Rounded to the nearest hundredth, the area of △ABC is 27.28 .
What is Area ?
Area is a measure of the amount of space inside a two-dimensional shape, such as a square, rectangle, triangle, circle, or any other shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, or square meters.
To find the area of △ABC, we can use the formula:
A = (1÷2)bh
where A is the area of the triangle, b is the length of the base, and h is the height.
In △ABC, we can use AB as the base and drop a perpendicular from A to BC to find the height. Let D be the foot of the perpendicular from A to BC.
First, we can find BD using the trigonometric ratio for the angle 27°:
tan(27°) = BD/AB
BD = AB * tan(27°)
BD = 7.8 ft * 0.5095
BD ≈ 3.97 ft
Next, we can find the length of CD:
CD = BC - BD
CD = 10.7 ft - 3.97 ft
CD ≈ 6.73 ft
Now we can use the Pythagorean theorem to find the length of AD:
AD*AD= AB*AB - BD*BD
AD* AD = (7.8 * 7.8 ) - (3.97 * 3.97)
AD ≈ 6.99 ft
Finally, we can use the formula for the area of the triangle:
A = (1÷2)bh
A = (1÷2)(7.8 ft)(6.99 ft)
A ≈ 27.28
Therefore, Rounded to the nearest hundredth, the area of △ABC is 27.28.
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the number of skittles in a giant-size bag is between 1150 and 1300 candies, and is uniformly distributed. what is the probability that a bag contains between 1200 and 1225 candies? enter your answer as a percentage accurate to two decimal places. for example, a probability of 0.4567 is 45.67% so it should be entered as 45.67.
The required probability of the candies in the bag having width between 1200 and 1225 is given by 16.67%.
The range of the number of skittles in the bag is 1150 to 1300 candies and is uniformly distributed.
This implies that the probability density function is a horizontal line over this interval.
The width of the interval we are interested in is 1225 - 1200 = 25 candies.
The total width of the interval is 1300 - 1150 = 150 candies.
The probability that the bag contains between 1200 and 1225 candies is equals to,
= ( Width of the required interval ) / (Total width of the interval )
= 25 / 150
= 0.1667
This means that the probability is 16.67% accurate to two decimal places.
Therefore, the probability of the bag contains candies between 1200 and 1225 is equal to 16.67%.
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You have $10,000 to invest, and three different funds from which to choose. The municipal bond
fund has a 7% return, the local bank's CDs have an 8% return, and the high‐risk account has an
expected (hoped‐for) 12% return. To minimize risk, you decide not to invest any more than $2,000
in the high‐risk account. For tax reasons, you need to invest at least three times as much in the
municipal bonds as in the bank CDs. Assuming the year‐end yields are as expected, what are the
optimal investment amounts?
Best investment amounts are $2,000 in high-risk account, $1,000 in bank certificates of deposit, and $7,000 in municipal bonds and remaining $4,000 placed in municipal bonds to optimize return while lowering risk.
We must adhere to two criteria in order to find the best investment amounts: reducing risk and satisfying tax obligations.
Let's think about the high-risk account first. We will only put $2,000 in this account because that is the most we are ready to risk because we want to keep the risk to a minimum.
Let's go on to the tax regulations. We must invest at least $3,000 in municipal bonds to reach the three times minimum investment requirement in municipal bonds compared to bank CDs. We will therefore put $1,000 into bank CDs and $3,000 into municipal bonds.
We currently have $2,000 set aside for the high-risk account, $1,000 for bank CDs, and $3,000 set aside for municipal bonds. We are now left with $4,000 to invest.
This $4,000 can be invested in a way that strikes a compromise between the need to reduce risk and the desire for great returns. We have the choice of investing the final $4,000 in either municipal bonds or CDs from a nearby bank, depending on our investment alternatives.
Our total investment would be $5,000 in bank CDs, $3,000 in municipal bonds, and $2,000 in the high-risk account if we choose to invest the additional $4,000 in the local bank CDs. The expected return from this is:
($5,000 x 8%) + ($3,000 x 7%) + ($2,000 x 12%) = $400 + $210 + $240 = $850.
If we choose to invest the $4,000 in municipal bonds, our overall investment will consist of $2,000 in the high-risk account, $1,000 in bank CDs, and $7,000 in municipal bonds. The expected return from this is:
($1,000 x 8%) + ($7,000 x 7%) + ($2,000 x 12%) = $80 + $490 + $240 = $810.
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the area of a rectangle is what
Answer:
The area of rectangle is Length × Breadth
Step-by-step explanation:
You have already learnt that perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around a closed figure while area is the part of plane or reason occupied by the closed figure.
[tex] \sf \: Squares \: and \: Rectangles[/tex]
Ananya and samira made pictures. Ananya made her picture on a rectangular sheet of length 60 cm and breadth 20 cm while samira made hers on a rectangular seat of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated.
Who has to pay more for farming is the cost of farming is $3.00 per cm?
If the cost of lamination is $2.00 per cm², who has to pay more for lamination?
For finding the cost of farming, we need to find perimeter and then multiply it by the rate for farming. For finding the cost of lamination we need to find area and then multiply it by the rate of lamination.
Example:-Find the area of the rectangle whose Length is 4 cm and breadth/width is 6 cm .
Answer:
The area of the rectangle is 24 cm²
Step-by-step explanation:
Length of rectangle = 4 cm
Breadth of rectangle = 6 cm
[tex] \bf \: Formula \: used[/tex]
[tex] \sf \: Area_ { \{Rectangle \}} = Length × Breadth[/tex]
Now put values
[tex] \sf \: Length = 4 cm [/tex]
[tex] \sf \: Breadth = 6 cm[/tex]
[tex] \sf \: Length × Breadth = 4 × 6 \: cm [/tex]
[tex] \sf \implies 24 \: cm \ {}^{2} [/tex]
Always remember if we find area :-
After units like centimetres,metres we always put (²) on these units.
Like :- 26 cm², 56 m ²
In words = Twenty six centimetre square, Fifty six centimetre square
Required Answer :The area of rectangle is 24 cm²
Additional informatioNPerimeter
Parallelogram = 2(Base + Height)Triangle = a + b + cRectangle = 2(Length + Width)Square = 4×sideTrapezoid = Base + Base + side + sideRhombus = 4 × sideHexagon = 6 × sideArea
Square area formula: = side×sideRectangle area formula: = L × BCircle area formula: = πr²Circle sector area formula: = r² × angle / 2.Ellipse area formula: = Axis× Axis × πTrapezoid area formula: = (base + base) × h / 2.Area of a Triangle = A = ½ (b × h)♦ Area of Rectangle
Length × Breadth[tex] \underline{ \rule{140pt}{4pt}}[/tex]
Additional Information :-Area - Region occupied by figure is called area.
[tex] \large \bf{ \mathfrak{{More \: Formulas \: \red{( Area)}}}}[/tex]
[tex] \large \sf \leadsto \: triangle = \frac{1}{2} \times bh[/tex]
[tex]\large \sf \leadsto \: \: Rectangle \: = \: lb[/tex]
[tex]\large \sf \leadsto \: \: Square \: = {s}^{2} [/tex]
[tex]\large \sf \leadsto \: \: Parallelogram \: = \: bh[/tex]
[tex]\large \sf \leadsto \: \: Rhombus \: = \: \frac{1}{2} \times \: d1 \times d2[/tex]
[tex]\large \sf \leadsto \: \: Trapezium \: = \frac{1}{2} \times (x + y) \times h[/tex]
[tex]\large \sf \leadsto \: \: Quadrilateral \: = \: \frac{1}{2} \times d(h1 + h2)[/tex]
[tex]\large \sf \leadsto \: Circle \: = {\pi \: r}^{2} [/tex]
[tex]\large \sf \leadsto \: \: Equilateral \triangle \: = \frac{ \sqrt{3} }{4} \times {s}^{2} [/tex]
PLEASE HELP!!!
I don’t know how to solve this.
The length a of the right angle triangle is 13.74 cm.
How to find the length of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the opposite side of the right triangle a cm. The side a cm can be found using Pythagoras's theorem or trigonometric ratios.
Let's use Pythagoras's theorem,
a² + b² = c²
where
a and b are the legsc is the hypotenuse side15² - 6² = a²
225 - 36 = a²
1809 = a²
square root both sides of the equation
a = √189
a = 13.7477270849
a = 13.74 cm
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f(x)=x^4+2x^3-9x^2-2x+6 and f(-4)=0 algebraically find all the zeros.
If we know that f(-4) = 0, we can say that:
x + 4 is a factor of the function f(x).
This is because when we substitute x = -4 into the function, we get:
f(-4) = (-4)^4 + 2(-4)^3 - 9(-4)^2 - 2(-4) + 6 = 0
This means that (x + 4) is one of the factors of the function.
Now, we can use polynomial division or synthetic division to find the other factors. If we divide the function f(x) by (x + 4), we obtain:
x^3 - 2x^2 - 17x + 3
We can use the Factor theorem on this cubic function f(x) = x^3 - 2x^2 - 17x + 3.
If we try to substitute a = 1 we find that f(1) = -15 which is not zero. If we try to substitute a = -1, we find that f(-1) = 23 which is not zero.
Now we can solve as follows:
Let x = t - 2/3. After substitution we get a cubic equation.
t^3 -25/3 t - 85/27 = 0
We can find one root of this cubic by rational root theorem which is t = 5 or t = -17/3.
Now, we can use synthetic division again to divide f(x) by the binomial (x - 5). This gives us:
(x - 5)(x^2 + 3x - 1)
Therefore, the complete factorization of f(x) is:
f(x) = (x + 4)(x - 5)(x^2 + 3x - 1)
Therefore, the zeros of the function are:
x = -4, 5, (-3 ± √13)/2
Thus, these are the zeros of the polynomial.
If you borrow $1200 at 14% interest, compounded monthly, and pay off the loan at the end of
2 years, how much interest will you have paid? Answer rounded to the whole number asap
Answer:
The first step is to convert the annual interest rate to a monthly rate. We divide 14% by 12 months to get a monthly interest rate of 1.17%.
Next, we need to calculate the total number of months for the loan. Since the loan is for 2 years, or 24 months, we will make 24 payments.
To calculate the interest paid, we can use the formula:
I = P[(1 + r)^n - 1]
where:
I = interest paid
P = principal (amount borrowed) = $1200
r = monthly interest rate = 0.0117
n = total number of compounding periods = 24
Plugging in these values, we get:
I = 1200[(1 + 0.0117)^24 - 1]
I = $357.72
Therefore, the interest paid is $358.
Hope This Helps!
Slice it for me pls
Thank you
The quadratic function graphed is defined as follows:
C) y = x² - x - 2.
How to define the quadratic function?The factored format of a quadratic function is given as follows:
y = a(x - x*)(x - x**)
In which the parameters are given as follows:
x* and x** are the x-intercepts of the graph of the quadratic function.a is the leading coefficient.From the graph, we have that it crosses the x-axis at x = -1 and x = 2, hence the x-intercepts are given as follows:
x* = -1, x** = 2.
Hence:
y = a(x + 1)(x - 2)
y = a(x² - x - 2).
When x = 0, y = -2, hence the leading coefficient a is given as follows:
-2a = -2
a = 1.
Thus the equation is:
y = x² - x - 2.
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GEOMETRY PLS HELP ASAP
Answer:
C) 56
Step-by-step explanation:
2(AE) = BD
AC = BD
2(2x + 6) = 6x - 10
4x + 12 = 6x - 10
-2x = -22
x = -22/-2 = 11
AC = 6(11) - 10 = 56
Violet goes to a store an buys an item that costs � x dollars. She has a coupon for 35% off, and then a 8% tax is added to the discounted price. Write an expression in terms of � x that represents the total amount that Violet paid at the register.
Answer:
The amount of discount is 35% of � x, which is (35/100)� x = 0.35� x. So, the discounted price is � x minus the discount, which is � x - 0.35� x = 0.65� x.
Then, the tax is added to the discounted price, which is 8% of the discounted price, or (8/100)(0.65� x) = 0.052� x.
Therefore, the expression for the total amount that Violet paid at the register is:
0.65� x + 0.052� x = 0.702� x
Which of the following appear in the diagram below? Check all that apply.
Answer:
C. ∠ZXY and D. YX
Step-by-step explanation:
C. ∠ZXY
because the middle letter is always the angle or the turning point of an angle and also it is in order based on the diagram. The angle won't change even if you look at it on a different point of view or if the diagram was flipped.
D. YX
because the line YX is a true statement because XY or YX is on the same line that goes on and on. You can tell because there's arrows on the end of the line.
Which is the BEST system to measure the likelihood of an event occurring? A between 0 and 12 B between 0 and 1 C between 0 and 10
D between 0 and 100
D) Between 0 and 100.
The best system to measure the likelihood of an event occurring would be option D between 0 and 100. This system allows for a greater level of granularity and precision in the measurement of probability, as it provides a wider range of possible values to represent different levels of likelihood. The other options may not provide enough resolution to accurately capture and distinguish between different probabilities.
5. a random sample of 484 consumers is surveyed about their online shopping habits, and 121 of these consumers admit to shopping online at least once a week. from this information, we know the sample proportion must be equal to a. 0.48. b. 0.12. c. 0.25. d. 0.37. e. 0.09. 6. return to question 5. a sample proportion is a a. statistic. b. parameter. c. standard deviation. d. level of confidence. e. margin of error. 7. what proportion of osu undergraduates have full-time jobs? you survey a random sample consisting of 920 osu undergraduates and find that 368 of them have full-time jobs. use this information to construct a 95% confidence interval in order to estimate the proportion of all osu undergraduates who have full-time jobs. as you construct the interval, try not to do a lot of rounding until you reach the end of your calculations, and then choose the answer below that is closest to what you calculate. a. 0.200 to 0.600 b. 0.384 to 0.416 c. 0.368 to 0.432 d. 0.350 to 0.450 e. 0.374 to 0.426
Now, we can construct the confidence interval: [tex]0.4 ± 1.96 * 0.0157 ≈ 0.4 ± 0.0308. [/tex]The resulting interval is 0.3692 to 0.4308, which is closest to option e. 0.374 to 0.426
5. To calculate the sample proportion, divide the number of consumers who shop online at least once a week (121) by the total number of consumers surveyed (484). So, the sample proportion is[tex] 121/484 = 0.25.[/tex] The correct answer is c. 0.25.
6. A sample proportion is a statistic because it is a measure derived from a sample of the population. The correct answer is a. statistic.
7. To construct a 95% confidence interval for the proportion of OSU undergraduates with full-time jobs, we first find the sample proportion:[tex] 368/920 = 0.4[/tex].
Next, we find the standard error (SE) for the sample proportion: SE = sqrt(0.4 * (1 - 0.4) / 920) ≈ 0.0157. For a 95% confidence interval, the critical value (z-score) is approximately 1.96.
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Can someone please help me ASAP it’s due today!! I will give brainliest if it’s correct.
Answer:
C
Step-by-step explanation:
About 16 days because 0.58 x 28 is 16.24
So how do I solve this?
Answer:
x = y = 2√7 = 5.292
Step-by-step explanation:
We have a right isosceles triangle, so the length of the hypotenuse is √2 times the length of each leg. Since the hypotenuse is 2√14, each leg measures 2√7.
The length of the sides of the right isosceles triangle is 5.292units.
What is right isosceles triangle?A right isosceles triangle is a special type of triangle that has two equal-length legs and a right angle between them. Because it has two equal legs, it is also an isosceles triangle. The name "right isosceles" comes from the fact that it has a right angle and two equal legs.
In the given question,
In a right isosceles triangle, the two legs are congruent, and the length of the hypotenuse can be found using the Pythagorean theorem:
a² + b² = c²
Since this is an isosceles triangle, we know that a = b, so we can simplify the equation to:
2a² = c²
Taking the square root of both sides, we get:
a√2 = c
In this case, we are given that the hypotenuse has a length of 2√14, so we can set c equal to that value and solve for a:
a√2 = 2√14
a = (2√14)/√2
Simplifying the expression by canceling the square root of 2 in the denominator, we get:
a = 2√7
Therefore, each leg of the isosceles triangle has a length of 2√7, which agrees with your answer.
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If a cereal box (rectangular prism) has the dimensions of 6
inches by 4 inches by 14 inches, what is the volume?
Answer:
336in^2
Step-by-step explanation:
6 x 4 x 14
"The buetiful thing about learning is that no one can take it away from you" :)
Answer: 336
Step-by-step explanation: I just multiplied them all
After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function f(x) = 120 (0.86)x. Find and interpret the given function values and determine an appropriate domain for the function
Answer:
The appropriate domain for the function is [0, ∞).
Step-by-step explanation:
Given function: f(x) = 120 (0.86)x
To find the function values, we can substitute the given value of x into the function:
f(0) = 120 (0.86)^0 = 120 (1) = 120
Interpretation: When the medication is first taken, there are 120 milligrams of medicine in the person's bloodstream.
f(2) = 120 (0.86)^2 ≈ 84.24
Interpretation: After 2 hours, there are approximately 84.24 milligrams of medicine remaining in the person's bloodstream.
f(6) = 120 (0.86)^6 ≈ 34.17
Interpretation: After 6 hours, there are approximately 34.17 milligrams of medicine remaining in the person's bloodstream.
The domain of the function is all non-negative real numbers, since the amount of medicine in the bloodstream can't be negative and time is measured in non-negative hours. So the appropriate domain for the function is [0, ∞).
True or false? If you took a true “if-then” statement, inserted a not in each clause, and reversed the clashes, the new statement would also be true
Answer:
True
Step-by-step explanation:
If you took a true if-then statement, inserted not in each clause and reversed the clauses you will have created the contrapositive. The contrapositive of an if-then statement has the same true value as the original statement.
Statement:
If p, then q.
Contrapositive:
If not q, then not p
If the statement is true, then the contrapositive is also true.
Help in this too because in this I am so confused
The value of x in given figure is a whole number that is x = 6.6
What do you mean by Secant Theorem ?When two tangent segment are drawn from an outside point to a circle, the sum of the dimensions of the first tangent segment and its exterior tangent segment equals the sum of the dimensions of the other secant segments and its exterior secant segment.
Given the image and the labelled measurement of two secant segments outside the predetermined circle that have a similar endpoint. We are required to determine what x's value is.
With these measurements, we can use the secant-secant theorem to solve for the value of x as we refer to and analyse the figure. We will therefore have this theorem applied.
(5) [(5) + ( x+4)] = (6) [6 + 7]
(5) [5+x+4] = (6) [13}
5 [9 + x] = 78
45 + 5x = 78
5x = 33
x = 6.6
Therefore the value of x is 6.6
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You can model the arch of a building entrance using the equation y = − 1/3(x + 6)(x − 6), where x and y are measured in feet. The x-axis represents the ground. Find the width of the arch at ground level.
The arch has a width of 6 - (-6) = 12 feet at ground level.
To find the width of the arch at ground level, we need to find the x-values where y = 0, since the width of the arch is the distance between these two x-values.
So, we set y = 0 and solve for x:
0 = − 1/3(x + 6)(x − 6)
Either x + 6 = 0 or x - 6 = 0
If x + 6 = 0, then x = -6.
If x - 6 = 0, then x = 6.
To find the width of the arch at ground level, we need to find the x-values where y=0.
y = − 1/3(x + 6)(x − 6)
Setting y=0:
0 = − 1/3(x + 6)(x − 6)
We can solve for x using the zero product property:
0 = x + 6 or 0 = x - 6
x = -6 or x = 6
The arch intersects the ground at x = -6 and x = 6.
Therefore, the arch has a width of 6 - (-6) = 12 feet at ground level.
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f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668 [mean valuation of homes]. a. true b. false
Given statement "f the null hypothesis is correct, the probability of getting a sample mean greater than $189,500 is .0668" is true. Because, It's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.
The null hypothesis is a general statement that there is no significant effect or difference between the considered groups or variables.
In this case, the null hypothesis would be that the true mean valuation of homes is equal to or less than $189,500.
The probability of 0.0668, mentioned in the question, represents the likelihood of getting a sample mean greater than $189,500 if the null hypothesis is true.
In other words, it's the probability of observing a sample mean at least as extreme as the one obtained in the study, assuming the null hypothesis is correct.
This probability (0.0668) is also known as the p-value.
The p-value helps to determine the significance of the results.
If the p-value is less than a predetermined significance level (usually 0.05), the null hypothesis is rejected in favor of the alternative hypothesis.
In this case, the p-value of 0.0668 is higher than the common significance level of 0.05.
We cannot reject the null hypothesis, meaning the probability of getting a sample mean greater than $189,500 is indeed 0.0668 if the null hypothesis is correct
Hence, the statement is true.
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For a class project, a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches. how much paper is wasted? (60 â€" 15Ï€) square inches 15Ï€ square inches 45 square inches (60 â€" Ï€) square inches
If a teacher cuts out 15 congruent circles from a single sheet of paper that measures 6 inches by 10 inches, then (60 - 1.5 π) square inches paper is wasted.
The area of each circle is given by the formula [tex]A = \pi r^2[/tex], where r is the radius of the circle. Since all 15 circles are congruent, they all have the same radius.
Let's first find the radius of each circle. Since the circles are cut from a 6 by 10 inch sheet of paper, we know that the diameter of each circle cannot be greater than 6 inches or 10 inches. Let's take the smaller dimension (6 inches) and divide it by 15 to find the maximum possible diameter of each circle:
6 inches ÷ 15 = 0.4 inches
Therefore, the maximum possible radius of each circle is 0.2 inches.
Now we can calculate the total area of all 15 circles:
Total area of circles = [tex]15 * \pi * (0.2)^2[/tex]
[tex]= 1.5 \pi[/tex] square inches
The area of the original sheet of paper is 6 inches * 10 inches = 60 square inches. Therefore, the amount of paper wasted is:
Amount of paper wasted = Area of sheet - Total area of circles
= 60 square inches - 1.5 π square inches
= 60 square inches - 4.71 square inches (using π ≈ 3.14)
= 55.29 square inches (rounded to two decimal places)
Therefore, the answer is (60 - 1.5π) square inches.
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Bill buys 4.8 pounds of oranges for $10.
About how much do they cost per pound?
$8
$4
$2
A study was performed on a type of bearing to find the relationship of amount of wear y to x1 = oil viscosity and x2 = load. The following data were obtained. Estimate the unknown parameter for x1 of the multiple linear regression equation. Use 4 decimal places.
y x1 x2 y x1 x2
193 1.6 851 230 15.5 816
172 22.0 1058 91 43.0 1201
113 33.0 1357 125 40.0 1115
The estimated coefficient for x1 in the multiple linear regression equation is 2.3529.
How we find the multiple linear regression equation coefficient for x1?To estimate the coefficient for x1 in the multiple linear regression equation, we can use the following formula:
b1 = [(nΣxy) - (Σx)(Σy)] / [(nΣx^2) - (Σx)^2]where n is the number of data points, x and y are the respective variables, and Σ denotes the sum of the values.
Using the provided data, we can calculate the coefficient for x1 as follows:
n = 6Σx1 = 115.1Σy = 772Σx1y = 18822.1Σx1^2 = 1952.86b1 = [(6 x 18822.1) - (115.1 x 772)] / [(6 x 1952.86) - (115.1)^2]= 2.3529 (rounded to 4 decimal places)
In this problem, we are given data on the amount of wear of a type of bearing, as well as the oil viscosity and load that the bearing was subject to. We want to estimate the coefficient for oil viscosity (x1) in the multiple linear regression equation for this data.
To do this, we can use the formula for calculating the coefficient for x1 in the multiple linear regression equation. This formula takes into account the number of data points, the sums of the values for x1 and y, and the sum of the products of x1 and y, as well as the sum of the squares of x1.
Using the provided data and this formula, we find that the estimated coefficient for x1 is 2.3529. This means that, for this data, the amount of wear of the bearing is estimated to increase by 2.3529 units for every one unit increase in oil viscosity, while holding the load constant.
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jack is 30 years older than his son jim. FIve years ago jack was 3 times as old as his son. How old are they today?
Answer:
They are 50 and 20 years old.
Step-by-step explanation:
5 years ago jack was 45 and his son was 15, which makes jack 3 times older than his son and has a 30 year difference.
Describe the translation from the pre-image to the image please
Step-by-step explanation:
Look at point A ====> A'
x goes from 1 to 4 so X: x + 3
y goes from 7 to 3 so Y: y - 4
3 √5 + 3 √5
I need help adding this please
The answer is 6√5
In 3√5 and 3√5, √5 is multiplied with 3 in both terms,
∴ 3 is the common factor
∴ 3√5+3√5= 3(√5+√5)
= 3×2√5
= 6√5
Hence the answer is 6√5
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a report on high school graduation stated that 85 percent of high school students graduate. suppose 3 high school students are randomly selected from different schools. what is the probability that exactly one of the three graduates? question 4 options: 0.019 0.003 0.614 0.057 0.850
The probability that exactly one of three randomly selected high school students graduate, given an 85% graduation rate, is 0.057. This calculation was based on the combination formula and the binomial probability distribution.
This problem involves calculating the probability of a specific outcome (exactly one of the three students graduating) in a binomial distribution. We know that the probability of any one student graduating is 0.85, so the probability of one student not graduating is 0.15. Using the binomial probability formula, we can calculate the probability of exactly one student graduating out of three as:
P(X = 1) = (3 choose 1) * (0.85)^1 * (0.15)^2 = 3 * 0.85 * 0.0225 = 0.057
Therefore, the answer is 0.057, or approximately 5.7%. This means that if we randomly select three high school students from different schools, there is a 5.7% chance that exactly one of them will graduate.
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There are 12 boys and 14 girls in Mr. Rowe's class. Each week, Mr. Rowe puts pieces
of paper with each student's name in a box and randomly pulls one out. The chosen
student spins the arrow on the spinner shown.
10 free
points
Free
assignment
5 free
points
Which expression can be used to find the probability that this week a boy will be
chosen and the arrow will land on "Free assignment"?
Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.
Which expression can be used to find the probability that this week a boy will be?
chosen and the arrow will land on "Free assignment"?
The probability of a boy being chosen is the ratio of the number of boys to the total number of students, which is:
[tex]P(boy) = 12 / (12 + 14) = 12/26 = 6/13[/tex]
The probability of the arrow landing on "Free assignment" is 1/3, since there are 3 equal sectors on the spinner.
To find the probability that both events occur (i.e., a boy is chosen and the arrow lands on "Free assignment"), we multiply the probabilities:
[tex]P(boy and "Free assignment") = P(boy) x P("Free assignment")[/tex]
[tex]P(boy and "Free assignment") = (6/13) x (1/3) = 2/13[/tex]
Therefore, the expression that can be used to find the probability that a boy will be chosen, and the arrow will land on "Free assignment" is 2/13.
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In a scale drawing, an airplane has a length of 35 centime-
ters. The length of the actual plane is 87.5 feet.
What is the scale of the drawing?
Be sure to write the scale in simplest form.
How do u write 6x-3y=15 in slope intercept format?
Answer: y= 2x-5
Step-by-step explanation:
y = mx + b
where m is the slope of the line and b is the y-intercept.
To get the equation into slope-intercept form, you need to isolate the y-term on one side of the equation and simplify the rest of the equation. So, let's start with 6x - 3y - 15:
6x - 3y - 15 = 0 (I'm assuming this equation represents a line)
Now, let's isolate the y-term by subtracting 6x from both sides:
-3y = -6x + 15
Finally, let's solve for y by dividing both sides by -3:
y = 2x - 5