x^-2 matches 1/36
x^-1 matches -1/6
x^0 matches 1
x^1 matches -6
x^2 matches 36
Explanation:When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:
x^-2: (-6)^-2 = 1/(-6)^2 = 1/36
x^-1: (-6)^-1 = 1/(-6) = -1/6
x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)
x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)
x^2: (-6)^2 = (-6) * (-6) = 36
Therefore, the matches are as listed above.
I found a place that will give me 20% discount if i spend over $50.My nill $75.How much money will i save?
Caleb's puppy weighs 2,250 grams. If the puppy weighed 600 grams at his last visit to the veterinarian's office, what is the percent increase in the puppy's weight rounded to the nearest whole number?
Answer: 275%
Step-by-step explanation:
Given : The current weight of the puppy : 2,250 grams
The weight of the puppy at the last visit = 600 grams
Increase in weight :-
[tex]2250\text{ grams}-600\text{ grams}=1650\text{ grams}[/tex]
Now, the formula to calculate the percentage increase is given by :-
[tex]\dfrac{\text{Increase in quantity}}{\text{Previous quantity}}\times100[/tex]
The percentage increase in weight is given by :-
[tex]\dfrac{1650}{600}\times100=275\%[/tex]
Hence, the percent increase in the puppy's weight = 275 %.
Emma is building a wall around her burning it has taken 45 minutes and she is 75% done what is the time it will take to finish building her wall
➷ 45 minutes is 3/4 of the total time
A simple way to do this is to find 1/4 of the time
To do this, divide by 3:
45/3 = 15
15 minutes is 1/4 of the time
To find the whole time, multiply this value by 4:
15 x 4 = 60
Subtract the time already passed from this:
60 - 45 = 15
It will take her 15 more minutes to finish building her wall.
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Find the lowest common denominator for these fractions and then add and simplify. 2/3 and 1/6
Answer:
Step-by-step explanation:
12 is the common denominator
The answer will be 6!!
A 65 inch wide screen television actually describes the length of the diagonal of a rectangular television with a length of 63 inches. What is the width of the television?
For this question we need to use the Pythagorean Theorem (a2+b2=c2) since the rectangle is being divided into two triangles.
we know the length of the triangle (63) and we know the hypotenuse (65) but not the width. To find the width, we can plug the values we know into our formula.
(63) squared + b squared = (65) squared
solve.
3969 + b squared = 4225
subtract 3969 from both sides.
b squared = 256
√b² = √256
b=16
Are the polygons similar? If they are, choose the correct similarity statement and scale factor.
The similarity is ΔRST ~ Δ UVW and Scale Factor is 5/6.
What is Similarity?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
From the Two Triangles we can see that
<VUW = <SRT = 32
and, SR / VU = TR / WU
10/ 12 = 15/ 16
5/6 = 5/6
So, By SAS similarity Criteria both Triangles are Similar.
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Elephant calves are expected to gain a certain amount of weight each day after birth. After the elephant keepers switched to a new formula for daily feedings of the youngest elephants, the keepers tracked the elephants’ weight gains to make sure that it was within a desired range. Would a bar graph or a histogram be better for displaying this data?
A Histogram would be better for displaying the data
A histogram would be better for displaying the data of elephant calves' weight gains after the switch to a new formula for daily feedings.
Explanation:A histogram would be better for displaying the data of elephant calves' weight gains after the switch to a new formula for daily feedings. A histogram is useful for displaying the distribution and frequency of a continuous dataset, such as the weight gains of elephant calves. It can show how many calves fall within each weight range, and provide a visual representation of the desired range of weight gain.
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Please help if you can i keep getting stuck
Ice cream in the shape of a sphere sits atop a cone as shown in the diagram below. Assume there is no ice cream inside the cone until after the ice cream melts. The diameter of the sphere and the diameter of the cone are both 4cm, and the height of the cone is 7.5 cm.
Part A: Determine whether the cone could contain all of the ice cream if it melted.
Part B: What would be the smallest cone in height in whole centimeters that would allow the cone to contain all of the melted ice cream if the diameter of the cone remains unchanged.
Part C: If the container of the ice cream changed to a cylinder as shown in the diagram below, what would be the smallest height of the cylinder needed to the nearest whole centimeter to contain the melted ice cream. Assume there is no ice cream n the cylinder before the ice cream melts. Please provide explanations so i can see where i messed up?
Answer:
Part A) The cone couldn't contain all the ice cream if it melted.
Part B) The height of the cone would be [tex]8\ cm[/tex]
Part C) The height of the cylinder would be [tex]3\ cm[/tex]
Step-by-step explanation:
Part A) Determine whether the cone could contain all of the ice cream if it melted
step 1
Find the volume of the ice cream (sphere)
The volume is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
substitute
[tex]V=\frac{4}{3}\pi (2)^{3}=\frac{32}{3}\pi\ cm^{3}[/tex]
step 2
Find the volume of the cone
The volume is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=7.5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}\pi (2)^{2}(7.5)=\frac{30}{3}\pi\ cm^{3}[/tex]
step 3
Compare the volume of the sphere and the volume of the cone
[tex]\frac{30}{3}\pi\ cm^{3} < \frac{32}{3}\pi\ cm^{3}[/tex]
The volume of the cone is less than the volume of the sphere
therefore
The cone couldn't contain all the ice cream if it melted.
Part B) What would be the smallest cone in height in whole centimeters that would allow the cone to contain all of the melted ice cream if the diameter of the cone remains unchanged
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
we have
[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]
[tex]r=2\ cm[/tex]
substitute in the formula and solve for h
[tex]\frac{32}{3}\pi=\frac{1}{3}\pi (2)^{2}h[/tex]
simplify
[tex]32=(2)^{2}h[/tex]
[tex]32=4h[/tex]
[tex]h=32/4=8\ cm[/tex]
Part C) If the container of the ice cream changed to a cylinder as shown in the diagram below, what would be the smallest height of the cylinder needed to the nearest whole centimeter to contain the melted ice cream
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]
[tex]r=2\ cm[/tex]
substitute in the formula and solve for h
[tex]\frac{32}{3}\pi=\pi (2)^{2}h[/tex]
simplify
[tex]\frac{32}{3}=(2)^{2}h[/tex]
[tex]\frac{32}{3}=4h[/tex]
[tex]h=\frac{32}{12}=2.67\ cm[/tex]
Round to the nearest whole centimeter
[tex]2.67=3\ cm[/tex]
Let u=ln x and v= ln y. Write ln( √x · y^2) in terms of u and v.
Answer:
C
Step-by-step explanation:
We can use 2 properties of logarithms to write this:
1. ln(x*y) = lnx + ln y
2. ln(a^b) = b ln a
Using property 1, we can write as:
[tex]ln(\sqrt{x} *y^{2})\\=ln(\sqrt{x} )+ln(y^2)\\=ln(x^{\frac{1}{2}})+2lny\\=\frac{1}{2}lnx+2lny[/tex]
We know u = lnx and v = ln y, we simply substitute it now:
[tex]\frac{1}{2}lnx+2lny\\=\frac{1}{2}u+2v[/tex]
the correct answer is C
Answer:
c
Step-by-step explanation:
Let u= ln x and v=ln y. Write ln(x^3y^2) in terms of u and v.
a. 3u + 2v
Step-by-step explanation:To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called the logarithm of a product is the sum of the logarithms, that is:
[tex]log_{b}(MN)=log_{b}(M)+log_{b}(N)[/tex]
From the function, it is then true that:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})[/tex]
The other property we must use is Logarithm of a Power:
[tex]log_{b}M^{n}=nlog_{b}M[/tex]
Then:
[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2}) \\ \\ ln(x^{3}y^{2})=3ln(x)+2ln(y)[/tex]
Since:
[tex]u=ln(x) \\ v=ln(y)[/tex]
Then:
[tex]ln(x^{3}y^{2})=3u+2v[/tex]
Finally, the correct option is:
a. 3u + 2v
Answer:
A edge
Step-by-step explanation:
Use factoring and the zero-product property to solve the following problems.
Answer:
see explanation
Step-by-step explanation:
Divide through by 2
2a² - 5a + 3 = 0
To factor the quadratic
Consider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 3 = 6 and sum = - 5
The factors are - 2 and - 3
Use the factors to split the a- term
2a² - 2a - 3a + 3 = 0 ( factor the first/second and third/fourth terms )
2a(a - 1) - 3(a - 1) = 0 ← factor out (a - 1)
(a - 1)(2a - 3) = 0
Equate each factor to zero and solve for a
a - 1 = 0 ⇒ a = 1
2a - 3 = 0 ⇒ 2a = 3 ⇒ a = [tex]\frac{3}{2}[/tex]
Answer:
a = 3/2 or 1
Step-by-step explanation:
4a²-10a+6=0
(Divide by 2)
2a²-5a+3=0
(Now factorise)
(2a-3)(a-1)
a = 3/2 or 1
Max is 33 and smokes. How much would he save next year on a $75,000 policy if he quit smoking compared to if he continued smoking? Show your work or explain how you got your answer.
Answer:
Max would save $126 if he quit smoking.
Step-by-step explanation:
It is given that the age of max is 33.
From the given table it is clear that the monthly premium for every $25000 of coverage for age group 31-40 non smoker male is 5.50 and smoker male is $9.00.
Total yearly premium for $75000 for non smoker male of 33 age is
[tex]P_1=5.50\times 3\times 12=198[/tex]
Total yearly premium for $75000 for smoker male of 33 age is
[tex]P_2=9.00\times 3\times 12=324[/tex]
If he quit smoking then he save
[tex]Saving=P_2-P_1[/tex]
[tex]Saving=324-198[/tex]
[tex]Saving=126[/tex]
Therefore max would save $126 if he quit smoking.
Given kite LNOM, what are the lengths of MX and XN ?
Answer:
Step-by-step explanation:
MX = XN
5r² + 2r + 52 = 4r² + 12r + 27
5r² - 4r² + 2r - 12r + 52 - 27 = 0
r² - 10r + 25 = 0
(r - 5)² = 0
r - 5 = 0
r = 5
4r² + 12r + 27
4•5² + 12•5 + 27
4•25 + 60 + 27
100 + 60 + 27
187
The Second one
I hope I helped you.
If the Laffite family deposits $8500 in savings account at 6.75% interest, compounded continuously, how much will be in the account after 25 years
Answer:
Option b
Step-by-step explanation:
We have a compound interest problem. With an annual interest rate of 0.675 and an initial payment of 8500, with t = 25 years
Then you must use the annual compound interest formula, which is represented by a growing exponential function:
[tex]y = e ^{ht}[/tex]
Where:
h is the interest rate of 0.675
y is the money in the savings account as a function of time
Then substitute the values in the formula and we have:
[tex]y = e ^{0.675(25)}[/tex]
[tex]y = 45,950.57[/tex]
A supervisor has asked her team to improve its average talk Time Performance the team's average talk time is 13 minutes per call in the average for the call center is 8 minutes per call the following week the supervisor reports the following results John's went from 15 minutes to 16.5 minutes George's went to from 15 minutes to 14 minutes Paul's went from 12 minutes to nine minutes and Ringoes went from 12 minutes to 2 minutes whose performance improve the most While most likely giving the best service to customers?
Answer:
john
Step-by-step explanation:
Eight boys and seven girls showed up to one of the team's games. League rules limit each team to 10 players at a time (five girls and five boys) per game. Given this rule, how many combinations of 10 players are there among the 15 boys and girls who showed up at this particular game?
Answer:
1176 Combinations
Step-by-step explanation:
As mentioned in the question, there are total 8 boys and 7 girls.
Our objective is to create a team with 5 boys and girls each.
To select 5 boys out of 8, we will use combination.
=> 8C5 = [tex]\frac{8!}{5!(8-5!)}[/tex]
=> [tex]\frac{8.7.6.5!}{5!.3!}[/tex]
=> [tex]\frac{8.7.6}{6}[/tex]
=> 56
Similarly,
5 girls are selected using 7C5
=> 21
Therefore, the total combination of players are 56 * 21 = 1176
If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function". C = {(9, 1) (8, -3) (7, 5) (-5, 3)} Domain: {9, 8, 7, -5} Range: {1, -3, 5, 3} Domain: {1, -3, 5, 3} Range: {9, 8, 7, -5} not a function
Answer:
Domain: {9, 8, 7, -5}Range: {1, -3, 5, 3}Step-by-step explanation:
The function is a special relationship where each input has a single output.
We have C = {(9, 1); (8, -3); (7, 5); (-5, 3)}.
It's a function:
each values of x: 9, 8, 7, -5 has one value of y: 1, -3, 5, 3.
The doimain is set os x: {9, 8, 7, -5}.
The range is set of y: { 1, -3, 5, 3}.
F = {(x, y ) | x + y = 10}.
Domain: {10} Range: {10}
The prices of five used cars are given below. Which price is an outlier to the data set?
$16,250, $11,495, $10,022, $9,053, $12,244
$9,053
$11,495
$12,244
There are no outliers.
Answer:
There are no outliers
Step-by-step explanation:
An outlier is a number thats far different than the numbers selected. All of these numbers are close to each other.
Answer:
Option D. there are no outliers.
Step-by-step explanation:
The given prices of five used cars in the data set we have to find the outlier number.
Outlier number in a data set is very different from the data set values. It may be more greater or more lower numbers from the other numbers.
In the given data set all the numbers are close to each other.
Therefore, Option D. there are no outliers.
How many terms are in the following sequence? 131072, ..., 8, 4, 2
Answer:
17 terms
Step-by-step explanation:
131072 = 2^17
8 = 2^3
4 = 2^2
2 = 2^1
Apparently, the sequence is powers of 2 from 17 down to 1, so there are 17 terms in the sequence.
Do you think this graph looks more like a quadratic or exponential function? Why do you think so?
Answer:
Exponential Function
Step-by-step explanation:
The y-axis represents the number of Bacteria and x-axis represents the number of hours. If you observe closely you will see that the number of bacteria are doubling after each hour. For example, at time = 4 hours the number of Bacteria were about 50, at time = 5 hours the number of Bacteria were about 100 and at time = 6 hours the number of Bacteria increased to about 200.
This type of behavior is a property of exponential functions where we see a multiplicative rate of change in the values i.e. each value is a multiple of previous value. A rough model for this function would be:
[tex]f(x)=f(0)(2)^{x}[/tex]
Where, f(0) represents the number of bacteria at time = 0 hours i.e. number of Bacteria initially present and "x" represents the number of hours.
I NEED HELP PLEASE!!
if Q=2.1R+5 find Q when R=5
Answer:
If Q=2.1(R)+5, then it would be 2.1(5)+5=15.5 ?
Step-by-step explanation:
how does the area of triangle ABC Compare to the area of parallelogram ghjk
Answer:
Area of parallelogram divided by 2 is the triangles are.
Area of parallelogram = B x H and triangle area = 1/2 x B x H
Step-by-step explanation:
Answer:
A ) The area of Δ ABC is 2 units greater than area of parallelogram GHJK.
Step-by-step explanation:
Which translation results in a circle whose center is at the origin? Question 5 options: Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down. Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down. Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up. Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up.
Answer:
case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down
Step-by-step explanation:
Verify the 4 Options
case 1) Circle open parentheses x plus 2 close parentheses squared plus open parentheses y minus 6 close parentheses squared equals 4 translated 2 units right and 6 units down
The equation of the circle is
[tex](x+2)^{2}+(y-6)^{2}=4[/tex]
The center of the circle is the point [tex](-2,6)[/tex]
The rule of the translation is
[tex](x,y)-------> (x+2,y-6)[/tex]
Applying the rule to the center
[tex](-2,6)-------> (-2+2,6-6)[/tex]
[tex](-2,6)-------> (0,0)[/tex]
Therefore
The translation results in a circle whose center is at the origin
case 2) Circle open parentheses x minus 1 close parentheses squared plus open parentheses y plus 2 close parentheses squared equals 4 translated 1 unit left and 2 units down
The equation of the circle is
[tex](x-1)^{2}+(y+2)^{2}=4[/tex]
The center of the circle is the point [tex](1,-2)[/tex]
The rule of the translation is
[tex](x,y)-------> (x-1,y-2)[/tex]
Applying the rule to the center
[tex](1,-2)-------> (1-1,-2-2)[/tex]
[tex](1,-2)-------> (0,-4)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
case 3) Circle open parentheses x minus 2 close parentheses squared plus open parentheses y plus 3 close parentheses squared equals 4 translated 2 units right and 3 units up
The equation of the circle is
[tex](x-2)^{2}+(y+3)^{2}=4[/tex]
The center of the circle is the point [tex](2,-3)[/tex]
The rule of the translation is
[tex](x,y)-------> (x+2,y+3)[/tex]
Applying the rule to the center
[tex](2,-3)-------> (2+2,-3+3)[/tex]
[tex](2,-3)-------> (4,0)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
case 4) Circle open parentheses x minus 3 close parentheses squared plus open parentheses y minus 5 close parentheses squared equals 4 translated 3 units left and 5 units up
The equation of the circle is
[tex](x-3)^{2}+(y-5)^{2}=4[/tex]
The center of the circle is the point [tex](3,5)[/tex]
The rule of the translation is
[tex](x,y)-------> (x-3,y+5)[/tex]
Applying the rule to the center
[tex](3,5)-------> (3-3,5+5)[/tex]
[tex](3,5)-------> (0,10)[/tex]
Therefore
The translation results in a circle whose center is not at the origin
Find the rectangular coordinates of the point with the polar coordinates (8, 3 divided by 2 pi ). (1 point) (0, -8) (0, 8) (8, 0) (-8, 0)
Answer:
(x,y) = (0,-8)
Step-by-step explanation:
We know that a point in polar coordinates is represented by
(r, θ)
Where r is the distance from the origin and θ is the angle.
Rectangular coordinates can be found by
x = r*cos(θ)
y = r*sin (θ)
x = r*cos(θ) = 8* cos (3π/2)
y = r*sin (θ) = 8 sin(3π/2)
x = 8* cos (3π/2) = 8*0 = 0
y = 8* sin (3π/2) = 8*(-1) = -8
(x,y) = (0,-8)
Correct option is (A) (0,-8)
Now any point in polar coordinates is represented by
(r, θ)
where 'r' is the distance from the origin
and 'α' is the angle.
Rectangular coordinates can be found by using the formula:
[tex]x=r*cos(\alpha )\\y=r*sin(\alpha )[/tex]
Thus the x coordinate would be given as :
[tex]x=r*cos(\alpha )\\x=8*cos(\frac{3\pi }{2} )\\x=8*0\\x=0\\[/tex]
Similarly the y coordinate would be given as :
[tex]y=r*sin(\alpha )\\y=8*sin(\frac{3\pi }{2} )\\y=8*(-1)\\y=-8\\[/tex]
Thus (x, y) = (0,-8) is the required coordinates
20 points!!! Please Help
Does the equation x2 - 4x + y2 = -3 intersect the x-axis?
Answer:
Yes, twice
Step-by-step explanation:
The equation will intersect the x-axis when y = 0, so we have
x² - 4x = -3 now solve this quadratic for x...
x² - 4x + 3 = 0
factor...
(x - 3)(x - 1) = 0,
so at x = 1 and x = 3, the function crosses the x-axis
See the graph below
Yes, because the center is on the x-axis, the circle will intersect 2 times, at x=1 and at x=3
The perimeter of a playing field for a certain sport is 320 ft. The field is a? rectangle, and the length is 48 ft longer than the width. Find the dimensions.
Answer:
length: 104 ftwidth: 56 ftStep-by-step explanation:
Let L and W represent the length and width of the field. Then the perimeter is given by ...
P = 2(L +W)
Filling in the given information, we have ...
320 = 2(L +W)
L = W +48 . . . . . . the length is 48 ft longer than the width
Using the second equation in the first, we get
320 = 2((W +48) +W)
320 = 4W +96 . . . . . . simplify
224 = 4W . . . . . . . . . . subtract 96
56 = W . . . . . . . . . . . . .divide by 4
L = 56 +48 = 104 . . . . find L using the above relation
The width of the field is 56 ft; the length is 104 ft.
The width of the playing field is 56 ft and the length is 104 ft.
Explanation:To solve this problem, let's set up an equation using the information given. Let's say the width of the field is x ft. Since the length is 48 ft longer than the width, the length can be represented as x + 48 ft. The formula for the perimeter of a rectangle is P = 2(l + w), so we can set up the equation: 320 = 2(x + 48 + x). Now, we can solve for x by simplifying and solving the equation.
320 = 2(2x + 48)
320 = 4x + 96
4x = 320 - 96
4x = 224
x = 224/4
x = 56
So, the width of the field is 56 ft and the length is 56 + 48 = 104 ft.
To solve this problem, we must use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
According to the question, the length is 48 ft longer than the width, therefore we could express the length as L = W + 48. The perimeter provided is 320 ft. Now we can plug these values into the perimeter formula.
320 = 2(W + 48) + 2W
After simplification, this formula becomes 320 = 4W + 96.
To isolate W, you subtract 96 from both sides to get: 320 - 96 = 4W + 96 - 96, which simplifies to 224 = 4W. Dividing both sides by 4 gives W = 56 ft. This is the width of the field. The length, then, is 56 ft + 48 ft = 104 ft (since the length is 48 ft longer than the width).
So, the dimensions of the field are 104 feet by 56 feet
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A fair coin is tossed three times in succession. Find the probability if getting exactly one tail
Answer:
If a fair coin is tossed three times, sample = 2^3 = 8 (hhh, hht, hth, thh, htt, tht, tth, ttt) where h=head and t=tail.
Probability of getting one:
Outcomes with one head (h) = 3
P(1 h) = 3/8 = 0.375
The probability of getting exactly one tail when a fair coin is tossed three times in succession is 37.5%.
Explanation:The probability of getting exactly one tail when a fair coin is tossed three times in succession can be found using the binomial probability formula.
Let's denote success as getting a tail and failure as getting ahead. The probability of success, denoted as p, is 0.5 since the coin is fair and has an equal chance of landing on heads or tails. The probability of failure, denoted as q, is also 0.5.
Using the binomial probability formula: P(X = k) = [tex]C(n, k) * p^k * q^(n-k)[/tex], we can calculate the probability as follows:
n = 3 (number of trials) k = 1 (number of tails desired) C(n, k) = C(3, 1) = 3 (number of ways to choose 1 tail from 3 trials)[tex]p^k = 0.5^1[/tex] = 0.5 (probability of getting 1 tail)[tex]q^(n-k) = 0.5^(3-1)[/tex] = 0.25 (probability of getting 2 heads)Plug these values into the formula: P(X = 1) = 3 * 0.5 * 0.25 = 0.375 (or 37.5%)Therefore, the probability of getting exactly one tail when a fair coin is tossed three times in succession is 0.375 or 37.5%.
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jeffrey is flying a kite but it got caught at the top of a 15 foot tree tha is 60 feet away from where he is standing. if the strong is tight, how long is the string that he has let out?
Found this on a website! Hope this is helpful!
what is equivalent to (5x-6) (2x+3) ?
a. (5x-6) (2x) + (5x -6) (3)
b. (5x-6) (2x) - (5x-6) (3)
c. (5x) (2x) + (6) (3)
d. (5x-6) (2x) + (-6)(3)
The expression is equivalent to (5x-6) (2x) + (5x-6) (3).
Option (A) is correct.
It is to find equivalent of (5x-6) (2x+3).
What is polynomial?An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.
when we multiply to (5x-6) to (2x+3).
Each term of (5x-6) is multiply to (2x+3).
so (5x-6) is multiply to 2x and (5x-6) is multiply to 3 separately.
so, the expression is equivalent to (5x-6) (2x) + (5x-6) (3).
Learn more about polynomial here:
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Describe how to translate the graph of g(x) = ln x into the graph of f(x)= ln (-5)+5
Answer:
B
Step-by-step explanation:
We know:
1. Replacing -x into x of an equations reflects the graph on the y-axis
2. If f(x) is a function, then f(x)+a is a vertically translated graph of the original graph, a units up
Looking at the original function of ln x and the transformed graph of ln(-x) +5, we see that we have replaced x with -x, which means it is a reflection across the y-axis.
Also, we have added a five after the function, so that means it is a vertical translation of 5 units up.
Looking at the answer choices, we see that B is the correct answer.