrt[]{\frac{28(x-1)}{8x^2}}[/tex]As we are taking the square root, this opearation is only valid if and only if the expression inside the square root is a non negative number. That is, we must have that
[tex]\frac{28(x-1)}{8x^2}\ge0[/tex]As this is a quotient, we should also that the quotient is defined.
To understand this last point, we should make sure that we are not dividing by 0. So first, we want to exclude those value s of 0 for which the denominator becomes 0. So we have the following auxiliary equation
[tex]8x^2=0[/tex]which implies that x=0.
So, the second quotient is always defined whenever x is different from 0. However, assuming that x is not 0 we want to find the value of x for which
[tex]\frac{28(x-1)}{8x^2}\ge0[/tex]To start with this problem, we solve first the equality. So we have
[tex]\frac{28(x-1)}{8x^2}=0[/tex]since x is not 0, we can multiply both sides by 8x², so we get
[tex]28(x-1)=0\cdot8x^2=0[/tex]If we divide both sides by 28, we have that
[tex]x-1=\frac{0}{28}=0[/tex]now, by adding 1 on both sides we get that
[tex]x=1[/tex]so, whenever x=1, we have that the quotient inside the radical becomes 0.
Now, we will solve the inequality, that is
[tex]\frac{28(x-1)}{8x^2}>0[/tex]Note that on the left, we are mostly dividing two expressions. Recall that the quotient of two expressions is positive if and only if both expressions have the same sign.
Note that the expression
[tex]8x^2[/tex]is the product of number 8 (which is positive) with the expression x², which is also always positive for any value of x. This means that the expression 8x² is always positive.
So, taking this into account, we should focus on those values of x for which the numerator is positive, as the denominator is always positive. So we end up with the following inequality
[tex]28(x-1)>0[/tex]If we divide both sides by 28 we get
[tex]x-1>\frac{0}{28}=0[/tex]So, if we add 1 on both sides, we get
[tex]x>1[/tex]So, whenever x is greater than 1, the expression inside the radical is positive.
This means that the original quotient is defined whenever x=1 and whenever x>1. Thus, we would have
[tex]x\ge1[/tex]Find the slope and the y-intercept of the line. 4x + 2y= -6 Write your answers in simplest form. Undefined 08 slope: . X ? y -intercept: 0
Transform equation form Ax + By = C
to y = ax + b
THen
4x + 2y = -6
A= 4. B= 2. C= -6
y = (-A/B)•x +(D/B)
y= (-4/2)•x + (-6/2)
y = -2x -3
Therefore in new equation
Slope a = -2
Y intercept b = -3
Can someone please help me with this math, thank you
Given data:
The given growth rate is r=7.8%=0.078.
The final number of bacteias in terms of initial is P'=2P.
The expression for the bacterias growth rate is,
[tex]P^{\prime}=P(1+r)^t[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 2P=P(1+0.078)^t \\ 2=(1.078)^t \\ \ln (2)=t\ln (1.078) \\ t=\frac{\ln(2)}{\ln(1.078)} \\ =9.23\text{ hours} \end{gathered}[/tex]Thus, after 9.23 hours population of the bacterias doubled.
h(x) = 10x - x^2 find h(4)
We have the following expression
[tex]h(x)=10x-x^2[/tex]In our case x is equal to 4, then, we will evalute the given function h(x) when x is 4. It yields,
[tex]h(4)=10(4)-(4)^2[/tex]which gives
[tex]\begin{gathered} h(4)=40-16 \\ h(4)=24 \end{gathered}[/tex]Therefore, the asnswer is h(4)=24
Points S and T are midpoints of the sides of triangle FGH.Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.What is GF?
The measure of length of GF is 16 cm.
Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:
[tex]\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}[/tex]
We are given the following;
FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]
GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]
ST = 8 cm
Substitute the given values, we will get the following;
[tex]\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2[/tex]
GF = 2 * 8 = 16 cm
Thus, the measure of the length of GF is 16 cm.
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Which expression is equivalent to 6x + 7- 12.2 - (32 + 2) - x?(A)7x - 28B7x - 21©5x - 28D5x - 21please hurry
A school librarian would like to buy subscriptions to 7 new magazines. Her budget however, will allow her to buy only 4 new subscriptions. How many different groups of 4 magazines can she chose from the 7 magazines?
The number of groups of 4 magazines can she choose from the 7 magazines is 35
Total number of magazines that school librarian would like to buy subscription = 7 magazines
The number of subscription that she can afford = 4 new subscription
The different groups of 4 magazines can she choose from the 7 magazines = [tex]7C_4[/tex]
The combination is the method of selecting a particular items or objects from the group of collection. The combination can also be defined as the number of possible arrangement from the collection.
Then the value of
[tex]7C_4[/tex] = 7! / 4!(7 - 4)!
= 7! / (4! × 3!)
= (7 × 6 × 5 × 4!) / (4! × 3!)
= (7 × 6 × 5) / 3!
= (7 × 6 × 5) / 3 × 2 × 1
= 210 / 6
= 35
Hence, the number of groups of 4 magazines can she choose from the 7 magazines is 35
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Cuanto es 123 x 200?
Answer:
[tex]123\times200=24600[/tex]Explanation:
We want to find the product of 123 and 200;
Therefore, the product of 123 and 200 is;
El producto de 123 y 200 es;
[tex]123\times200=24600[/tex]lines m and n are paralle. Find the measures of angles x, y, and z in the figure
Explanation
From the image, angle x and 65 degrees form angles on a straight line. We will recall that the sum of angles on a straight line sums up to 180 degrees.
Therefore,
[tex]\begin{gathered} x+65^0=180^0 \\ x=180^0-65^0 \\ x=115^0 \end{gathered}[/tex]Angle y and 65 degrees form alternate angles, we will recall that alternate angles are equal
Therefore,
[tex]y=65^0[/tex]Angle x and angle z form corresponding angles, we will recall that corresponding angles are equal.
Therefore,
[tex]z=115^0[/tex]Answer:
[tex]x=115^0,y=65^0,z=115^0[/tex]Describe the shape of the graph of the cubic function by determining the end behavior and number of turning points. y=2x^3-x-1 What is the end behavior of the graph of the function?
Solution
What is the end behavior of the graph of the function?
[tex]y=2x^3-x-1[/tex]The end behaviors of the function describe the functions of x as it approaches +∝ and as x approaches -∝
Therefore the correct answer is
Option D
Final answer = Down and Up
Turning points = 2
Convert from Point-Slope Form into Slope-Intercept Form. Show your work!1. y + 1 = 7(x + 2) 2. y – 1 = –2(x – 1) 3. y – 2 = 1/4(x – 1) 4. y – 4 = 3(x – 3)
1. y+10=7(x+2) (applying the distributive law to the right side of the equation)
y= 7x+14-10 (substracting 10 in both sides of the equality)
y=7x+4
2. y-1=-2(x-1) (applying the distributive law to the right side of the equation)
y-1=-2x+2 (adding 1 in both sides of the equality)
y=-2x+2+1 (simplifying)
y=-2x+3
3. y-2=1/4(x-1) (applying the distributive law to the right side of the equation)
y-2=x/4 -1/4 (adding 2 in both sides of the equality)
y=1/4(x) -1/4+2 (simplifying)
y=1/4(x) +7/4
4. y-4=3(x-3) (applying the distributive law to the right side of the equation)
y-4=3x-9 (adding 4 in both sides of the equality)
y=3x-9+4 (simplifying)
y=3x-5
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29. How long will it take to double an investment at 3.7% compounded continuously? Round your answer to the nearest tenth of a year. years
The formula for compounding continuously is :
[tex]A=Pe^{rt}[/tex]where A is the future amount
P is the principal amount
e is a constant
r is the rate of interest
and
t is the time in years.
The question stated that the investment will be doubled, so the future amount will be twice the principal amount.
A = 2P
The rate of interest is 3.7%
e is a constant approximately equal to 2.71828..
Subsitute the values to the formula and solve the value of t :
[tex]\begin{gathered} A=Pe^{rt} \\ 2P=Pe^{0.037t} \\ 2=e^{0.037t} \end{gathered}[/tex]Take the natural logarithm of both sides,
note that ln e = 1
[tex]\begin{gathered} \ln 2=\ln e^{0.037t} \\ \ln 2=0.037t\ln e \\ \ln 2=0.037t(1) \\ t=\frac{\ln 2}{0.037}=18.73 \end{gathered}[/tex]The answer is 18.73 years
A group of 30 students rented small canoes and large canoes at a river park.
• The group
rented twice as many small canoes as large canoes.
• There were 3 students in each small canoe.
• There were 4 students in each large canoe.
Let x represent the number of small canoes and let y represent the number of large canoes
Create a set of equations that can be used to determine the number of each type of canoe the group rented.
Answer:
Im taking the test ill give the answers in 5 minutes
Step-by-step explanation:
Determine if the following equations are parallel, perpendicular, or neither. 7(x – 1) = 3y + 21 and 3.5x + 1.5y = 4.5
Given the two equations
7(x - 1) = 3y + 21
3.5x + 1.5y = 4.5
To determine if the lines are visible or perpendicular
Step 1: Expand the equations and make y the subject of the formula
7(x - 1) = 3y + 21
=> 7x - 7 = 3y + 21
=> 3y = 7x - 7 - 21
=> 3y = 7x -28
Divide both sides by 3
y = 7/3x - 28/3 ------equation 1
3.5x + 1.5y = 4.5
1.5y = -3.5x + 4.5
Divide both sides by 1.5
y = -3.5/1.5 x + 4.5/1.5
y = -7/3x + 3--------equation 2
Step 2: compare the two equations to the equation of a line, y = mx + c
For equation 1
m = 7/3
For equation 2
m= -7/3
The slopes are not the same
Also, the product of the gradients did not give -1
It can be seen that the lines are neither perpendicular nor parallel
Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(80°) – tan (20)1 + tan(80°)tan (20
Okay, here we have this:
Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:
[tex]\tan (A-B)=\frac{tan\mleft(A\mright)-tan\mleft(B\mright)}{1+tan\mleft(A\mright)tan\mleft(B\mright)}[/tex]We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:
[tex]\begin{gathered} \frac{tan\left(80°\right)-tan\left(20°\right)}{1+tan\left(80°\right)tan\left(20°\right)} \\ =\tan (80\degree-20\degree) \\ =\tan (60\degree) \end{gathered}[/tex]Finally we obtain that the original expression is equal to tan(60°).
Use the graph to find the slope and y-intercept of the line. Compare the values to the equation y= -3x+ 1
The y-intercept is at the point where the line cut the y-axis.
Hence, the y-intercept is 1
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-0}{-1-0} \\ m=\frac{3}{-1}=-3 \end{gathered}[/tex]
Hence, the slope is -3
Comparing the values to the equation y = =-3x +1, the equation is valid for the line.
A petrified stump that is 4 ft tall casts a shadow that is 2 ft long. Find the height of a tent that casts a 5 ft shadow
The petrified stump is 4 ft tall and cast a shadow that is 2 ft long .
2 ft shadow has a 4 ft height
5 ft shadow will have ? height
cross multiply
[tex]\begin{gathered} \text{height of tent = }\frac{5\times4}{2} \\ \text{height of tent = }\frac{20}{2} \\ \text{height of tent = 10 ft} \end{gathered}[/tex]810 А 30° E Given: Circle C. What is the value of angle x? B 99° 69° 132 30°
In this problem you can reflect the small triangle and you will see that the angle D is equal to the angle x, and the angle E is equal to the angle B so we can sum tyhe internal angles of the big triangle to find x so:
[tex]x+81+30=180[/tex]And we solve for x so:
[tex]\begin{gathered} x=180-81-30 \\ x=69 \end{gathered}[/tex]the angles x is equal to 69º
The volume of an iceberg that is below the water line is 2^5 cubic meters. the volume that is above the water line is 2^2 cubic meters. how many times greater is the volume below the water line than above it?
Let:
[tex]\begin{gathered} V_1\colon\text{ volume of iceberg below the water line} \\ V_2\colon\text{ volume of iceberg above the waterline} \end{gathered}[/tex]We want to finde some number k such that we can express the volume of the iceberg below the water line as the product of k and the volume of the iceberg above the waterline, this is:
[tex]V_1=k\cdot V_2[/tex]then, solving for k we have the following:
[tex]\begin{gathered} V_1=2^5m^3 \\ V_2=2^2m^3 \\ V_1=k\cdot V_2 \\ \Rightarrow k=\frac{V_1}{V_2}=\frac{2^5}{2^2}=2^{5-2}=2^3^{} \\ k=2^3 \end{gathered}[/tex]we have that k=2^3. This means that the volume of the iceberg above the water line is 2^3 times the volume of the iceberg below the water line