We have the following:
The distributive property of multiplication over addition can be used when multiplying a number by a sum.
[tex]\begin{gathered} \mleft(3+6\mright)\mleft(-8\mright)=9\cdot-8 \\ -72=-72 \end{gathered}[/tex]help me; its all explained in the picture thank you
The mean, mode, and mid-range of the given numbers are 13,13,16 respectively.
What are the mean, mode, and range?The total of all the numbers is represented by the mean. The median is the number in the center of an ordered list. The most frequent number is the mode. The highest number less the smallest number is the range.
Mean = sum of the number/ total no. of observations
Mean = 117/ 9
Mean = 13
Mode: The unique number that repeatedly comes
Given,
9, 9, 10, 11, 13, 13, 13, 14, 25
Mode = 13
Range: Deduct the smaller number from the greater one.
Range = 25-9
Range = 16
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Two boats leave the same marina. One heads north, and the other heads
east. After some time, the northbound boat has traveled 39 kilometers, and
the eastbound boat has traveled 52 kilometers. How far apart are the two
boats
The distance travelled by the two boats forms a right triangle. Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
It is given to us that -
There are two boats
One boat heads north while the other heads east
The boat travelling north has traveled 39 kilometers
The boat travelling south has traveled 52 kilometers
We have to find out the distance between the two boats after they have travelled the respective distances.
It is known to us that one boat heads north while the other heads east. We can see that the trajectory formed between the two boats resembles a right triangle as they start from the same point.
One leg of the right triangle formed equals to the distance travelled by the boat travelling north.
Let us say the distance travelled by the boat travelling north be "a".
=> a = 39 kilometers ----- (1)
Other leg of the right triangle formed equals to the distance travelled by the boat travelling east.
Let us say the distance travelled by the boat travelling east be "b".
=> b = 52 kilometers ------ (2)
Now, the distance between the two boats after they have travelled the respective distances is equal to the value of the hypotenuse of the right triangle formed.
Let us say the hypotenuse of the right triangle formed be "h".
According to the Pythagorean Theorem for a right triangle,
[tex]a^{2} +b^{2} =h^{2}[/tex] ---- (3)
where, a, b = legs of the right triangle
and, h = hypotenuse of the right triangle
Substituting the values of a and b from equations (1) and (2) respectively in equation (3), we have
[tex]a^{2} +b^{2} =h^{2}\\= > 39^{2} +52^{2} =h^{2}\\= > h^{2}=1521+2704\\= > h^{2}=4225\\= > h=65[/tex]
So, the value of the hypotenuse of the right triangle formed is 65 kilometers.
Thus, applying the Pythagorean Theorem we find out that the two boats are 65 kilometers apart from each other after travelling 39 kilometers north and 52 kilometers east. Thus, 1st option is correct.
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I need to use factorials and doing it step-by-step for the bio normal probability formula Please help me figure this A through C step-by-step they want the factorial symbol! When showing my workP(4 sucessses) n=15 P=0.04P(2 successors) n=12. P=0.2P( at most 3 sucesssors) n= 20 p=0.5Please help this is all very confusing to me I need to use a factorial symbol in the steps when using the bio or Al distribution formula
Given:
P(4 sucessses) n=15 P=0.04
P(2 successors) n=12. P=0.2
P( at most 3 sucesssors) n= 20 p=0.5
Required:
To calculate above equation
Explanation:
a)-P(4 sucessses) n=15 P=0.04
a=no of trials
p=probability of success
[tex]\begin{gathered} P(4\text{ successes\rparen=P\lparen x=4\rparen} \\ \\ USING: \\ \\ ^nc_x\times p\text{ x }\times(1-p)(n-x) \\ \\ ^{15}c_4\times0.4\text{ 4}\times(1-0.4)\div(15-4) \\ \\ =0.126775 \end{gathered}[/tex]b)-
n=12,p=0.2, find P(2 failures),
P(2 failures)=P(12-2)=p(10 success)
using the same formula after calculation we get
=0.000004325376
c)-n=20, p=0.05 , find P(at least 3 successes)
P(x>3)=p(3)+p(4)+p(5)........p(20)
To avoid the complicated calculations we can use the online bionomial probability distribution calculator we get 0.05748
Required answer:
a)- 0.126775
b)-=0.000004325376
c)-0.05748
you are in a hot air balloon that is 600 feet above the ground. if the angle from your line of sight to your friend is 20°, how far is he from the point on the ground.
Answer
x = 164.9 ft
Explanation:
Given the following figures
To find the distance from the point on the ground, we need to apply the SOH CAH TOA
[tex]\begin{gathered} \text{Height = 600 ft} \\ \text{Horizontal distance x} \\ \theta\text{ = 20} \\ \text{ }\tan \theta\text{ =}\frac{opposite}{\text{adjacent}} \\ \text{opposite = 600 ft} \\ \text{adjacent = x ft} \\ \tan \text{ 20 = }\frac{600}{x} \\ \text{Cross multiply} \\ x\cdot\text{ tan 20 = 600} \\ \text{x = }\frac{600}{\tan \text{ 20}} \\ \tan \text{ 20 = }0.3639 \\ \text{x = }\frac{60}{0.3639} \\ \text{x = }164\text{ .9 ft} \end{gathered}[/tex]Therefore, the distance is 164.9 ft
Which relationship can be represented by the equation y = 1/5x A) One wager jug hold 5 quarts. Let x represent the number of water jugs and y represent the number of quartsB) Bananas are on sale for $0.20 per banana. Let x represent the number of bananas and y represent the total cost, in dollars.C) David runs ar a constant rate. He runs 15 mines in 3 hours. Let x represent the number of hours and y present the number of miles.D) For every 10 gallons of water, Jasmine adds 2 cups of soap. Let x represent the number of hours and y represent the number of miles.E) The library charges a few at a rate of $5 for every 10 days a book is late. Let x represent the number of days late and y represent the fee, in dollars.
Answer:
Explanation:
Option A
[tex]\begin{gathered} \text{One wager jug hold 5 quarts} \\ y=kx \\ 5=1k \\ y=5x \end{gathered}[/tex]Option B
[tex]\begin{gathered} 1\text{ banana costs \$}$0.20$ \\ y=0.20x \\ y=\frac{1}{5}x \end{gathered}[/tex]The correct choice is B.
Pls help now You play a game that requires rolling a 6 sided die then randomly choosing a colored card from a deck containing 5 red cards,4blue cards, and 8 yellow cards find the probability that you will roll 3 on the die and choose a yellow card
Find the probability that you will get a 3 on a roll of a die. Since there is only one 3 in a die and there are 6 sides in a die, divide 1 by 6.
[tex]P(3)=\frac{1}{3}[/tex]Find the probability that you will get a yellow card. Divide the number of yellow cards by the total number of cards.
[tex]\begin{gathered} P(y)=\frac{8}{5+4+8} \\ =\frac{8}{17} \end{gathered}[/tex]Since the two events are independent, multiply the obtained probabilities.
[tex]undefined[/tex]what is the common difference in the sequence 25,20,15,10...?
We have a arithmetic sequence: 25, 20, 15, 10...
Tipically, arithmetic sequences can be written in recursive form as:
[tex]a_n=a_{n-1}+d[/tex]where a(n) and a(n-1) are consecutive terms and d is the common difference.
In this case, we can see that each term decreases by 5 units.
Then, we can describe this sequence as:
[tex]a_n=a_{n-1}-5[/tex]which means that d = -5.
Answer: the common difference is d = -5.
The graphs of y = f(x) and y = g(x) are shown on the coordinate plane below.y = g(x) 10y = f(x)210-10-9-8-7 -6 -5 -4 -3 -2 -1 0- 1-26789 10-6-107If g(x) = k·f(x), what is the value of k?
Answer:
Explanation:
The first step is to find the equation of both lines. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept. It is the value of y at the point where the line cuts the vertical axis.
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of selected initial and final points on the line.
x1 and x2 are the x coordinates of the selected initial and final points on the line.
Considering labelled points on y = f(x),
when x1 = 0. y1 = - 3
when x2 = 2, y2 = 1
m = (1 - - 3)/(2 - 0) = 4/2 = 2
y intercept, c = - 3
The equation would be
y = f(x) = 2x - 3
Considering labelled points on y = g(x),
when x1 = 0. y1 = 6
when x2 = 2, y2 = - 2
m = (- 2 - 6)/(2 - 0) = - 8/2 = - 4
y intercept, c = 6
The equation would be
y = g(x) = - 4x + 6
The solution of both equations is the coordinate of the point of intersection. Thus,
Solution = (1.5, 0)
Given that
g(x) = kf(x), it means that
- 4x + 6 = k(2x - 3)
Substituting x = 1.5 into the equation, we have
- 4(1.5) + 6 = k(2 * 1.5) - 3
- 6 + 6 = 3k - 3
0 = 3k - 3
3k = 3
k = 3/3
k = 1
Given the figure below, find the values of x and z. (9x + 70). (6x + 80).
( 9x+70)+(9x+70) + (6x + 80) + (6x+ 80 ) = 360
If you solve the equation you get that
x = --44/5
Now, since
z = ( 6x +80 ) = ( 6*(-44/5) + 80 ) = 136 / 5
So, there you have, x,z
A biologist measured the length and mass of 20 reptiles. The equation y = 0.3x - 2 is the line of best fit for the data, where x is the length, incentimeters, and y is the mass, in grams.Based on the equation, what is the approximate length of a reptile that has a mass of 20.5 grams?
If the mass is 20.5 grams, then you have to replace y = 20.5 in the equation.
20.5 = 0.3x - 2
and solve for x, as follows:
20.5 + 2 = 0.3x
22.5 = 0.3x
22.5/0.3 = x
75 = x
The approximate length is 75 cm
1/2 + 1/5 = * Your answer
We applied the rules for adding fractions with different denominators. This is a way to achieve this. Graphically, we do the operations in this way:
Answer:
7/10
Step-by-step explanation:
1/2 + 1/5
We need to get a common denominator
1/2 * 5/5 = 5/10
1/5 * 2/2 = 2/10
We can add these together
5/10 + 2/10 = 7/10
Question 8 of 10The function y: -2(x - 2)2 + 6 shows the daily profit (in hundreds of dollars)of a hot dog stand, where x is the price of a hot dog (in dollars). Find andinterpret the zeros of this function,Select two answers: one for the zeros and one for the interpretation,A. The zeros are the hot dog prices that give $0.00 profit (no profit).B. Zeros at x =23o C. The zeros are the hot dog prices at which they sell o hot dogs.D. Zeros at x = 2 and x = 6SUBMIT
For the interpret we have that the answer is: A. The zeros are the hot dog prices that give $0.00 profit (no profit).
the other answer is:
so the zeros are 0.27 and 3.37.
The weight (W kg) of a decaying radio active substance after n years is given by W= Wo(1/2)^n/100, where Wo kg is the initial weight of the substance. 1. Atleast how many years will it take for the radioactive substance to lose to 10% of its initial weight?
Answer:
332.19 years
Explanation:
The weight, W of the substance after n years is given by:
[tex]W=W_o\mleft(\frac{1}{2}\mright)^{\frac{n}{100}}[/tex]Let the initial weight = 100%
If the substance loses to 10% of its initial weight, then:
• Wo = 100%
,• W= 10%
Substitute these into the formula:
[tex]\begin{gathered} \frac{10}{100}=\frac{100}{100}\mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \\ \implies0.1=\mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \end{gathered}[/tex]We then solve the equation for the value of n.
Take the logarithm of both sides.
[tex]\begin{gathered} \log (0.1)=\log \mleft(\frac{1}{2}\mright)^{\frac{n}{100}} \\ \implies\log (0.1)=\frac{n}{100}\log (\frac{1}{2})^{} \end{gathered}[/tex]Then divide both sides by log(1/2):
[tex]\begin{gathered} \frac{\log (0.1)}{\log (\frac{1}{2})}=\frac{\frac{n}{100}\log(\frac{1}{2})^{}}{\log(\frac{1}{2})} \\ \implies\frac{n}{100}=\frac{\log (0.1)}{\log (\frac{1}{2})} \end{gathered}[/tex]Finally, multiply both sides by 100:
[tex]\begin{gathered} 100\times\frac{n}{100}=100\times\frac{\log (0.1)}{\log (\frac{1}{2})} \\ n=332.19\text{ years} \end{gathered}[/tex]It will take at least 332.19 years for the radioactive substance to lose to 10% of its initial weight.
to qualify for a police academy, candidates must score in the top 21% on a general abilities test. assume the test scores are normally distributed and the test has a mean of 200 and a standard deviation of 20. find the lowest possible score to qualify
The lowest value that is needed in order to qualify is given as 216.128
What is z score?The Z score is used to calculate how many standard deviations above or below the mean the raw score is. It comes from:
z = (raw score - mean) / standard deviation
Given; mean of 200 and a standard deviation of 20
P(z > c) = 21% = 0.21
1 - P(z < c) = 0.21
P(z < c) = 0.79
we are to find the critical value of z using excel function
=NORM.S.INV(1-0.21)
= 0.806421247
To get the lowest value we would have to put the values in the formula
0.8064 = (x - 200)/20
0.8064 * 20 = (x - 200)
16.128 = (x - 200
take like terms
x = 200 + 16.128
x = 216.128
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Frank has a circular Garden the area of the garden is 100 ft Square what is the approximate distance from the edge of Frank's garden to the center of the garden (A= 3.14r ² )
ANSWER
[tex]5.64ft[/tex]EXPLANATION
The approximate distance from the edge of the garden to the center is the radius of the garden.
The area of a circle is given as:
[tex]A=\pi\cdot r^2[/tex]We can find the radius by making r the subject of the formula:
[tex]\begin{gathered} \frac{A}{\pi}=\frac{\pi\cdot r^2}{\pi} \\ r^2=\frac{A}{\pi} \\ r=\sqrt[]{\frac{A}{\pi}} \end{gathered}[/tex]Therefore, the approximate distance from the edge of the garden to the center (radius) is:
[tex]\begin{gathered} r=\sqrt[]{\frac{100}{3.14}} \\ r=\sqrt[]{31.85} \\ r\approx5.64ft \end{gathered}[/tex]That is the answer.
I really need help pleasecheck if letter a is correct.
The angle of C and F are [tex]98^{0}[/tex] and [tex]108^{0}[/tex]
The sum of a triangle's angles equals the straight angle (180 degrees, radians, two right angles, or a half-turn) in Euclidean space. A triangle is defined by three angles, one at each vertex, and two adjacent sides.
Given that in ∆ ABC A =[tex]30^{0}[/tex] and B = [tex]52^{0}[/tex] and in ∆ DEF D =[tex]22^{0}[/tex] and E = [tex]50^{0}[/tex]
We have to find the angles of C and F
We know that sum of triangles = 180
Now from ∆ ABC
30 + 52 + C = 180
C + 82 = 180
C = 180 - 82
C = 98
Now from triangle DEF
22 + 50 + F = 180
72 + F = 180
F = 180 - 72
F = 108
Therefore the angle of C and F are 98 and 108
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200×200 dividend by 20
We need to find the value of 200×200 dividend by 20
So,
[tex]\frac{200\cdot200}{20}=\frac{40000}{20}=2000[/tex]In the following diagram, D Z B 30° 60° 150 a A i) Value of y = ii) Value of : (to the nearest tenth) =
Bricjk Ranger, this is the solution:
Part i.
y = Hypotenuse * sin (30)
y = 150 * 0.5
y = 75
Part ii.
Step 1: Let's calculate the lenght of the hypotenuse, as follows:
Hypotenuse or AB = 75/sin (60)
Hypotenuse or AB = 86.6 (to the nearest tenth)
Step 2: Now we can calculate the value of z, this way:
z = √86.6² - 75²
z = √7,500 - 5,625
z = √1,875
z = 43.3
Question 2 of 5
√16 =
Ο Α. 6
OB. 4
C. 8
OD. 3
Answer:
Uhm if this is the square root of 16 it's B.) 4
Marco and Jazmin each bought trees to plant from Lowe’s. Marco spent $188 on 7 lemon trees and 9 orange trees. Jazmin spent $236 on 13 lemon trees and 9 orange trees. How much did lemon trees cost? How much did orange trees cost?
Let x be the cost of each Lemon tree and y the cost of eache orange tree. So we get that
[tex]\begin{cases}7x+9y=188 \\ 13x+9y=236\end{cases}\rightarrow6x=48\rightarrow x=\frac{48}{6}=8[/tex]having that the lemon tree cost $8 we get that
[tex]56+9y=188\rightarrow9y=188-56=132\rightarrow y=\frac{132}{9}=\frac{44}{3}[/tex]so each orange tree cost $44/3
−5x+8?I need the Answer please!!
We have the next expression
[tex]-5x+8[/tex]And we must solve it for x
[tex]undefined[/tex]Divide 30.4cm into 8 equal parts.
Find the length of each part.
Answer:
304/10÷8/1
304/10×1/8
38/10
3.8
or
304÷8
=38
Express the ratio in simplest form:1.25naira ratio 5naira
Answer:
1:4
Explanation:
Given the ratio:
[tex]1.25\colon5[/tex]Written in fraction form, we have:
[tex]\frac{1.25}{5}=\frac{1.25}{1.25\times4}=\frac{1}{4}=1\colon4[/tex]The ratio in simplest form is 1:4.
Solve for n: 400(1.16)^n=35,120
The given equation is:
[tex]400\left(1.16\right)^n=35120[/tex]It is required to solve the equation for the value of n.
Divide both sides of the equation by 400:
[tex]\begin{gathered} \frac{400\left(1.16\right)^n}{400}=\frac{35120}{400} \\ \\ \Rightarrow\left(1.16\right)^n=\frac{439}{5} \end{gathered}[/tex]Take the logarithm of both sides of the equation:
[tex]\begin{gathered} \log(1.16)^n=\log\left(\frac{439}{5}\right) \\ \text{ Apply the power property of logarithms:} \\ \Rightarrow n\log(1.16)=\log\left(\frac{439}{5}\right) \end{gathered}[/tex]Divide both sides by log (1.16):
[tex]\begin{gathered} \frac{n\log(1.16)}{\log(1.16)}=\frac{\log\left(\frac{439}{5}\right)}{\log(1.16)} \\ \Rightarrow n=\frac{\operatorname{\log}(\frac{439}{5})}{\operatorname{\log}(1.16)}\approx30.151 \end{gathered}[/tex]The value of n is about 30.151.
find the probability for each situation. question 1. A number cube is a spun two times. find the probability that it will land on a event number both times.
In a number cube, the sample space is {1,2,3,4,5,6}.
The even numbers are {2,4,6}.
Determine the probability for cube landing with even number first times.
[tex]\begin{gathered} P(A)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Determine the probability for cube landing with even number in second time.
[tex]\begin{gathered} P(B)=\frac{3}{6} \\ =\frac{1}{2} \end{gathered}[/tex]Since both rolling of dices are independent to each other. So probability for getting even number on both time is,
[tex]\begin{gathered} P(AandB)=P(A)\cdot P(B) \\ =\frac{1}{2}\cdot\frac{1}{2} \\ =\frac{1}{4} \end{gathered}[/tex]Answer: 1/4
Graph the equation. y=9/x, x ≠ 0 Choose the correct graph below.
ANSWER
Option A
EXPLANATION
hello) i need some help with b) include an explanation if not a problem, thanks in advance)
What would happen if X doesn't lie on OM? If it is true that X lies on OM, if we suppose the opposite then we should have a contradiction, so the only way the contradiction doesn't happen is that it is true
Statements1. We know that BX:XA = 1:2
2. We know that M is the middle point between B and P
We need to prove that X lies on OM
Let's suppose X doesn't lie on OM
By 2, we know that 2BM = BP
If X doesn't lie on OM then the intersection between OM and BA is not X
Let's say the line that goes from O to the line BP and intersects BA on X is OX', where X'≠M
234Weight (pounds)OA. The weight of the package is a function of the number ofpackages.B. The shipping cost is a function of the number of packages.C. The shipping cost is a function of the weight of the package.OD. The weight of the package is a function of the shipping cost.SUBMIT
The graph representing the relation between the shipping cost and the weight of packages is shown.
It is required to choose which function is true about the functional relationship.
Since the shipping cost is at the vertical axis and the weight of packages is at the horizontal axis, it follows that the shipping cost is a function of the weight of the package.
The answer is C.
2. Calculate the gross pay for each of the following positions for a 30-hour work week: $8.50/hr $9.20/hr Locker room attendant Bus server Pantry help Waiter/Waitress $9.45/hr $7.00/hr a) Pantry help c) Waiter/Waitress b) Locker room attendant d) Bus server
We know that this position is paid with a ratio of $8.50 per hour. So, let's multiply to find the earnings for 30 hours.
[tex]8.50\cdot30=255[/tex]So, the earnings for this position is $255.
Bus server.This position is paid 9.20 per hour. So, 30 hours earnings would be
[tex]9.20\cdot30=276[/tex]Pantry help.The earnings for this position would be
[tex]9.45\cdot30=283.50[/tex]$283.50 for 30 hours.
Waiter/Waitress.The earnings for this position are
[tex]7\cdot30=210[/tex]$210 for 30 hours.
The function in the form f(x)=2/5x-5 is graphed below. What is the value of x when f(x)=-9?