Given:
[tex]\tan\frac{2\pi}{3}[/tex]Find-:
Exact value
Explanation -
So, the value is:
[tex]=\tan\frac{2\pi}{3}[/tex][tex]\begin{gathered} =\tan\frac{2\pi}{3} \\ \\ \pi=180\text{ then,} \\ \\ =\tan(\frac{2\times180}{3}) \\ \\ =\tan(120) \end{gathered}[/tex]So value is:
[tex]\tan(120)=-\sqrt{3}[/tex]Use (60° - 45°) = 15° to find the exact value of cos 15º.vaV2 + V6V-V6(b)(c)4(d)4+ V62
Answer;
[tex]B\text{. }\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]Explanation;
Given that;
[tex](60^0-45^0)=15^0[/tex]Hence;
[tex]\text{Cos 15}^0=Cos(60^0-45^0)[/tex]According to trigonometry identity;
[tex]\begin{gathered} Cos(60^0-45^0\text{) = Cos60 Cos45 + Sin60Sin45} \\ Cos(60^0-45^0\text{) }=\frac{1}{2}(\frac{1}{\sqrt[]{2}})+\frac{\sqrt[]{3}}{2}(\frac{1}{\sqrt[]{2}}) \end{gathered}[/tex]Evaluate the result by finding the LCM
[tex]Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}[/tex]Rationalize;
[tex]\begin{gathered} Cos(60^0-45^0\text{) }=\frac{1+\sqrt[]{3}}{2\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}(1+\sqrt[]{3})}{2\cdot2} \\ Cos(60^0-45^0\text{) }=\frac{\sqrt[]{2}+\sqrt[]{6}}{4} \end{gathered}[/tex]Hence the required reusult is;
[tex]\frac{\sqrt[]{2}+\sqrt[]{6}}{4}[/tex]Write an equation or inequality and solve:32 is at most the quotient of a number g and 8
The quotient of a number g and 8 can be written as:
[tex]\frac{g}{8}[/tex]Since it is given that 32 is at most( this quotient, then it follows that:
[tex]32\le\frac{g}{8}[/tex]Next, solve the resulting inequality:
[tex]\begin{gathered} 32\le\frac{g}{8} \\ \text{Swap the sides of the inequality and change the sign:} \\ \frac{g}{8}\ge32 \end{gathered}[/tex]Multiply both sides of the inequality by 8. Note that the sign will not change since you are multiplying a positive number:
[tex]\begin{gathered} \Rightarrow8\times\frac{g}{8}\ge8\times32 \\ \Rightarrow g\ge256 \end{gathered}[/tex]Hence, the inequality is:
[tex]32\le\frac{g}{8}[/tex]The solution is:
[tex]g\ge256[/tex]Find the area of a triangle with vertices at N(-4,2), A(3,2)and P(-1,-4).
The distance between points N and A is 7, and we can take that as the base of the tringle (up side down)
The distance between the base (NA) and the point P is 6, and we can take that as the height of the triangle
Area of a triangle = (Base x Height)/2
Area = (7 x 6)/2 = 42/2 = 21
Answer:
Area = 21
Bob buys a vase for $15 and spends $2 per flower.
4) Write an equation to represent the cost of buying flowers.
If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
The cost of flower vase = $15
The cost of each flower = $2
Consider the number of flowers as x
Then the linear equation that represents the cost of buying flowers = The cost of flower vase + The cost of each flower × x
Substitute the values in the equation
The equation that represents the cost of buying flowers = 15+2x
Hence, If Bob buys a vase for $15 and spends $2 per flower, then the equation to represent the cost of buying flowers is 15+2x
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Factor the following polynomials. Remember, factoring strategies for quadratic polynomials may be needed here.
For this problem, we are given a polynomial, and we need to factor it.
The polynomial is given below:
[tex]64-324x^4[/tex]We can use the difference between two squares to factor this polynomial. The base form of this notable product is shown below:
[tex]\begin{gathered} (a-b)(a+b)=a^2-b^2\\ \\ \end{gathered}[/tex]We can do the same with the original polynomial:
[tex]64-324x^4=8^2-(18x^2)^2=(8-18x^2)(8+18x^2)[/tex]The answer is (8-18x²)(8+18x²).
solve the following equation for pp/r+s=q
the initial equation is:
[tex]\frac{p}{r}+s=q[/tex]To solve for p we can rest s in bout sides so:
[tex]\begin{gathered} \frac{p}{r}+s-s=q-s \\ \frac{p}{r}=q-s \end{gathered}[/tex]Now we can multiply by r so:
[tex]\begin{gathered} \frac{p\cdot r}{r}=(q-s)\cdot r \\ p=(q-s)\cdot r \end{gathered}[/tex]For the two numbers listed find two factors of the first number such that their product is the first number and there sum is the second number
Given:
Product of two numbers is 24
Sum of two numbers is -11
-8 and -3 are the two numbers.
Kimberly has an empty cardboard box that weighs 0.5 pounds. She puts 10 loaves of bread and a 4-pound jar of peanut butter in the box. The total weight of the box and its contents is 19.5 pounds. One way to represent this situation is with the equation 0.5 - 106 + 4 = 19.5 In this situation, what does the solution to the equation represent? In other words, if you solved for b. what would the value of b tell you? You do not have to find the solution to answer the question
The equation is represented by:
0.5 + 10b + 4 = 19.5
In which 19.5 is the total weight of the box and it's contents.
0.5 is the weight of the cardboard box.
4 is the weight of the jar of peanut butter.
10b is the weight of all loaves of bread.
And b is the weight of a single loaf of bread
The answer is:
The solution of the equation, which is the value of b, represents the weight of a single loaf of bread.
Please help me with this question! Will give brainliest !!! I need it ASAP
Answer:
The number is not a square number because the exponent is an odd number.
Step-by-step explanation:
Square numbers or perfect squares are any numbers that once put to the square root equals a whole number. Such as 4 is a square number because the square root of 4 is 2 or 2 to the second power. Numbers that are raised to even powers also fall under this rule. For example, 16 is a square number as it is equal to 2 to the fourth power, or 16 to the fourth root is 2. Since 1953125 can also be written by 5 to the ninth power it does not go under this rule due to the power being 9. 9 is an odd number. For it to be a perfect square the exponent would have to be an even number.
Assume that a particular professional baseball team has 10 pitchers, 6 Infielders, and 9 other players. If 3 players' names are selected at random determine the probability that 2 are pitchers and 1 is an infielderWhat is the probability of selecting 2 pitchers and 1 infielder?Type an integer or a simplified fraction)
The probability of choosing 2 pitcher and one infielder out of the total number of player can be obtained as follows:
We need to slect two pitchers and one infielder out of 10 pitchers and 6 infielders, the number of ways we can do this is:
[tex](_{10}C_2)(_6C_1)=270[/tex]Out of the 25 players if we choose 3 we can do this in the following number of possibilities:
[tex]_{25}C_3=2300[/tex]Then the probability is:
[tex]P=\frac{270}{2300}=\frac{27}{230}[/tex]Therefore, the probability of choosing 2 pitchers and one infielder is 27/230.
There is a bag with 7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons. You are drawing thebuttons one at a time. Each time you draw a button, you keep it.P(red then green) =Show Your Work
7 red buttons, 4 green buttons, 2 blue buttons, and 5 orange buttons
In total there are
= 7 + 4 + 2 + 5
= 18 buttons
P (red) = 7/18
P(green) = 4/18
P(red then green) = 7/18 * 4/18
=7/81
answer yes or no and explain why or why not.if a/5 = 8 + 9, does a/5 + 9 = 8 + 9?
Equations
We are given the following equation:
a/5 = 8+ 9
Adding 9 to both sides of the equation we have:
a/5 + 9 = 8 + 9 + 9
It's evident that a/5 + 9 is not equal to 8 + 9, but to 8+9+9 instead.
Answer: No
ax-5y = -2
3x+4y = b
(x+?)(x+3)=x squared+5x+6
The given expression is :
(x + ) (x + 3) = x² + 5x + 6
The polynomial is factorize and then written in the form of (x + ) (x + 3)
Let the missing number is "b" substitute in the equation and simplify :
(x + b ) (x + 3) = x² + 5x + 6
x² +bx + 3x + 3b = x² + 5x + 6
x² +x(b +3) + 3b = x² + 5x + 6
Comparing the constant term together :
3b = 6
Divide both side by 3
3b/3 = 6/3
b = 2
Since b is the missing term so, Missing term is 2
(x + 2 ) (x + 3) = x² + 5x + 6
Answer :(x + 2 ) (x + 3) = x² + 5x + 6
Retest: ProbabilityFor problems 1-3: Johnny Awesome has three red marbles, two blue marbles, five green marbles, and 7 yellowmarbles in a bag. What is the probability that'Johnny.....3) draws a blue marble, does not replace it, and then draws a green marble?
Answer
5/136
Step-by-step explanation
Events
• A: a blue marble is drawn
,• B: without replacing the first marble, a green marble is drawn
There are 17 (= 3 + 2 + 5 + 7) marbles in total in the bag. Two of them are blue, then the probability of drawing a blue marble is:
[tex]P(A)=\frac{2}{17}[/tex]After a blue marble is drawn, 16 marbles are left in the bag. Five of them are green, then the probability of drawing a green marble is:
[tex]P(B)=\frac{5}{16}[/tex]Finally, the probability of drawing a blue marble and then a green marble without replacement is:
[tex]\begin{gathered} P(A\text{ and }B)=P(A)\cdot P(B) \\ P(A\text{ and }B)=\frac{2}{17}\cdot\frac{5}{16} \\ P(A\text{ and }B)=\frac{5}{136} \end{gathered}[/tex]The 250 m between Sam's house and the tennis court corresponds to 5 cm on a town
map. What is the actual distance between Sam's school and the library if they are 8.4
cm apart on the same map?
Sam's school and the library are actually 420m apart.
What is the Scale Drawing?A scale drawing is a more compact representation of the original image, structure, or object.
The town is depicted at scale on the town map.
Original dimensions divided by the scale drawing's dimensions gives the drawing's scale.
The first step is to establish the map's scale in order to calculate the precise distance between Sam's school and the library.
Map scale: 250 m / 5 cm = 50
In this scale, 1 cm equals 50 m.
Scale of the drawing times the distance on the map equals the actual distance between Sam's school and the library.
50 x 8.4 = 420m
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The highly temperature one day was -3 the low temperature was -7 what was the difference
How do you know when an equation has infinite many solution?A. The coefficients are differentB. The coefficients are the same and the constants are differentC. The coefficients are the same and the constants are same
Solution:
An equation has infinitely many solutions when the coefficients are the same and the constants are the same.
This is illustrated as shown below:
[tex]\begin{gathered} 2a+5+a=\text{ 5+3a,} \\ thus,\text{ we have infinitely many solution} \end{gathered}[/tex]Hence, the correct option is C.
What is the slope of the line in the graph?A. 2/3B. -2/3C. 3/2D. -3/2
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
graph
Step 02:
slope of the line:
we must analyze the graph to find the solution.
point 01 (0, 8)
point 02 (12, 0)
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{0-8}{12-0}=\frac{-8}{12}=\frac{-2}{3}[/tex]The answer is:
m = - 2/3
Determine the value of k for which f(x) is continuous.
These are the conditions of the continuity in a function:
First, the value of x must have an image.
Second, the lateral limits must be equal:
[tex]\lim_{x\to a^+}f(x)=\lim_{x\to a^-}f(x)[/tex]Finally, the value of the limit must be equal to the image of x. This means that:
[tex]f(a)=\lim_{x\to a^}f(x)[/tex]In this case, we must find a value of k that can make the two lateral limits equal in x =3:
[tex]\lim_{x\to3^+}x^2+k=\lim_{x\to3^-}kx+5[/tex]We can solve these two limits easily by replacing the x with the value of 3
[tex]3^2+k=3k+5[/tex][tex]\begin{gathered} 9+k=3k+5 \\ 4=2k \\ k=2 \end{gathered}[/tex]Finally, we can see that the answer is k=2.
Is 5/6 equivalent to 0.832
Answer: No
Step-by-step explanation:
1 divided by 6 would be 16 and 4/6. So you would have to multiply 16 and 4/6 by 5, add them together, and then divide by 10 to get the decimal. 16 * 5 = 80. 4/6 * 5 = 20/6. 80/10 = 8. 20/6 divided by 10 = 10/6. 8+10/6 is not equal to .832
The rat population in major metropolitan city is given by the formula n(t)=40e^0.015t where t is measured in years since 1991 and n(t) is measured in millions. What does the model predict the rat population was in the year 2008?
To use the model we need to find the value of t. To do this we substract the year we want to know from the year the model began, then:
[tex]t=2008-1991=17[/tex]Now that we have t we plug it in the function:
[tex]n(17)=40e^{0.015\cdot17}=51.618[/tex]Therefore the model predict that there were 51.618 millions of rats in 2008.
Show all five steps of the hypothesis test. You can either type them in here, or write them out on paper and send me a scan/picture of your work.The average movie ticket in 2010 cost $7.89. A random sample of 15 movie tickets from the suburbs of a large U.S. city indicated that the mean cost was $11.09 with a standard deviation of $4.86. At the 0.01 level of significance, can it be concluded that the mean in this area is higher than the national average?
Step 1
State the null and alternative hypothesis
[tex]\begin{gathered} H_o=7.89 \\ H_a>7.89 \end{gathered}[/tex]Step 2
State the p-value of the significance level.
[tex]\begin{gathered} \alpha=0.01 \\ p=\frac{\alpha}{2}=\frac{0.01}{2}=0.005 \end{gathered}[/tex]Step 3
Calculate the statistical test
[tex]\begin{gathered} n=15 \\ \mu(\operatorname{mean})=11.09 \\ \sigma(s\tan dard\text{ deviation)=4.86} \end{gathered}[/tex]The t-test formula is given as
[tex]t=\text{ }\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]Where
[tex]\begin{gathered} \bar{x}=\operatorname{mean} \\ \mu=theoretical\text{ }value \\ \end{gathered}[/tex][tex]\begin{gathered} t=\frac{7.89-11.09}{\frac{4.86}{\sqrt[]{15}}} \\ t=\frac{7.89-11.09}{1.254846604} \\ t=\frac{-3.2}{1.254846604} \\ t=-2.550112492 \end{gathered}[/tex]Step 4
Find the p-value from the t-test.
[tex]\text{The p-value from the t-test is 0.01}209[/tex]Step 5
Conclusion
The result is not significant at p<0.01. Therefore, the null hypothesis is rejected. It cannot be concluded that the mean in this area is higher than the national average because the p-value is greater than 0.01t
HELP ASAP
What is the size of the smallest angle in Triangle A? Give your answer correct to one
decimal place. Show your calculations.
Answer:
A is an included angle between 3 and 5
How many solutions does the system formed by x − y = 4 and ay − ax + 4a = 0 have for a nonzero number a? Give your answer and complete the explanation.
Given system of equations have no solutions that is nonzero.
We have been given the system of equations formed by x − y = 4 and ay - ax + 4a = 0
We need to find the number of non-zero solutions the system have for a nonzero number 'a'
x - y = 4 ............(1)
ay - ax + 4a = 0 ............(2)
From equation (1),
x = 4 + y
Substitute x = 4 + y in equation (2),
ay - a(4 + y) + 4a = 0
ay - 4a - ay + 4a = 0
-4a + 4a = 0
0 = 0
This means that the system have no solutions that is nonzero.
Therefore, given system of equations have no solutions that is nonzero.
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The bases of the prism below are rectangles. If the prism's height measures 3 units and its volume is 198 units^3. solve for x
The volume of a rectangular prism is given by
V=L*W*H
where
V=198 units3
L=6 units
W=x units
H=3 units
substitute given values
198=(6)*(x)*(3)
solve for x
198=18x
x=198/18
x=11 unitsWitch phrase best describes the position of the opposite of +4
To find the position that is opposite to +4, we need to consider 0 as a "mirror point", then we check which point has the same distance to 0 as the distance from +4 to 0:
The position which is opposite to +4 is the position -4.
This position is 4 units to the left of 0 and 8 units to the left of +4.
Looking at the options, the correct option is the second one.
given which of the following describes the boundary line and shading for the second inequality in the system
Answer:
Solid Line, Shade Above
Explanation:
Given:
[tex]\left\{\begin{array}{l} y<-2 x+3 \\ y \geq x-4 \end{array}\right.[/tex]The second inequality in the system is:
[tex]y\geq x-4[/tex]The intercepts of the boundary line (y=x-4) are (0, -4) and (4,0).
Since the inequality has an equal to sign attached, we use a solid line.
At (0,0)
[tex]\begin{gathered} y\geq x-4 \\ 0\geq-4 \end{gathered}[/tex]Since the inequality 0≥-4 is true, shade the side that contains (0, 0) as shown in the graph below:
So, we use a solid line and shade above the boundary line.
The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges to rent trucks plus an additional fee of for each ton of sugar. The second company charges to rent trucks plus an additional fee of for each ton of sugar.For what amount of sugar do the two companies charge the same? What is the cost when the two companies charge the same?
step 1
Find the equation of the line First Company
y=100.25x+6,500
where
y is the total charge
x is the number of ton of sugar
Second Company
y=225.75x+4,492
Part a)
Equate both equations
100.25x+6.500=225.75x+4,492
solve for x
225.75x-100.25x=6,500-4,492
125.50x=2,008
x=16
answer part a is 16 tonPart b) For x=16 ton
substitute the value of x in any of the two equations (the result is the same)
y=100.25(16)+6,500
y=$8,104
answer Part b is $8,104Previous Answer: 12 Things to consider! • What are the solid/solids of the figure? • What are you being asked to find? • What are you being given? The volume is 60mi?. What is the height of the Pyramid of Giza?
The length of base is l = 5.
The width of base is b = 4.
The volume of pyramid is V = 60.
The formula for the volume of the pyramid is,
[tex]V=\frac{1}{3}l\cdot b\cdot h[/tex]Determine the height of the pyramid.
[tex]\begin{gathered} 60=\frac{1}{3}\cdot5\cdot4\cdot h \\ h=\frac{60\cdot3}{20} \\ =9 \end{gathered}[/tex]So height of the pyramid is 9 mi.