Answer:
P = 7/12
Explanation:
There are 12 letters in the hat and 7 of them (S, M, T, R, P, C, L) are consonants. The probability of drawing a consonant is the ratio of the number of consonants to the total number of letters, so the probability is
P = 7/12
I need help on this, I need it answered in steps
Let's solve the given logarithmic expression:
[tex]\text{ log}_4(64)\text{ = m}[/tex]We get,
[tex]\text{ log}_4(64)\text{ = m}[/tex][tex]\mathrm{Factor\: the\: number\colon\: }\: 64=4^3[/tex][tex]=\log _4\mleft(4^3\mright)[/tex][tex]\mathrm{Apply\: log\: rule}\colon\quad \log _a\mleft(a^x\mright)=x[/tex][tex]\log _4\mleft(4^3\mright)\text{ = 3 = m}[/tex]Therefore, m = 3.
I need help with this practice problem, I am struggling to solve It’s from my trigonometry prep guide
Answer:
Corey stepped 59.71 ft away
Explanation:
The situation is sketched in the following diagram.
The distance from the foot of the tree is y and x for angles 41 and 68 degrees respectively.
Therefore, the distance Corey has to step away is y - x.
Now, from trigonometry, we know that
[tex]\tan (68^o)=\frac{\text{opposite}}{\text{adjacent}}[/tex][tex]\Rightarrow\tan (68^o)=\frac{\text{8}0}{\text{x}}[/tex]We solve for x and get
[tex]\begin{gathered} \Rightarrow x\tan (68^o)=80 \\ \Rightarrow x=\frac{80}{\tan (68^o)} \end{gathered}[/tex]since tan (68) = 2.475.., the above becomes
[tex]x=\frac{80}{2.75\ldots}=32.32[/tex]Now, for angle 41 we have
[tex]\tan (41^o)=\frac{opposite}{\text{adjacent}}[/tex][tex]\tan (41^o)=\frac{80}{y}[/tex]solving for y gives
[tex]y=\frac{80}{\tan (41^o)}[/tex]since tan(41) = 0.869..., the above becomes
[tex]y=\frac{80}{0.869\ldots}[/tex][tex]\Rightarrow y=92.0295\ldots[/tex]Therefore, the distance Corey has to step away from the tree to get a better view is (rounded to the nearest hundredth)
[tex]y-x=92.0295-32.322[/tex][tex]\boxed{y-x=59.71.}[/tex]Can you help me with number 11? Thank you I am having trouble with it.
N 11
Remember that
The law of sines
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]In this problem
[tex]\frac{14.9}{\sin X^o}=\frac{25.5}{\sin 71^o}[/tex]Solve for x
sinX=(14.9*sin71)/25.5
Use the point highlighted in the graph below to write the equation in point slope form for the line provided.
Making the equation of the graph using the Point-Slope Form:
[tex]\text{ y - y}_1=m(x-x_1)[/tex]Since slope was not given, let's compute first for the slope (m) using this formula,
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1_{}}[/tex]From the graph, we have one set of coordinates given: (2, 3)
However, we cannot solve the slope with one point alone, thus let's find another point that's along the line and easier to find. From the graph, we get (0,4).
Let's now compute for the slope (m).
[tex](x_1,y_1)=(0,4);(x_{2,}y_2)=(2,3)_{}[/tex][tex]\text{ m = }\frac{3\text{ - 4}}{2\text{ - 0}}\text{ = }\frac{-1}{2}[/tex]Let's now make the equation using the Point-Slope Form using (2,3) as (x1,y2),
[tex]\text{ y - y}_1=m(x-x_1)[/tex][tex]\text{ y - 3 = (}\frac{-1}{2})(x-\text{ 2)}[/tex][tex]\text{ y - 3 + 3 = -}\frac{1}{2}x\text{ + }\frac{2}{2}\text{ + 3}[/tex][tex]\text{ y = }\frac{-1}{2}x\text{ + 1 + 3 = }\frac{-1}{2}x\text{ + 4}[/tex]Thus, the equation of the line is,
[tex]\text{ y = }\frac{-1}{2}x\text{ + 4}[/tex]Kyla is filling a water bucket that holds 5 and 1/4 gallons using a container that holds 3/4 of a gallon per container (a) Create a division problem that finds how many containers Kyla will need to use. Evaluate this quotient(b) Check your answer to (a) by using a product. Show your work
Given a water bucket that holds
[tex]5\frac{1}{4}gallons[/tex]A container with the measurement below was used to fill the water bucket
[tex]\frac{3}{4}\text{gallon}[/tex](a) The division problem that shows how many containers are needed to fill the water bucket is
[tex]\frac{5\frac{1}{4}}{\frac{3}{4}}[/tex]The quotient is as solved below:
[tex]5\frac{1}{4}=\frac{5\times4+1}{4}=\frac{21}{4}[/tex][tex]\begin{gathered} \frac{5\frac{1}{4}}{\frac{3}{4}}=\frac{\frac{21}{4}}{\frac{3}{4}} \\ \frac{21}{4}\frac{\square}{\square}\frac{3}{4} \\ =\frac{21}{4}\times\frac{4}{3} \end{gathered}[/tex][tex]\frac{7\times1}{1\times1}=7[/tex]Hence, the quotient is 7 Containers
(b) Checking the answer using a product as shown below
[tex]\begin{gathered} 7\times\frac{3}{4}=5\frac{1}{4} \\ \frac{7\times3}{4}=\frac{21}{4} \end{gathered}[/tex][tex]\frac{21}{4}=5\frac{1}{4}[/tex]Hence, the product of 7 and 3/4 gallons container will fill 5 1/4 water bucket
Marcus is playing dodge ball with hisfriends. He catches 2 out of every 5 ballsthrown in his direction. If he catches14 balls, how many balls were thrownat him?balls
Step 1
Given;
[tex]\begin{gathered} \text{Marcus is playing dodge ball with his friends.} \\ He\text{ catches 2 out of every 5 balls thrown in his direction.} \end{gathered}[/tex]Required; To find out how many balls are thrown at him if he catches 14 balls.
Step 2
There are two approaches to determine the number of balls thrown at Marcus
Approach 1
[tex]\begin{gathered} \text{Marcus catches 2 balls for every 5 balls thrown in his direction.} \\ we\text{ can draw up a table and add up 2 balls caught and 5 balls } \\ \text{thrown respectively until we arrive at 14 balls caught.} \end{gathered}[/tex]Draw the table;
we will now sum the total number of balls caught by Marcus and the total number of balls thrown at him to find out he had 35 balls thrown at him when 14 balls were caught by him.
Answer=35 balls
Approach 2
[tex]\begin{gathered} We\text{ will use the ratio} \\ \frac{2\text{ balls caught}}{14\text{ balls caught}}=\frac{5\text{ balls thrown }}{x\text{ balls thrown}} \\ \text{cross multiply} \\ 2x=5(14) \\ \text{simplify} \\ 2x=70 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{70}{2} \\ x=35\text{ balls thrown} \end{gathered}[/tex]Hence, 35 balls were thrown at Marcus
hello I am stuck on this problem in need of help please thank you
First let's do a quick table to help us, when we have S = 0 we cannot make any cookies, then N = 0. When we have one cup of sugar S = 1 we can make 30 cookies, then N = 30. For S = 2, which means, 2 cups of sugar we can make 60 cookies, and so on, then we can do a table like
Then we can see that the relation between N and S is 30, because N = 30.S, for each unit of S that we put we get 30 more cookies, then the equation is
[tex]N=30S[/tex]And if we want to solve it for S
[tex]S=\frac{N}{30}[/tex]Looking at the graph we can see that S is in the y-axis, therefore we are going to use the equation where we have S on the left side, which means, solved for S. Then we are going to plot the equation:
[tex]S=\frac{N}{30}[/tex]This equation is a line, a very simple graph! you can plot two points and then draw a line, for example, use the point (30,1) and (60,2), if we plot these points we get
Now we draw a line that connects these two points, and we have the graph!
1. P(video games and kid is 10 to 12 years old)2. P(basketball/kid is 13 to 15 years old)3. P(kid is 13 to 15 years old/basketball)4. P(darts/kid is 10 to 15 years old)5. P(basketball and darts)6. P(basketball and kid is 13 to 18 years old)Answer the following problems about two way frequency tables fill in the missing cells on table and make sure to reduce your fraction.
Horizontal addition
Row 1 a + 12 + b +6 =37
[tex]\begin{gathered} a+12+b+6=37 \\ a+b+18=37 \\ a+b=37-18 \\ a+b=19 \end{gathered}[/tex]Row 2
[tex]\begin{gathered} 8+c+16+11=d \\ c+35=d \end{gathered}[/tex]Row 3
[tex]\begin{gathered} 17+5+e+18=f \\ 40+e=f \end{gathered}[/tex]Row 4
[tex]\begin{gathered} g+34+45+h=143 \\ g+h+79=143 \\ g+h=143-79 \\ g+h=64 \end{gathered}[/tex]Now Let us add the columns
Column 1
[tex]a+8+17=g[/tex]Column 2
[tex]\begin{gathered} 12+c+5=34 \\ c+17=34 \\ c=34-17 \\ c=17 \end{gathered}[/tex]Column 4
[tex]\begin{gathered} 6+11+18=h \\ h=35 \end{gathered}[/tex]Column 2
[tex]\begin{gathered} b+16+e=45 \\ b+e=45-16 \\ b+e=29 \end{gathered}[/tex]Hence, Video games under 10-12 is c=17, gotten from column 2
Vertical total under 16-18 is h=35 gotten from column 4
Hence, the horizontal total of the video game is 52
Since h is gotten, we can solve for 7 to 9 vertical total
[tex]\begin{gathered} g+h=64 \\ g=64-h \\ g=64-35 \\ g=29 \end{gathered}[/tex]Hence, the 7 to 9 vertical total is 29
[tex]\begin{gathered} a+25=g \\ a=g-25 \\ a=29-25 \\ a=4 \end{gathered}[/tex]Hence, Darts under 7 to 9 is 4
Darts under 13 to 15 is b
[tex]\begin{gathered} a+b=19 \\ b=19-a \\ b=19-4 \\ b=15 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 15
Basket ball under 13 to 15 is e
[tex]\begin{gathered} b+e=29 \\ e=29-b \\ e=29-15 \\ e=14 \end{gathered}[/tex]Hence, Darts under 13 to 15 is 14
Video Games Horizontal total is d,
[tex]\begin{gathered} c+35=d \\ 17+35=d \\ d=52 \end{gathered}[/tex]Hence, the Horizontal total of the Video game is 52
Basketball horizontal total is f
40+e=f
[tex]\begin{gathered} 40+e=f \\ 40+14=f \\ 54=f \end{gathered}[/tex]Hence, the horizontal total of the Video game is 54.
Hence, the above table fill the empty space
PQR is a right triangle. If PQ=8, what is PR?
Sine formula
[tex]\sin (angle)=\frac{\text{ opposite side}}{\text{ hypotenuse}}[/tex]Considering angle Q = 60°, the opposite side is PR, and the hypotenuse is PQ = 8. Substituting this information into the formula, we get:
[tex]\begin{gathered} \sin (m\angle Q)=\frac{PR}{PQ} \\ \sin (60\degree)=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}=\frac{PR}{8} \\ \frac{\sqrt[]{3}}{2}\cdot8=PR \\ 4\sqrt[]{3}=PR \end{gathered}[/tex]lax and tip word pr You might need: 3 Calcu The sales tax in your city is 4.4%. and an item costs $3 before tax. How much tax would you pay on that item?
Tax = $0.13(nearest hundredth)
Write and solve addition equations3/8 + n = 7/8
So,
We're going to solve:
[tex]\frac{3}{8}+n=\frac{7}{8}[/tex]For n:
[tex]\begin{gathered} n=\frac{7}{8}-\frac{3}{8} \\ \\ n=\frac{4}{8} \end{gathered}[/tex]Therefore, n=4/8
What is the answer for x?
By the concept of parallels lines the value of x is 4 .
What are parallels lines?Coplanar, straight lines that don't intersect anywhere are considered parallel lines in geometry. Lines in the same three-dimensional space that never cross one another and are said to be parallel. Curves that are parallel to each other and maintain a setting a minimum distance do not touch or intersect. Lines in a plane that consistently have the same separation are said to be parallel. Nothing can cross a parallel line. Lines that cross at a straight angle of 90 degrees are called perpendicular lines. Two lines in the same plane that are equally spaced apart and never cross each other are referred to in geometry as parallel lines. Both vertical and horizontal can be used. Parallel line examples abound in daily life, such as the rows of notebooks and zebra crossings.
9x - 6 = 6x + 6
3x = 12
x = 4
To know more about parallels lines , visit:
brainly.com/question/16701300
#SPJ1
write your own multiple event probability problem and solve it as if you are explaining your reasoning to a friend.
Problem:
You and your sister have six-sided dice each one. What is the probability that if both roll your dice, you get an even number and your sister get an odd number.
Now, each dice has 6 numbers: 1,2,3,4,5,6
The even numbers are: 2,4,6 (3 options)
The odd numbers are: 1,3,5 (3 options)
Now, the probability of rolling an even number is:
[tex]P(e)=\frac{3}{6}[/tex]And the probability of rolling an odd number is:
[tex]P(o)=\frac{3}{6}[/tex]Then, the probability that you get an even number and your sister an odd number is the product of the probabilities of each event:
[tex]\begin{gathered} P(e\cap o)=P(e)*P(o) \\ \\ P(e\cap o)=\frac{3}{6}*\frac{3}{6} \\ \\ P(e\cap o)=\frac{9}{36}=\frac{1}{4} \end{gathered}[/tex]The probability is 1/4
Now finish solving the equation. What is the value of m?-(m - 6) = 3m + 14-m + 6 = 3m + 14-m + 6 - 3m = 3m + 14 - 3m-4m + 6 = 14m=
D − 37 = 40D =Check your solution.− 37 = 40
We have to solve this equation:
[tex]D-37=40[/tex]We can solve it for D by adding 37 on both sides of the equation as this won't change the equality:
[tex]\begin{gathered} D-37+37=40+37 \\ D=77 \end{gathered}[/tex]Answer: D = 77
1 2 3 At the beginning of the day the temperature was - 17°C. At noon the thermometer read -2°C What is the total change in degrees Celsius?
The total change in temperature = temperature at noon minus temperature at the beginning of the day
[tex]=-2^0^{}c-(-17^0c)=-2^0c+17^0c=15^0c[/tex]In New York State, the minimum wage has grownexponentially. In 1966, the minimum wage was$1.25 an hour and in 2015, it was $8.75.Algebraically determine the rate of growth to thenearest percent.
The Solution.
In 1966, which is the initial year(t); t = 0, and minimum wage(y), y = $1.25
Similarly.
In 2015, t = 49 years , (that is, 1966 to 2015), and y = $8.75
The rate of growth to the nearest percent is
[tex]\text{Rate of growth =}\frac{y_2-y_1}{t_2-t_1}\times100[/tex][tex]\begin{gathered} \text{Where y}_2=8.75,t_2=49\text{ years} \\ y_1=\text{ \$1.25},t_1=0 \end{gathered}[/tex]Substituting into the formula above, we get
[tex]\text{Rate of growth =}\frac{8.75-1.25}{49-0}\times100[/tex][tex]\text{Rate of growth = }\frac{7.5}{49}\times100=15.31\approx15\text{ \%}[/tex]Hence, the correct answer is 15%
Find the lateral surface area of the following cylinder:r = 3 cmh = 3 cmLSA = [?]π cm?Leave your answer in terms of pi
In order to calculate the lateral surface area of the cylinder, we can use the following formula:
[tex]\text{LSA}=2\pi rh[/tex]Where r is the radius and h is the height of the cylinder.
Using r = 3 and h = 3, we have:
[tex]\begin{gathered} \text{LSA}=2\pi\cdot3\cdot3 \\ \text{LSA}=18\pi \end{gathered}[/tex]So the LSA is equal 18π cm², therefore the answer is 18.
The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red).Write down the expression for h *(x)The function f is defined * x/-=(x)/^ q
Alexa read a total of 54 books over 9 months. If Alexa has read 120 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.
If the relation between the book read by Alexa and the number of months she takes to read them is directly proportional, then, if x is the number of months she took to read 120 books, you can write:
[tex]\frac{x}{120}=\frac{9}{54}[/tex]By solving for x and simplifying, you obtain:
[tex]\begin{gathered} x=\frac{9}{54}\cdot120 \\ x=20 \end{gathered}[/tex]Hence, Alexa read 120 books in 20 months
Rewrite the area formula with the info given from the problem then find the value of x , then how many feet of fencing should me Korber buy ?
Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:
[tex]A=\frac{1}{2}x^2[/tex]Now, let's use the given area and solve it for x:
[tex]\begin{gathered} 4232=\frac{1}{2}x^2\\ \\ x^2=8464\\ \\ x=92\text{ ft} \end{gathered}[/tex]Since the "path" already has fence, the amount of fence needed is 2x:
[tex]2x=2\cdot92=184\text{ ft}[/tex]what is the value of x to the nearest tenth on problem 5
Answer:
Explanation:
In problem 5, we can see that there is a right triangle with legs x and 16 and a hypotenuse equal to (x + 8).
So, by Pythagorean theorem, we can write the following equation
[tex](x+8)^2=x^2+16^2[/tex]Now, we can expand the left side
[tex]\begin{gathered} x^2+2(8)(x)+8^2=x^2+16^2 \\ x^2+16x+64=x^2+256 \end{gathered}[/tex]Then, subtract x² from both sides
[tex]\begin{gathered} x^2+16x+64-x^2=x^2+256-x^2 \\ 16x+64=256 \end{gathered}[/tex]Subtract 64 from both sides
[tex]\begin{gathered} 16x+64-64=256-64 \\ 16x=192 \end{gathered}[/tex]Finally, divide by 16
[tex]\begin{gathered} \frac{16x}{16}=\frac{192}{16} \\ \\ x=12 \end{gathered}[/tex]Therefore, the value of x is 12
if f is defined by the function f(x)=x-4/x-2 then lim f(x) is equivalent to which of the following
Answer:
The correct answer is the third option:
[tex]\lim_{x\to4}(\sqrt{x}-2)[/tex]Explanation:
We have the function:
[tex]f(x)=\frac{x-4}{\sqrt{x}-2}[/tex]In the numerator, we have x - 4. We can rewrite it as a difference of squares, since:
[tex]\begin{gathered} x=(\sqrt{x})^2 \\ 4=2^2 \end{gathered}[/tex]Thus:
[tex]x-4=(\sqrt{x}-2)(\sqrt{x}+2)[/tex]Then, the limit:
[tex]\begin{gathered} \lim_{x\to4}(\frac{(\sqrt{x}-2)(\sqrt{x}+2)}{(\sqrt{x}-2)} \\ \end{gathered}[/tex]We can cancel out the terms, since we are taking limit, this is, numbers that infinitely close to 4, bt never 4. This way we can cancel the terms, and get:
[tex]\lim_{x\to4}(\sqrt{x}+2)[/tex]
13. A table costs $439. It is on sale for 40%off. a How much do you save? b. What isthe sales price? Solve question#3 parts a &b.a. I saveb. The sales price isу
A table costs 439, and it is on sale for 40%. That means we shall deduct 40% of 439 from the actual cost as follows;
[tex]\begin{gathered} \text{Sales}=\text{Cost}-\text{Discount} \\ \text{Sales}=439-(439\times\frac{40}{100}) \\ \text{Sales}=439-(439\times0.40) \\ \text{Sales}=439-175.60 \\ \text{Sales}=263.40 \end{gathered}[/tex]Therefore,
The savings is $175.60
The sales price is $263.40
15% of 80 is 60% of what number?
Let x be the required number.
[tex]15\text{ \% of 80 =}60\text{ \% of x}[/tex][tex]15\text{ \% }\times\text{ 80 =}60\text{ \% }\times\text{ x}[/tex][tex]\frac{15}{100}\text{ }\times\text{ 80 =}\frac{60}{100}\text{ }\times\text{ x}[/tex]
Using the cross-product method, we get
[tex]\frac{15\times80}{100}\times\frac{100}{60}=x[/tex][tex]x=20[/tex]Hence 15% of 80 is 60% of 20.
The answer is 20.
Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.9 ft13 ft6 ft
The area of the triangle is 27 square feet
Explanation:The area of a triangle is given as:
[tex]A=\frac{1}{2}bh[/tex]Where b and h are the base and height of the triangle respectively
[tex]\begin{gathered} A=\frac{1}{2}(9\times6) \\ \\ =27ft^2 \end{gathered}[/tex]aThecity of Huntsville, TX has approximately 25,000 registered voters. There are two candidates forcity council in an upcoming election: Brown and Solano. The day before the election, a telephone pollof 550 randomly selected registered voters was conducted. 243 said they'd vote for Brown, 253 saidthey'd vote for Solano, and 54 were undecided.give the simple statistic for the proportion of voters surveyed
The surveyors are really interested in all registered boters in Huntsville, therefore the first answer is F.
Since they are only doing a sample of people with phones the real population is all registered voters with telephones, therefore the second answer is C.
The sample for this survey is the 550 voter surveyed.
To find the proportion of people who said they vote for brown we divide the number of this people by the total of people surveyed:
[tex]\frac{243}{550}=0.4418[/tex]Therefore the proportion was 0.4418
Find the absolute value of -1818-181/18-1/18Find the opposite of -2525-251/25-1/25
the absolute value of a number does not contain negative sign
so the absolute value of the given expression (-18) is,
= 18
thus, the answer is option A.
3
the opposite of -25 will be,
= -(-25)
= 25
thus the answer is for the second question is option A
Lynn got a $50 gift card to an online music store she uses the gift cards to buy an album for 9.99 she also wants to use the gift card to buy some songs. Each song cost 1.29. What equality is described the situation where n is the number of songs like monster by
ANSWER
B. 9.99 + 1.29n ≤ 50
EXPLANATION
The total amount of money she spends at the store has to be at most, the value of the gift card $50. This is the cost of the album, 9.99, and then 1.29 for each song. If the total number of songs is 'n', then for n songs, she'll spend 1.29n. In total she spends: 9.99 + 1.29n at the store. The equation is
[tex]9.99+1.29n\le50[/tex]Find the exponential function f(x)=Ca^x whose graph is given below.
Answer:
f(x) = 2[tex](\frac{1}{3}) ^{x}[/tex]
Step-by-step explanation:
exponential in the form
f(x) = C[tex]a^{x}[/tex]
to find C and a use points from the graph
using (0, 2 ) , then
2 = C[tex]a^{0}[/tex] ( [tex]a^{0}[/tex] = 1 ) , so
C = 2
f(x) = 2[tex]a^{x}[/tex]
using (2, [tex]\frac{2}{9}[/tex] )
[tex]\frac{2}{9}[/tex] = 2a² ( divide both sides by 2 )
[tex]\frac{1}{9}[/tex] = a² ( take square root of both sides )
[tex]\sqrt{\frac{1}{9} }[/tex] = a ⇒ a = [tex]\frac{1}{3}[/tex]
f(x) = 2 [tex](\frac{1}{3}) ^{x}[/tex] ← exponential function