The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes.
We have only two black eights on the deck and two black kings on the deck, therefore, the amount of favourable outcomes is equal to their sum, which is 4. The total amount of possible outcomes are the amount of cards, 52. The probability of selecting a black eight or a black king is:
[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]The length of a rectangle is 1 inch shorter than twice the width (x).Which is the width (x) when the area (y) = 3321 square inches?
the width (x) of the rectangle = 41 inches
Explanation:
let the width = x
twice the width = 2x
The length of a rectangle is 1 inch shorter than twice the width (x) = 2x - 1
length = 2x -1
Area of rectangle = length × breadth
area (y) = 3321 square inches
y = x × 2x - 1 = x(2x - 1)
3321 = 2x² - x
2x² - x - 3321 = 0
We use factorisation to find x:
a = 2, b = -1, c = -3321
a × c = 2(-3321) = -6642
The factors which gives -1 when we sum together but gives -6642 when we multiply together are -82 and +81
2x² -82x + 81x - 3321 = 0
2x(x - 41) + 81(x - 41) = 0
(2x + 81) (x - 41) = 0
(2x + 81) = 0 or (x - 41) = 0
2x + 81 = 0
2x = -81
x = -81/2 inches
(x - 41) = 0
x - 41 = 0
x = 41 inches
Since we can't have a negative number as the width, the width (x) of the rectangle = 41 inches
wich of the following is the correct value of 0.22 0.4?
Answer:
The decimal place will be placed to the left by the total number of digits after the two numbers.
Explanation:
The multiplication we are asked to perform is
[tex]1.35\times4.2[/tex]which has a total of 3 digits after the decimal point.
Now we know that
[tex]135\times42=5670[/tex]therefore, to find 1.35 x 4.2 we just shift the decimal place in the above to the left by 3 units
therefore
[tex]1.35\times4.2=5.67[/tex]which is our answer!
Destiny needs a new coat for the winter and she found one at Old Navy for $48.88. The sale tax is 8%. How much will she pay for the sales tax? How much will she pay all together? SHOW ALL OF YOUR WORK.
Hello!
First, let's consider the value of $48.88 as 100%. Then, we have to find how many correspond to 8% of it. We can calculate it using the rule of three:
[tex]\begin{gathered} \frac{48.88}{x}=\frac{100}{8} \\ \\ \text{ multiplying across} \\ x\cdot100=8\cdot48.88 \\ 100x=391.04 \\ x=\frac{391.04}{100} \\ x\cong3.91 \end{gathered}[/tex]So, the sales tax is $3.91.
Now, we have to add the price of the coat with the sale tax:
$48.88 + $3.91 = $52.79
If she pays all together, the cost will be $52.79.
The circumference of a circle is 37.68 meters, what is the radius?
The formula for calculating the distance, d, in miles that one can see to the horizon on a clear day is approximated by d=1.22radical x, where x is the elevation in feet of a person's eyes. a. approximately how far, to the nearest mile, can a person whose eyes are 600 feet above sea-level see? b. approximately how high, to the nearest foot, would a person's eyes need to be to see 100 miles?
The expression to calculate the distance a person can see is below, where x is the height in feet of a person's eyes above see-level:
[tex]d=\sqrt[1.22]{x}\lbrack mi\rbrack[/tex]a) A person who is 600 feet height will see:
[tex]d=\sqrt[1.22]{600}=189.30mi[/tex]b) In order to get the height a person needs to be so that he/she could see 100 miles long, we solve the equation for x:
[tex]\begin{gathered} d=x^{\frac{1}{1.22}} \\ d^{1.22}=(x^{\frac{1}{1.22}})^{1.22}=x \\ x=100^{1.22}=275.42ft \end{gathered}[/tex]I’m the diagram below, C is the midpoint of AB. If AC is 4 centimeters, what is the length of CBA.4cmB.8cmC.6cmD.2cm
Consider that a mid-point is at equal distances from each end of the line segment.
Given that C is the mid point of AB, so point C must be at equal distance from ends A and B,
[tex]AC=CB[/tex]Given that AC measures 4 centimeters,
[tex]AC=4\text{ cm}[/tex]Substitute the value,
[tex]CB=4\text{ cm}[/tex]Therefore, option A is the correct choice.
A park walkway surrounds a fountain as shown. Find the area of the walkway. Round to the nearest foot.
The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.
From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.
The area of the rectangle is;
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=30\times42.5 \\ \text{Area}=1275ft^2 \\ \text{The area of the semicircle is,} \\ \text{Area=}\frac{1}{2}(\pi\times r^2) \\ \text{The diameter is 18 ft, and therefore the radius is 9 ft} \\ \text{Area}=\frac{1}{2}(3.14\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=\frac{1}{2}(254.34) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]Therefore, the area of the shaded region would be,
Area = 1275 - 127.17
Area = 1147.83
Next step is to calculate the other half of the figure (the right side), as follows;
Observe that the outer semi-circle is the shaded region while the inner one is the white portion.
The area is
[tex]\begin{gathered} \text{Shaded region;} \\ \text{Area}=\frac{1}{2}(\pi\times r^2) \\ \text{Area}=\frac{1}{2}(3.14\times15^2) \\ \text{Area}=\frac{1}{2}(3.14\times225) \\ \text{Area}=\frac{1}{2}(706.5) \\ \text{Area}=353.25ft^2 \\ \text{White region;} \\ \text{Area}=\frac{1}{2}(\pi\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]The area of the shaded region is;
Area = 353.25 - 127.17
Area = 226.38
Therefore the total area of the walkway surrounding the fountain is;
Area = 1147.83 + 226.38
Area = 1374.21
Area = 1,374 feet squared (rounded to the nearest foot)
Find the equation that results from completing the square into the following equation X squared -14 X +40 equals zero
Given:
The equation is
[tex]x^2-14x+40=0[/tex]Required:
Find the equation that results from completing the square into the given equation.
Explanation:
The given equation is:
[tex]x^{2}-14x+40=0[/tex]Subtract 40 on both sides.
[tex]\begin{gathered} x^2-14x+40-40=0-40 \\ x^2-14x=-40 \end{gathered}[/tex]Add 49 on both sides.
[tex]\begin{gathered} x^2-14x+49=-40+49 \\ x^2-14x+49=9 \end{gathered}[/tex]Use the following formula:
[tex]a^2-2ab+b^2=(a-b)^2[/tex][tex](x-7)^2=9[/tex]Final answer:
The second option is the correct answer.
First, let's look at the measures of the length and width of the wall the boys arepainting. The problem says that the wall is 7 feet wide and 6 feet tall. Frank paints14 square feet of the wall, and Ryan paints the rest.How can you draw one straight line on this grid to divide it into two sections toshow the part of the wall Frank paints and the part of the wall Ryan paints?
Let's draw the 7ft by 6ft wall that is being painted by Frank and Ryan.
If Frank paints 14 square feet of the wall, we can say that Frank painted two rows of 7ft wide. See illustration below.
The darker horizontal line is the straight line that divides the wall into two sections.
So, the orange part is the section where Frank paints and the blank (white) part is the part of the wall that Ryan paints.
Michael says that 5 = 5 Is his answer correct? Explain. (1 O A. 00:00 Yes. Both expressions are equal to 625 СВ. 00:00 Yes Both expressions are equal to O C. 00:00 No. The first expression is equal to and the second expression is equal to 625 00:00 No. The first expression is equal to 625 and the second expression is equal to
Michael says that
[tex]5\cdot(\frac{1}{5^3})=5(5^3)[/tex]We are asked whether he is correct or not?
Let us simplify the equa
Drag each label to the correct location on the table. Each label can be used more than once, but not all labels will be used.after constant its 6x squared -x-1
For polynomial 1: simplified form
[tex]6x^2-x-1[/tex]Name by Degree: Quadratic
Number of Terms: 3
Polynomial 2:
Simplified form is 3x+4
Name by Degree: Linear
Number of Terms: 2
Polynomial 3:
Simplified form: 2
Name by Degree: Number
Number of Terms: 1
[tex]3x+4[/tex]Given (12 ,7)and (X,-8) find all x such that the distance between these two points is 17 separate multiple answers with a comma
X=20
Explanationthe distance between 2 points is given by
[tex]\begin{gathered} for \\ P1(x_1,y_1) \\ P2(x_2y_2) \\ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}[/tex]so
Step 1
a)given
[tex]\begin{gathered} P1(12,7) \\ P2(x,-8) \\ d=17 \end{gathered}[/tex]b) now, replace in the formula and solve for x
[tex]\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ 17=\sqrt{(x-12)^2+(-8-7)^2} \\ 17=\sqrt{(x-12)^2+(-15)^2} \\ raise\text{ both sides to power 2} \\ 17^2=(\sqrt{(x-12)^2+(-15)^2})^2 \\ 289=(x-12)^2+225 \\ subtract\text{ 225 in both sides} \\ 289-225=(x-12)^2+225-225 \\ 64=(x-12)^2 \\ square\text{ root in both sides} \\ \sqrt{64}=\sqrt{(x-12)^2} \\ 8=x-12 \\ add\text{ 12 in both sides} \\ 8=x-12 \\ 8+12=x-12+12 \\ 20=x \end{gathered}[/tex]therefore, the answer is
X=20
I hope this helps you
Simplify or expand each expression and then Classify it by its degree and number of terms
2x^3 (7x^2 + 3x + 1) - 4x^4
multiply 2x^3 in
14x^5 + 6x^4 + 2x^3 - 4x^4
14x^5 + 2x^4 + 2x^3
3 terms, the degree is 5
terms are single expressions such as (2x^3)
the degree is the highest exponent
(6x - 2x^4 + 5x^6) + (7x^4 - 3x^6 + 9)
combine
6x - 2x^4 + 5x^6 + 7x^4 - 3x^6 + 9
simplify
2x^6 + 5x^4 + 6x + 9
4 terms, the degree is 6
(x^2 + 9)(x^2 - 9)
FOIL, (a + b)(c + d) -> ac + ad + bc + bd
x^2 * x^2 + x^2 * -9 + 9 * x^2 + 9 * -9
simplify
x^4 - 81
2 terms, the degree is 4
A dairy needs 396 gallons of milk containing 6% butterfat. How many gallons each of milk containing 8% butterfat and milk containing 2% butterfat must be used to obtain the desired 396 gallons?
ANSWER:
264 gallons of milk containing 8% butterfat
132 gallons of milk containing 2% butterfat
STEP-BY-STEP EXPLANATION:
From the statement we can propose the following system of equations:
Let x be the milk that contains 8% butterfat and let y be the 2%.
[tex]\begin{gathered} x+y=396\rightarrow y=396-x\text{ (1)} \\ 0.08x+0.02y=0.06\cdot396\rightarrow0.08x+0.02y=23.76\text{ (2)} \end{gathered}[/tex]We substitute in equation (1) in equation (2) and substitute for x, just like this:
[tex]\begin{gathered} 0.08x+0.02\cdot(396-x)=23.76 \\ 0.08x+7.92-0.02x=23.76 \\ 0.06x=23.76-7.92 \\ x=\frac{15.84}{0.06} \\ x=264 \end{gathered}[/tex]Knowing the value of x, we can calculate the value of y, substituting in equation 1, like this:
[tex]\begin{gathered} y=396-264 \\ y=132 \end{gathered}[/tex]Therefore, 264 gallons of milk containing 8% butterfat and 132 gallons of milk containing 2% butterfat are needed.
Find the value of the logarithmic expression. log subscript 6 216log subscript 6 216=____?
Solution
For this case we have the following:
[tex]\log _6(216)=3[/tex]The reason is because:
[tex]6^3=6\cdot6\cdot6=216[/tex]Which expressions have the fewest significant Figures?A. 18.8 - 6.5B. 4350 - 2210C. 15.4 - 8.1D. 54.5 * 30.7
Answer
Option C is obviously the answer.
Explanation
It will be easy to answer this by providing the answers to the expressions.
Option A
18.8 - 6.5 = 12.3 (3 significant figures)
Option B
4350 - 2210 = 2140 (4 significant figures)
Option C
15.4 - 8.1 = 7.3 (2 significant figures)
Option D
54.5 * 30.7 = 1673.15 (6 significant figures)
Hope this Helps!!!
What is the solution to the following equation? X +(-13) = -5 A. X= 18 B. X = 8 C. x -18 D. X = -8
Given the following expression:
X + (-13) = -5
Let's determine the value of X.
X + (-13) = -5
X - 13 = -5
X = -5 + 13
X = 8
Therefore, X = 8.
What is the value??8+(-3)+15-(-40)
We applied the rules that said:
- If we add a negative number, it is the same as substracting its negative. That is why "+(-3)" is equal to "-3".
- If we substract a negative number is equal to add the negative of this number. That is why "-(-40)" is equal to "+40".
how long will it take for the population to get to 2552 alligators?
we have the equation
[tex]P(t)=319(2)^{(\frac{t}{3})}[/tex]For P(t)=2,552
substitute in the given equation
[tex]2,552=319(2)^{(\frac{t}{3})}[/tex]solve for t
[tex]\begin{gathered} 2,552=319(2)^{(\frac{t}{3})} \\ \frac{2,552}{319}=(2)^{(\frac{t}{3})} \end{gathered}[/tex]Apply log both sides
[tex]\begin{gathered} \log \lbrack\frac{2,552}{319}\rbrack=\log \lbrack(2)^{(\frac{t}{3})}\rbrack \\ \log \lbrack\frac{2,552}{319}\rbrack=\frac{t}{3}\cdot\log (2) \end{gathered}[/tex]t=9 yearsthe answer is 9 years from the time of introductionWhat is the equation in standard form of the line that passes through the point (6,-1) and isparallel to the line represented by 8x + 3y=15?A 8x+3y=-45B 8x-3y = -51C 8x+3y=45D 8x - 3y=51
The slope of the given line is:
[tex]s=-\frac{8}{3}\text{.}[/tex]Therefore, the slope of a parallel line to the given line must be -8/3.
Using the slope-point formula for the equation of a line we get:
[tex]y-(-1)=-\frac{8}{3}(x-6)\text{.}[/tex]Taking the above equation to its standard form we get:
[tex]\begin{gathered} y+1=-\frac{8}{3}(x-6), \\ 3y+3=-8(x-6), \\ 3y+3=-8x+48, \\ 8x+3y=48-3, \\ 8x+3y=45. \end{gathered}[/tex]Answer: Option C.
For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. Which equation can be used to find the maximum and minimum temperatures at which nitrogen is a liquid, x?
The maximum and minimum temperatures at which nitrogen is a liquid is -320.44°F and = -346°F.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F.
The minimum temperature will be:
= -333.22 - 12.78
= -346°F
The maximum temperature will be:
= -333.22 + 12.78
= -320.44°F
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
what's the answer please help
Domain are the "x"'s in this example Domain = [-2, 2]
Range are the "y" in this example Range = [-3, 3]
The second choice is correct.
Find the surface area and volume of the figure .The surface area is _ft2.(Round to the nearest tenth as needed .)
Question:
Find the surface area and volume of the figure.
Solution:
1) The surface area:
This shape is composed of a cylinder and hemisphere. Now, we know that the surface area of the sphere is:
[tex]SA\text{ sphere = 4}\pi\text{ }r^2[/tex]So that, the surface area of the hemisphere would be:
[tex]SA\text{ hemisphere = }2\pi r^2[/tex]On the other hand, the area of the circle is:
[tex]A\text{= }\pi r^2[/tex]thus, the surface area of the cylinder would be:
[tex]SA\text{ cylinder = }2\pi rh[/tex]replacing the data given in the problem in the formulas of the surface area of the hemisphere, area of the circle, and surface area of the cylinder, we get:
[tex]SA\text{ hemisphere = }2\pi(9)^2\text{ = 162}\pi[/tex]and
[tex]SA\text{ cylinder = }2\pi(9)(12)\text{ = }216\pi[/tex]and
[tex]A\text{= }\pi(9)^2=\text{ 81}\pi[/tex]then, we can conclude that the surface area of the given figure is:
[tex]SA\text{ = 162}\pi\text{ + 216}\pi+81\pi\text{ = 459}\pi\approx1441.9\text{ }\approx1442[/tex]that is:
[tex]SA\text{ }\approx1441.9\text{ }\approx1442[/tex]
2) The volume
The volume of a cylinder is given by the following formula:
[tex]V_C=\pi r^2h[/tex]and the volume of a hemisphere is :
[tex]V_H=\frac{1}{2}(\frac{4}{3}\pi r^3)\text{ = }\frac{2}{3}\pi r^3[/tex]thus, the volume of the figure would be:
[tex]V=V_C+V_H=\text{ }\pi r^2h\text{+}\frac{2}{3}\pi r^3[/tex]Then replacing the data given in the problem in the above formula we get:
[tex]V=\pi(9)^2(12)\text{+}\frac{2}{3}\pi(9)^3\text{ = 972}\pi\text{+486}\pi=\text{ 1458}\pi\approx4580.4\approx4580[/tex]that is;
[tex]V\approx4580.4\approx4580[/tex]Graph the function and then determine the asymptote of the function.
We need to graph the following function:
[tex]y=\log _{1/2}(x)-4[/tex]We know that the domain of a logarithmic function can't be negative, then our domain is
[tex]x\in(0,\infty)[/tex]We need to analyze this function at its extremes to find the asymptotes.
Let's calculate the limit of this function at x = 0 and at infinity.
[tex]\begin{gathered} \lim _{x\to0}\log _{1/2}(x)-4=\infty \\ \lim _{x\to\infty}\log _{1/2}(x)-4=-\infty \end{gathered}[/tex]By definition, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity. From our limits, we have an vertical asymptote at x =0 and no horizontal asymptotes.
This logarithmic function, comes from infinity at x = 0, an decays to minus infinity as x grows. We have the following graph:
x=72+(m*14)when m=6 to the third power
The value of x is 3096
Here, we want to find the value of x when m is 6 raised to its third power
We proceed as follows;
[tex]\begin{gathered} m=6^3\text{ = 216} \\ Substitute\text{ this value} \\ x\text{ = 72}+\text{(216 }\times\text{ 14)} \\ x\text{ = }72\text{ + 3024} \\ x\text{ = 3096} \end{gathered}[/tex]Try It! On Saturday, the vacation resort offers a discount on water sports. To takea surfing lesson and go parasailing costs $130. That day, 25 people takesurfing lessons, and 30 people go parasailing. A total of $3,650 is collected.What is the discounted price of each activity?CHECK ANSWER
Let the cost of surfing lesson be x and the cost of Parasiling be y
From the question, both surfing lesson and parasailing cost $130
Hnece;
x + y = 130 ---------------------------(1)
From the question, 25 people take surfing lesson and 30 pupil went for parasailing and a total of $3, 650 was collected
Hence;
25x + 30y = 3650--------------------------------(2)
We can now solve equation (1) and (2) simultaneously
Using elimination method,
multiply through equation(1) by 30
30 x + 30 y = 3900 ------------------(3)
subtract equation(1) from equation (3)
5x = 250
divide both-side of the equation by 5
x = 50
substitute x = 50 into equation (1) and then solve for y
x + y = 130
50 + y = 130
subtract 50 from both-side of the equation
y = 130 - 50
y =80
Therefore, the discount price of Surfing lesson is $50 while the discount price for parasailing is $80
To prepare an aquarium for use, you can clean it with saltwater solution.The amount of salt varies directly with the volume of the water.The solution has 3 teaspoons of aquarium salt for every 2 gallons of water.
teaspoons of water = y
gallons of water = x
• a)
y = k x
Where k is the constant of proportionality.
Replace x,y by the values given and solve for k:
3= k 2
3/2 = k
k= 1.5
Equation:
y= 1.5x
• b) replace x=10 and solve for y
y= 1.5x
y= 1.5 (10)
y= 15
15 teaspoons of aquarium salt
• c) replace y= 39 and solve for x
y=1.5x
39 = 1.5 x
39/1.5= x
x = 26
26 gallons of water
Solve the following equation:
-3(5+4x)-7=14
The value of x is, x = -3.
What is solving an equation?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Consider, the given equation
-3(5 + 4x) - 7 = 14
Solving the parenthesis
-15 - 12x - 7 = 14
Simplifying,
-22 - 12x = 14
Adding 22 on both sides,
-22 - 12x + 22 = 14 + 22
-12x = 36
Divide both sides by 12,
-12x/12 = 36/12
-x = 3
Multiply both sides by -1.
-x(-1) = 3(-1)
x = -3
Hence, the value of x is, x = -3.
To know more about the solving an equation, click on the link
https://brainly.com/question/22688504
#SPJ1
The figure below is a net for a right rectangular prism. Its surface area is 396 cm2 andthe area of some of the faces are filled in below. Find the area of the missing faces,and the missing dimension.
hello
to solve this question, let's add up all the areas from the sides given and equate it to the total area of the prism. Then we can also denote the side with the missing area as x
[tex]\begin{gathered} 396=42+72+42+72+x+x \\ 396=228+2x \\ 2x=396-228 \\ 2x=168 \\ \text{divide both sides by the coefficient of x} \\ \frac{2x}{2}=\frac{168}{2} \\ x=84 \end{gathered}[/tex]now we have established the area of the missing sides as 84cm^2
but then from careful observation, the figure with the missing side have a shape of a rectangle and we can use the formula of area of a rectangle to find the missing side.
[tex]\begin{gathered} a=l\times w \\ a=84\operatorname{cm}^2 \\ l=? \\ w=7\operatorname{cm} \\ 84=l\times7 \\ 84=7l \\ \frac{84}{7}=\frac{7l}{7} \\ l=12\operatorname{cm} \end{gathered}[/tex]from the calculations above, the missing side is equal to 12cm
Peter is thinking of a number. If he adds 23 to that number, the sum is 31.A. Write an algebraic equation you can use to find Peter’s number. Let n be Peter’s number.