Multiply the number of possible outcomes of pulling a marble out times the number of possible outcomes o rolling the die to find the total amount of outcomes in the sample space.
There are 4 different possibilities of pulling a marble out of a box: white, green, blue and orange. Since the die has 12 outcomes, then the total amount of outcomes in the sample space is:
[tex]4\times12=48[/tex]A bag contains the following marbles: 12 black marbles, 8 blue marbles, 16 brown marbles and 14 green marbles. what is the ratio of black marbles to blue marbles.
Let:
Nbk = Number of black marbles = 12
Nb = Number of blue marbles = 8
The ratio of black marbles to blue marbles will be given by:
[tex]Nbk\colon Nb=12\colon8=\frac{12}{8}=\frac{3}{2}[/tex]cit Formula = 18 + 7(58 - 1) 58 CRIBE EN ORACIONES COMPLETAS
a. As you can see, the sequence starts at -3, and increases by 7 each time, Amanda is wrong because she found the following formula:
an = 18 + 7(n - 1)
For n =1 the result should be -3:
n = 1
a1 = 18 + 7(1 - 1) = 18 + 7(0) = 18 + 0 = 18, she miscalculated the first term, and the whole sequence in general.
b. A possible sequence identification could be:
an = 7n - 10
Let's verify it:
n=1
a1 = 7(1) - 10 = 7 - 10 = -3
n=2
a2 = 7(2) - 10 = 14 - 10 = 4
n=3
a3 = 7(3) - 10 = 21 - 10 = 11
and so on...
Now for n=58
a58 = 7(58) - 10 = 396
-------------------------------------------------------------------------
32 = 2 + 3(n - 1)
Solving for n:
Use distributive property on the right hand side:
32 = 2 + 3n - 3
32 = 3n - 1
Add 1 to both sides:
32 +1 = 3n - 1 + 1
33 = 3n
Divide both sides by 3:
33/3 = 3n/3
11 = n
n = 11
What is the the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds?
SOLUTION:
Step 1:
In this question, we are asked to find the musical instrument that is a pair of clash cymbals, originating in the Indian subcontinent, which makes high- pitched percussion sounds.
Step 2:
The details of the solution are as follows:
The Taal is a pair of clash cymbals, originating in the Indian subcontinent, which makes high-pitched percussion sounds. In its simplest form, it consists of a pair of small hand cymbals.
usi
the dealer in a card game draws three cards from a deck of 52 cards and places them face-up on the table select all the correct probabilities
Explanation:
nCx give us the number of ways in which we can select x cards from a group of n cards.
So, the number of ways in which we can select 3 cards from 52 is:
52C3.
On the other hand, the number of ways to select 3 cards but none of them are kings is 48C3 because there are 48 cards that aren't kings. So:
[tex]P(no\text{ Kings)=}\frac{_{48}C_3}{_{52}C_3}[/tex]The number of ways to draw 2 fives is: 4C2*48C1
Because the dealer needs to draw 2 cards from the 4 that are fives and 1 card from the other 48 cards. So, P(2 fives) is:
[tex]P(\text{ 2 fives)=}\frac{_4C_2\times_{48}C_1}{_{52}C_3}[/tex]The number of ways to draw 1 heart and 2 spades is: 13C1*13C2
Because there are 13 heart cards and 13 spades cards. So, P(1 heart and 2 spades) is:
[tex]P(1\text{ Heart and 2 spades) = }\frac{_{13}C_1\times_{13}C_2_{}}{_{52}C_3}[/tex]Finally, the number of ways to select 4 aces and 1 ten is
1 Write the missing power of ten.0.04 x 10 = 0.4
Notice that in the number 0.4, the decimal point appears shifted one place to the right with respect to the number 0.04. When we multiply a number by the power 10^n, the decimal point is shifted n places to the right. Therefore, the power of 10 needed to move the decimal point from 0.04 one place to the right to get 0.4 is 1.
Therefore, the missing power of the base 10 is:
[tex]1[/tex]So, we can write:
[tex]0.04\times10^1=0.4[/tex]What is 2902 divided by 3
Answer:
967.333333
Step-by-step explanation:
If you need to round it, it's 967.33
As a fraction, it's 2902/3 or 967 1/3
calculate the surface area of a tetrahedron with four faces and a base of 1 square foot and a height of 0.866 foot
The surface area is given by:
[tex]SA=B+\frac{1}{2}ph[/tex]Where:
B = Area of the base
h = height
p = Perimeter of the base
so:
[tex]\begin{gathered} SA=1+\frac{1}{2}(4)(0.866) \\ SA=2.732ft^2 \end{gathered}[/tex]Find the area of the region enclosed by y = 7x and y = 8x^2.
Solution
Hence the area under the region is
[tex]A=\int_0^{0.875}7x-8x^2=\frac{343}{384}unit^2[/tex]What are the solution(s) to the quadratic equation 9x² = 4?O x = and x = -- 90x = ² and x = -1/33O= and x = --X=no real solutionM/NK
Given:
The quadratic equation is:
9x² = 4
Required:
Find the solutions to the given equation.
Explanation:
The given equation is:
[tex]9x²=4[/tex]Divide both sides by 4.
[tex]x^2=\frac{4}{9}[/tex]Take the square root on both sides.
[tex]\begin{gathered} x=\pm\sqrt{\frac{4}{9}} \\ x=\pm\frac{3}{2} \end{gathered}[/tex]the solutions to the equation are
[tex]x=\frac{3}{2}\text{ and x =-}\frac{3}{2}[/tex]Final Answer:
Option third is the correct answer.
Write a recursive definition for the following function. 40, 120,360,1080,3240
The recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
What is geometric series?
Geometric series are those series in which ratio between the consecutive terms of the series are same.
Here the series is in geometric progression with a common ratio of 3
and first term 40
So the recursive definition of the given geometric series is [tex]40 \times (3)^n[/tex]
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I need help with my math
identify the beginning of a sample period for the function
Given:
[tex]f(t)\text{ = 2csc\lparen t + }\frac{\pi}{4})-1\text{ }[/tex]The graph of f(t) is shown below:
From the graph, we can see that
[tex]x=\text{ }\frac{\pi}{4}\text{ is a good start for the period of f\lparen t\rparen}[/tex]Answer: Option D
Hey can you help me with my homework also can you tell me the points so I can put them into the graphs
Step 1
Find the equation of f(x)
[tex]\begin{gathered} The\text{ absolute value function is;} \\ y=a|x-h|+k \end{gathered}[/tex][tex]From\text{ the graph the vertex \lparen h,k\rparen is 3,3}[/tex][tex]\begin{gathered} h=3,k=3 \\ y=1,x=5 \end{gathered}[/tex][tex]1=a|5-3|+3[/tex][tex]\begin{gathered} 1=2a+3 \\ 2a=1-3 \\ 2a=-2 \\ \frac{2a}{2}=-\frac{2}{2} \\ a=-1 \end{gathered}[/tex]Thus f(x) will be;
[tex]y=-1|x-3|+3[/tex]Step 2
Find the equation of y= -f(x) then plot the graph
[tex]\begin{gathered} y=-(-1|x-3|+3) \\ y=1\left|x-3\right|-3 \end{gathered}[/tex]Thus the graph using the points below will look like;
[tex](-4,4),(0,0),(3,-3),(6,0),(8,2)[/tex]. Kelly makes $475 per week as an assistant I the human resource department of a law firm. What is her annual salary?
Week salary = $475
In a year there are 52 weeks
Use a rule of three to find the answer
1 week --------------------$475
52 weeks ----------------- x
x = (52 x 475) / 1
x = $24700
Her annual salary is $24700
Given vector v equals open angled bracket negative 11 comma negative 5 close angled bracket comma what are the magnitude and direction of v? Round the magnitude to the thousandths place and the direction to the nearest degree.
We will begin by finding the magnitude of a vector, denoted |v|.
The formula we can use is
[tex]|v|=\sqrt{a^2+b^2}[/tex]where a and b represent the vector components. Since we are given the vector <-11,-5>, we will let a be -11 and b is -5.
Substituting those values, we have
[tex]\begin{gathered} |<-11,-1>|=\sqrt{(-11)^2+(-5)^2} \\ \sqrt{121+25} \\ \sqrt{146} \\ \approx12.083 \end{gathered}[/tex]So far, your answer is either the first option or the second option.
Next, we want to find the direction of the vector. We can use another helpful formula:
[tex]\tan\theta=\frac{b}{a}[/tex]Substituting our original values for a and b, we have:
[tex]\tan\theta=\frac{-5}{-11}[/tex]Be careful here! Since the both the a-value and b-value are negative, we are going to be in the third quadrant. After finding our angle (which will be in quadrant 1), we will need to add 180 degrees.
Take the inverse tangent of both sides to get the angle:
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{-5}{-11}) \\ \theta\approx24^{\circ} \end{gathered}[/tex]We'll add 180 degrees to get our final angle:
[tex]24+180=204[/tex]Since our final angle is 204 degrees, the correct answer is the second option.
Answer:
12.083; 24°
explanation:
Magnitude of v = sqrt((-11)^2 + (-5)^2)
Direction of v = atan(-5 / -11)
Calculating these values:
Magnitude of v = sqrt(121 + 25) ≈ 12.083 (rounded to the thousandths place)
Direction of v = atan(-5 / -11) ≈ 0.435 radians
Converting radians to degrees:
The direction of v ≈ 0.435 * (180 / π) ≈ 24.881° ≈ 24° (rounded to the nearest degree)
Therefore, the correct answer is 12.083; 24°.
what would the length of segment BC have to be in order for line BC to be tangent to circle
Given data:
The first given length is AC=53.
The second given length is AB= 45.
The expression for the Pythagoras theorem is,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ (45)^2+BC^2=(53)^2 \\ BC^2=784 \\ BC=28 \end{gathered}[/tex]Here, consider only positive sign of BC length as side cannot negative.
Thus, the BC length is 28.
Determine algebraically if f(x)=x^2-8 is a function even, odd, or neither.
For a function to be even, it has to meet the following condition:
[tex]f(x)=f(-x)[/tex]To check if the given is an even function, evaluate the function at x and -x:
[tex]\begin{gathered} f(x)=x^2-8 \\ f(-x)=(-x)^2-8=x^2-8 \\ f(x)=f(-x) \end{gathered}[/tex]It means that the function is even.
For a function to be odd, it has to meet this condition:
[tex]f(-x)=-f(x)[/tex]We already know the values of f(-x) and f(x) and from this we can state that the function is not odd.
If _____________, then the graph of the polynomial function is symmetric about the origin.f(x) = -f(-x)f(x) = -f(x)f(x) = f(-x)f(x) = f(x + 1)
ANSWER:
1st option: f(x) = -f(-x)
STEP-BY-STEP EXPLANATION:
The polynomial function is symmetric about the origin in the odds functions, where the following is true:
[tex]\begin{gathered} f(-x)=-f(x) \\ \\ \text{ Therefore:} \\ \\ f(x)=-f(-x) \end{gathered}[/tex]Then it would be:
If f(x) = -f(-x), then the graph of the polynomial function is symmetric about the origin.
The correct answer is the 1st option: f(x) = -f(-x)
Introduction to Chord LengthsINPlace the following expressions so that they can be used to solve for X11 781211 7.8 1211 INN111712
SOLUTION
We know that the diameter of the circle is 18.8.
Therefore the value of its radius will be.
[tex]\frac{18.8}{2}[/tex]And we also know that the radius from the diagram is:
[tex]x+4.2[/tex]So we can equate both equations together to have an idea of what will give us the value of x.
[tex]\begin{gathered} \frac{18.8}{2}=x+4.2 \\ \text{Collect like terms} \\ \frac{18.8}{2}-4.2=x \end{gathered}[/tex]So going by the above solutions, the answers we will drag into the two boxes will be the 4th expression and the 6th expression
THAT IS:
[tex]\begin{gathered} \frac{18.8}{2} \\ \text{and} \\ -4.2 \end{gathered}[/tex]Carmelo puts $2,200.00 into savings bonds that pay a simple interest rate of 3.4%. How much money will the bonds be worth at the end of 5.5 years? (Find the total worth of the bonds in 5.5 years)
Let's begin by listing out the information given to us:
Principal (P) = $2,200, Interest rate (r) = 3.4% = 0.034, Time (t) = 5.5 years
[tex]\begin{gathered} I=P\cdot r\cdot t=2200\cdot0.034\cdot5.5 \\ I=\text{ \$414.40} \end{gathered}[/tex]The bond will be worth the sum of the Principal and the Interest:
[tex]\begin{gathered} P+I=2200+411.40 \\ \Rightarrow\text{ \$}2611.40 \end{gathered}[/tex]give some examples in mathematics for a 4th grader.
• Equivalent Fractions
Two or more fractions are called equivalent fractions if they keep the same proportion. For example:
[tex]\begin{gathered} \frac{1}{2}=\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{5}{10} \\ \frac{3}{9}=\frac{6}{18}=\frac{9}{27}=\frac{12}{36} \end{gathered}[/tex]Notice that we multiplied the numerator and the denominator by the same number to produce those equivalent fractions. We did by two on the first line, and by 3 on the 2nd line.
These fractions are equivalent since we can simplify all of them and reduce them to 1/2. Dividing both numerator and denominator by the same number.
• Mixed Fractions and Improper fractions
Whenever we divide the numerator by the denominator and it is greater than or equal to 1. We can use Mixed Numbers.
For example:
[tex]\begin{gathered} \frac{9}{8}\longrightarrow\text{ 9}\colon8=1.125 \\ \frac{9}{8}=\text{ 1 +}\frac{1}{8}=1\text{ }\frac{1}{8} \\ \frac{12}{10}=1.2\text{ = 1 + }\frac{1}{5}\text{ =1}\frac{1}{5} \end{gathered}[/tex]We use mixed numbers for recipes (in daily life), and to better understand fractions.
When we need to operate them we must turn those Mixed Numbers into improper fractions (fractions whose denominator is lesser than its denominator (bottom number).
solve for 18 degreex 29
The given triangle is a right angle triangle. Considering angle 18 as the reference angle,
x = hypotenuse
29 = adjacent side
We would find the hypotenuse, x by applying the cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Thus, we have
Cos18 = 29/x
29 = xCos18
x = 29/Cos18 = 29/0.95
x = 30.53
Find the perimeter of each circle. Use 3 for pi.
Part 1
We need to find the perimeter of a circle with a diameter of 18 inches.
The relation between the perimeter P and the diameter d is given by:
[tex]P=\pi d[/tex]Since d = 18 inches and we need to use 3 for π, we obtain:
[tex]P=3\cdot18\text{ inches }=54\text{ inches}[/tex]Therefore, the ribbon needs to be 54 inches long.
Part 2
We need to find the perimeter of a semicircle with a radius of 8 in.
The perimeter of this semicircle is the sum of half the perimeter of the whole circle and the line segment formed by two radii.
The relation between the perimeter P and the radius r of a circle is:
[tex]P=2\pi r[/tex]Thus, half the perimeter is:
[tex]\frac{P}{2}=\pi r[/tex]Since we need to use 3 for π and r = 8 in, we obtain:
[tex]\frac{P}{2}=3\cdot8\text{ in }=24\text{ in}[/tex]And the line segment measures:
[tex]2\cdot8\text{ in }=16\text{ in}[/tex]Therefore, the perimeter of the calzone is:
[tex]24\text{ in }+16\text{ in }=40\text{ in}[/tex]Answer: 40 in.
1. The diagram below, not drawn to scale, shows a flexible piece of paper in the shape of a sector of a circle with centre 0 and radius 15 cm. 22 Use . B А 126 0 15 cm C (a) Show that the perimeter of the paper is 63 cm. [3] (b) Calculate the area of the paper OABC. 121 (c) The paper is bent and the edges OA and OC are taped together so that the paper forms the curved surface of a cone with a circular base, ABC. (1) Draw a diagram of the cone formed, showing clearly the measurement 15 cm, the perpendicular height, h, and the radius, r, of the base of the cone. [1] (ii) Calculate the radius of the circular base of the cone. 121 (iii) Using Pythagoras' Theorem, or otherwise, determine the perpendicular height of the resulting cone. 121
Given
Circle of radius 15 cm and angle at the centre equal to 126 degree.
Find
(a) Perimeter of the paper is 63cm.
(b) Area of the paper OABC
(c) i) Draw a cone
ii) radius of circular base
iii) determine the height
Explanation
(a)
Perimeter of sector = Arc length ABC + AO + OC
Arc Length of ABC =
[tex]\begin{gathered} \frac{\theta}{360}\times2\Pi r \\ \frac{126}{360}\times2\times\frac{22}{7}\times15 \\ 33 \end{gathered}[/tex]so , perimeter = 33 +15 +15 = 63
Hence we proved that perimeter is 63 cm
(b) Area of sector =
[tex]\begin{gathered} \frac{\theta}{360}\times\Pi r^2 \\ \frac{126}{360}\times\frac{22}{7}\times15\times15 \\ 247.5 \end{gathered}[/tex](c) i)
ii) Circumference of base =
[tex]\begin{gathered} 2\Pi r=\text{33} \\ r=\frac{33\times7}{2\times22} \\ r=\frac{21}{4} \end{gathered}[/tex]iii) l = 15 cm, r= 21/7
By pythagoras theorem,
[tex]\begin{gathered} h^2=l^2-r^2 \\ h^2=15^2-(\frac{21}{4})^2 \\ h=\text{ 14.05} \end{gathered}[/tex]Final Answer
(a) 63
(b) 247.5
how many FULL cases of oil can you get from a 150-gallon oil tank?
Given
The job is to fill the quart size of bottles, from a full 150 gallon oil tank.
And, the oil is packed into 24 quart's of oil.
To find the number of full cases of oil.
Explanation:
It is given that,
The total amount of oil is 150 gallon.
The number of cases it has to be filled is, 24.
Then, the number of the full cases of oil is,
[tex]\begin{gathered} Number\text{ of full cases of oil}=\frac{150}{24} \\ =\frac{50}{8} \\ =\frac{25}{4} \\ =\frac{24}{4}+\frac{1}{4} \\ =6+\frac{1}{4} \\ =6\frac{1}{4} \end{gathered}[/tex]Hence, the number of full cases of oil is 6.
Find the slope of the line that goes through the points (14,-13) and (2,3).
Answer
The slope of the line is -4/3
Step-by-step explanation:
Given the following coordinates point
(14, -13) and (2, 3)
Slope = rise / run
rise = y2 - y1
run = x2 - x1
Slope = y2 - y1 / x2 - x1
Let; x1 = 14, y1 = -13, x2 = 2, and y2 = 3
Slope = 3 - (-13) / 2 - 14
Slope = 3 + 13 / - 12
Slope = 16 / -12
Slope = -4/3
Hence, the slope of the line is -4/3
The glass portion of a small window is 12 inches by 24 inches. The framework on each side adds on x inches. Express the area of the entire window as a function of x. 72 + x square inches 36+x square inches x² + 36x + 288 square inches 288 + x² square inches
The area of the entire window expressed as a function of x is x²+36x+288 square inches
How to express the area of the window as a function of x?
Given that: The glass portion of a small window is 12 inches by 24 inches
The framework on each side adds on x inches
That means (x+12) by (x+24) inches. This is the representation of the area of the entire window as a function of x. Thus:
(x+12)(x+24) = x(x+24) + 12(x+24) (Clear the brackets)
= x²+24x+12x+288 (Add like terms)
= x²+36x+288 in²
Therefore, the area of the entire window as a function of x is x²+36x+288 square inches
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A straight line passes through points (1, 15) and(5, 3) What isthe equation of the line?Select one:A) y = - 3x + 18B) y = – 7x + 18C) y = 2x + 18D) y = 3x + 18
Points (1,15) and (5,3)
Find the slope (m)
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where:
(x1,y1) = (1,15)
(x2,y2) = (5,3)
Replacing:
[tex]m=\frac{3-15}{5-1}=\frac{-12}{4}=-3[/tex]the function has a slope m= -3
slope intercept form:
y=mx+b
Where
m= slope
so, the correct function is
y=-3x+18 (A)
A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million
Answer:
1/14
Explanation:
The number of ways or combinations in which we can select x objects from a group of n can be calculated as:
[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]So, if we are going to select 3 pens from the drawer that contains 8 pens, the number of possibilities is:
[tex]8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56[/tex]Then, if we didn't end up with a pen that works is because we select the three pens from the 4 that didn't work. In this case, the number of possibilities is:
[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4[/tex]Therefore, the probability required is equal to the ratio of these quantities:
[tex]P=\frac{4}{56}=\frac{1}{14}[/tex]So, the answer is 1/14
3(x + 10) < 2 (20 – x)
3(x + 10) < 2 (20 – x)
Distributing multiplication over the addition and the subtraction, we get:
3x + 3*10 < 2*20 - 2x
3x + 30 < 40 - 2x
30 is adding on the left, then it will subtract on the right.
2x is subtracting on the right, then it will add on the left.
3x + 2x < 40 - 30
5x < 10
5 is multiplying x on the left, then it will divide on the right.
x < 10/5
x < 2