Answer:
34/69
Step-by-step explanation:
2 are jelly-filled
5 are lemon-filled
17 are custard-filled
Total: 24
First drawing:
There are 24 donuts in total, 17 of which are custard filled.
p1(custard filled) = 17/24
Second drawing:
There are now a total of 23 donuts, 16 of which are custard filled.
p2(custard) = 16/23
The two drawings are independent events, so the overall probability is the product of the individual probabilities.
Overall probability of drawing two custard filled donuts:
p(2 custard filled) = p1 * p2 = 17/24 * 16/23 = 17/3 * 2/23 = 34/69
Price, in dollars, of bicycles: 150, 134, 136, 120, 145, 170, 125, 130, 145, 190, 140 box plots
Answer:
Arrange this data in numerical order:
120, 125, 130, 134, 136, 140, 145, 145, 150, 170, 190
We have 11 observations.
Minimum = 120
First quartile = 130
Median = 140
Third quartile = 150
Maximum = 190
Check for outliers:
130 - 1.5(150 - 130) = 100
150 + 1.5(150 - 130) = 180, so 190 is an outlier.
See the attachment.
Which type of function best models the set of data points?
(0,11). (1,7), (2,7), (3,11). (4,19)
wait I try it !! ,!!!!!!
Answer:
the best model function of the set is 3,11
Lots of points plz help
Answer:
= 480 u2
Step-by-step explanation:
=
1
2 bh + bh +
1
2 (b1 + b2)h + bh
=
1
2 (16)(6) + (16)(6) +
1
2 (16 + 32)(6) + (32)(6)
= 48 + 96 + 144 + 192
Answer:
Once the height of the figures are the same and the total height is 24, each one height is 6.
Note: I wil consider square metre as the unit of area.
First, I will calculate the half-length of the triangle base using the pythagorean theorem:
[tex]10^{2}=6^2+x^2\\ 100=36+x^2\\64=x^2\\x=8m[/tex]
∴The base is equal to 16m
Let's calculate the area of the triangle:
[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2} (16)(6)\\\\A=\frac{1}{2} (16)(6)= 48m^2[/tex]
Now, let's calculate the first rectangle Area:
[tex]A=wh\\A=(16)(6)\\A=96m^2[/tex]
Now, the trapezoid area:
The width length of the longer side is equal to 16 plus the length of 2 little triangles. Those triangles base length equal to half-length of the first triangle. Therefore, the longer side/base is equal to 32.
[tex]A=\frac{1}{2} (longerSide+shorterSide)height\\A=\frac{1}{2} (32+16)6\\A=144m^2[/tex]
Now, the last rectangle:
[tex]A=wh\\A=(32)(6)\\A=192m^2[/tex]
Therefore, the figure Total Area is the sum of the triangle, trapezoid and rectangles:
[tex]48+96+144+192=480m^2[/tex]
A = 480 unit of area
Angel has finished 75% of an art project that has taken
him a total of 9 hours so far. If he continues to work at
the same rate, how many hours will it take for him to
complete the entire project?
Answer: 12 hours
Step-by-step explanation: For this problem we will write a percent equation to solve for 100% and how many total hours it will take angel to finish the entire project.
Lets write a equation to solve for w, total amount of hours.
9/w = 75/100
9/w x w = 75/100 x w
9 = 75w/100
9 x 100/75 = 75w/100 x 100/75
w = 12
So, it will take Angel 12 hours to finish his entire project.
Final answer:
Angel will need 3 more hours to complete the art project, for a total of 12 hours when he continues to work at the same rate.
Explanation:
Angel has completed 75% of his art project in 9 hours. To find out how much time it will take to complete the entire project, we need to determine the time taken to complete 100% of the project. First, we calculate the time taken for 1% of the work, which is 9 hours divided by 75 (the percentage completed so far). This gives us 0.12 hours per percent.
Now, we can find out the total time for 100% completion by multiplying 0.12 hours by 100, which totals 12 hours. Since Angel has already completed 9 hours of work, the remaining time to finish the project is 12 hours minus 9 hours, which equals 3 more hours of work.
What is the measurement of the longest line segment in a right rectangular prism that is 26 inches long, 2 inches wide, and 2 inches tall?
Answer:
[tex]6\sqrt{19} \approx 26.153[/tex] inches.
Step-by-step explanation:
The longest line segment in a right rectangular prism is the diagonal that connects two opposite vertices. On the first diagram attached, the green line segment connecting A and G is one such diagonals. The goal is to find the length of segment [tex]\mathsf{AG}[/tex].
In this diagram (not to scale,) [tex]\mathsf{AB} = 26[/tex] (length of prism,) [tex]\mathsf{AC} = 2[/tex] (width of prism,) [tex]\mathsf{AE} = 2[/tex] (height of prism.)
Pythagorean Theorem can help find the length of [tex]\mathsf{AG}[/tex], one of the longest line segments in this prism. However, note that this theorem is intended for right triangles in 2D, not the diagonal in a 3D prism. The workaround is to simply apply this theorem on two different right triangles.
Start by finding the length of line segment [tex]\mathsf{AD}[/tex]. That's the black dotted line in the diagram. In right triangle [tex]\triangle\mathsf{ABD}[/tex] (second diagram,)
Segment [tex]\mathsf{AD}[/tex] is the hypotenuse. One of the legs of [tex]\triangle\mathsf{ABD}[/tex] is [tex]\mathsf{AB}[/tex]. The length of [tex]\mathsf{AB}[/tex] is [tex]26[/tex], same as the length of this prism.Segment [tex]\mathsf{BD}[/tex] is the other leg of this triangle. The length of [tex]\mathsf{BD}[/tex] is [tex]2[/tex], same as the width of this prism.Apply the Pythagorean Theorem to right triangle [tex]\triangle\mathsf{ABD}[/tex] to find the length of [tex]\mathsf{AB}[/tex], the hypotenuse of this triangle:
[tex]\mathsf{AD} = \sqrt{\mathsf{AB}^2 + \mathsf{BD}^2} = \sqrt{26^2 + 2^2}[/tex].
Consider right triangle [tex]\triangle \mathsf{ADG}[/tex] (third diagram.) In this triangle,
Segment [tex]\mathsf{AG}[/tex] is the hypotenuse, while[tex]\mathsf{AD}[/tex] and [tex]\mathsf{DG}[/tex] are the two legs.[tex]\mathsf{AD} = \sqrt{26^2 + 2^2}[/tex]. The length of segment [tex]\mathsf{DG}[/tex] is the same as the height of the rectangular prism, [tex]2[/tex] (inches.) Apply the Pythagorean Theorem to right triangle [tex]\triangle \mathsf{ADG}[/tex] to find the length of the hypotenuse [tex]\mathsf{AG}[/tex]:
[tex]\begin{aligned}\mathsf{AG} &= \sqrt{\mathsf{AD}^2 + \mathsf{GD}^2} \\ &= \sqrt{\left(\sqrt{26^2 + 2^2}\right)^2 + 2^2}\\ &= \sqrt{\left(26^2 + 2^2\right) + 2^2} \\&= 6\sqrt{19} \\&\approx 26.153\end{aligned}[/tex].
Hence, the length of the longest line segment in this prism is [tex]6\sqrt{19} \approx 26.153[/tex] inches.
The longest line segment in a right rectangular prism with dimensions 26 inches by 2 inches by 2 inches is found using the Pythagorean theorem: d = sqrt(l^2 + w^2 + h^2), which gives approximately 26.2 inches.
Explanation:To find the measurement of the longest line segment in a right rectangular prism, we need to calculate the space diagonal, which is the diagonal that cuts through the body of the prism. In this case, the dimensions of the right rectangular prism are 26 inches long, 2 inches wide, and 2 inches tall. We use the Pythagorean theorem in three dimensions to calculate this, which is the square root of the sum of the squares of the length, width, and height. The formula can be written as:
d = \sqrt{l^2 + w^2 + h^2}Where d is the diagonal, l is the length, w is the width, and h is the height. Plugging in the given dimensions:
d = \sqrt{26^2 + 2^2 + 2^2}Calculating the square of each term and adding them gives:
d = \sqrt{676 + 4 + 4}So:
d = \sqrt{684}Finally, taking the square root gives us the length of the longest line segment:
d = 26.2 inchesTherefore, the longest line segment of the rectangular prism measures approximately 26.2 inches.
A frame is 9 in wide and 6 in tall. If it is reduced to a width of 3 in then how tall will it be?
What is the y- intercept of y= -3x
Answer: (0,0) or y=0
In order to find the y-intercept, we need to find the point that crosses the y-axis. To find that x=0 or (0,y)
When x=0, y=0 on the graph since there are no transformations.
Which equation has a solution of x=1.5
Answer:
y=3
x=1.5
Step-by-step explanation:
if :
y=3
x=1.5
then:
y-x=1.5
Find the exact volume of the cylinder,
A)
80
ft?
B)
1601 ft
2007 ft
D)
400
ft
Answer:
i believe the answer on the photo is C. 200
The options are different on the question and the photo
What's |5| + |–7|?
Question 8 options:
A)
–12
B)
–2
C)
12
D)
2
Answer:
C) 12
Step-by-step explanation:
Absolute value always means it is the positive version of the number
This switches -7 to 7 and 5 stays the same.
5 + 7 = 12
The absolute value returns the "positive version" of a number. This means that if the number is already positive, it does nothing. Otherwise, it gets rid of the negative sign.
So, you have
[tex]|5|=5,\quad |-7|=7[/tex]
and thus
[tex]|5|+|-7|=5+7=12[/tex]
The question is the photo.
Answer:
w=5
Step-by-step explanation:
the triangle has the same size of area as the side of the rectangle so therefore 5
Answer:
The area of a triangle is [tex]A\Delta=\frac{1}{2}(base)(height)[/tex]
So, the area of the given triangle is:
[tex]A\Delta=\frac{1}{2}(5)(6)\\A\Delta=\frac{1}{2}(30)\\A\Delta=15cm^2[/tex]
The area of a rectangle is
[tex]A=(length)(width)\\A=(6)w\\A=6wcm^2[/tex]
Once the area of both are the same:
[tex]6w=15\\w=\frac{15}{6} \\w=2.5cm[/tex]
Question 5(Multiple Choice Worth 6 points)
(07 02 LC)
Which statement is true for the equation 3x - 3x - 21-22
It has no solution
It has one solution
It has two solutions
It has infinitely many solutions
Answer:
can u please add more detail
Step-by-step explanation:
Help ASAP please ! Explain too!
Answer: D
Step-by-step explanation:
simplify
Answer:
When dealing with area (2 dimensions) when we deal with a one dimensional quantity (distance) it changes a 2 dimensional quantity by the square of the difference.
Comparing a 3, 4, 5 triangle to a 6, 8, 10 triangle, the larger triangle has 4 times the area of the smaller triangle.
20) 6 / 4 = 1.5 1.5 ^2 = 2.25
Therefore, ABC's area is 2.25 larger than A'B'C's area.
21) 21 / 7 = 3 and 3^3 = 9
Therefore, ABC's area is 9 times larger than A'B'C's area.
Step-by-step explanation:
mimominutnemendonasinipudmamimil ian
16. There are 3 adults for
every 8 children at a
birthday party. If there are
a total of 55 people at the
party, how many adults are
there?
Answer:
15adults
Step-by-step explanation:
Ratio of Children : Adult = 8 : 3
Number of children = 8x
Number of Adult = 3x
8x + 3x =55
11x = 55
x = 55/11
x = 5
Number of Adults = 3x = 3*5 = 15
Answer:
40 adults
Step-by-step explanation:
Let x:y represent the ratio of children to adults. As of now, x:y is 3:8.
To solve this problem, all we need to do is find a solution where x + y = 55. Let's begin by using the guess-and-check method.
First, I will multiply the ratio by 2.
When x = 6, y = 16
6 + 16 = 22
Not applicable; I need higher numbers
Next, I'll multiply the ratio by 4.
When x = 12, y = 32.
12 + 32 = 44
Not applicable, I need slightly higher numbers
I'll multiply the ratio by 5.
When x = 15, y = 40
15 + 40 = 55
Since 55 is the total number of people, 15 children and 40 adults is the correct answer. Therefore, the total number of adults is 40.
Solve cot x + 2cot x * sin x = 0 for U^ <= x<=180
Answer:
Step-by-step explanation:
hello :
cot x + 2cot x sin x = 0 0≤ x≤ 180
cotx(1+2sinx) =0 means : cotx=0 or 1+2sinx=0
1) cotx=0 so : cosx=0 and sinx ≠ 0 because cotx = cosx/sinx
when : 0≤ x≤ 180 : x=90°
2) 1+2sinx=0 means : sinx = -1/2
when : 0≤ x≤ 180 : no solutions because : sinx ≥ 0
conclusion : one solution : x=90°
|x+3|=-2
This answer does not have two solutions...why?
Step-by-step explanation:
|x+3| = -2 doesn't have a solution because the exact values can't be negative
Find the sum.
a. 64 + (-15)
b. -121 + (-34)
C. -86 +92
d. 109+(-162)
ANSWER QUICKLY PLEASE!!!!
Look at the attached picture ⤴
Hope it will help u...
What is the value of y in the equation 3y - 8 = 22?
10
Step-by-step explanation:
3y-8=22
3y=22+8
3y=30
y=30/3
y =10
I need to find x and y
Answer:
[tex]x = - 2 \\ y = - 4[/tex]
Step-by-step explanation:
[tex] - 2x + 2y = - 4 \: \: \: \: \: \\ i.e. \: \: \: - x + y = - 2 \: \: \: \: \: \: \: ...(1)\\ \\ 3x + 3y = - 18 \\ i.e. \: \: \: \: \: \: x + y = - 6\: \: \: \: \: \: \: ...(2)[/tex]
From (1) we get
[tex] x = 2 + y[/tex]
Now put x = 2 + y in equation (2)
[tex]2 + y + y = - 6 \\ 2 + 2y = - 6 \\ 2y = - 6 - 2 \\ 2y = - 8 \\ \\ y = - \frac{8}{2} \\ \\ y = - 4[/tex]
now put y = -4 in equation (1) we get
[tex] - x + ( - 4) = - 2 \\ - x - 4 = - 2 \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2[/tex]
Round the following numbers to 2 decimal place.
a) 65.874
b) 326.59
c)
13.555
d)
7.959
Answer:
A) 65.87
B) 326.59
C) 13.56
D) 7.96
Step-by-step explanation:
I NEED HELP DUE TOMORROW! Suppose Mr. Grant decides to buy square tiles that have side lengths of
3 foot. How many of these tiles will he need to buy?
To find out how many square tiles Mr. Grant needs, you need to know the total area he wants to cover. The area of each tile is 9 square feet. Divide the total area by 9 to find the number of tiles he needs.
Explanation:In order to figure out how many square tiles Mr. Grant needs to buy, more information is needed, such as the size of the area he needs to cover. The area of a single tile can be calculated using the formula Area = length × width. Since the tiles are squares, the length and width are the same, so if each side is 3 feet, then the area of a single tile is 9 square feet. If, for example, Mr. Grant needed to cover an area of 27 square feet, he would divide the total area by the area of a single tile: 27 ÷ 9 = 3, so he would need 3 tiles.
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Which of the following triangles are impossible? Check all that apply. a triangle with sides of 3 cm, 3 cm, and 6 cm a triangle with sides of 3 cm, 4 cm, and 6 cm a triangle with sides of 9 cm, 5 cm, and 2 cm
Answer:
A and C
Step-by-step explanation:
I did the test and got a 100%
Find a 15% tip on a restaurant bill of $32.60.
Answer:
32.60/100*15 = $4.89 = 15%
Step-by-step explanation:
Answer:
$4.89
Step-by-step explanation:
To find the tip, multiply the tip rate by the price of the bill
tip rate * bill
15% * 32.60
Convert 15% to a decimal by dividing by 100, or moving the decimal 2 spaces to the left
15%/100=0.15
15.0 -->0.15
Substitute the decimal in for the percent and multiply
0.15* 32.60=4.89
So, a 15% tip on $32.60 is $4.89
Which point is located at (4,8)?
A) A
B) B
C) C
D) D
Answer:
C
Step-by-step explanation:
Start at the origin
Go to the right 4 units
Go up 8 units
We will end up at point C
Answer:
The coordinate of C is (4,8)
2. Jaclyn estimates the square root of 50 in the following way:
/50 = 2/ 25 = 2 □5=10
(A) Explain why her reasoning is incorrect.
(B) Estimate the square root of 50 to the nearest tenth without using your calculators. Show your work.
Answer:
Answer:
(B) 7.1 is the estimated square root of 50
Step-by-step explanation:
A. √50 = √2 √25
= 5√2.
Jaclyn did not take the square root of 2.
B. We estimate the square root of 2.
Trial and improvement:
It must lie between 1 and 2 so we try 1.5:
1.5 * 1.5 = 2.25
Its < 1.5 so try 1.4
1.4 * 1.4 = 1.96.
So it is a little above 1.4.
Try 1.45:
1.45 * 1.45
1.45
* 1.45
-------
725
5800
14500
2.1025
= 2.1025.
- this is above 2 so the answer is between 1.40 and 1.45 but closer to 1.4.
A good estimate is 1.42
So the square root of 50 is about 5*1.42 = 7.1
Answer:
B is 7.1!
Step-by-step explanation:
Solve this in quadratic formula please and thank you.
Answer:
(2/3) + or - .943i
Step-by-step explanation:
Use quadratic formula.
[tex]x = \frac{-b \frac{+}{}\sqrt{b^2 - 4ac} }{2a}[/tex]
A = 3
B = -4
C = 4
[tex]\sqrt{16 - 2(3)(4)} = \sqrt{-8}[/tex] or 2.828i
4/6= 2/3
Answer: 2, -2/3 ********************************************************************************************************
What is the mean (average)of the data 4.7
4.5
5
4
Help fast
Answer:
4.55
Step-by-step explanation:
You add up all the numbers which is 18.2 and then you divide by the # of data.
Answer:
It's 4.55 because you add all the numbers together and then divide it by the numbers there are.
If you ignore friction, the amount of time required for a box to slide down an inclined plane is a
ne is Vg sin 0 cos o 'W
i me, where a is the
horizontal distance defined by the inclined plane, g is the acceleration due to gravity and is the angle of the inclined plane. For what
values of g is the expression undefined?
a. 0°
c. both a &b
b. 90°
d. none
Answer:
Option C is correct.
The expression is undefined when theta is equal to 0° or 90°.
Step-by-step explanation:
If you ignore the friction, the amount of time required for a box to slide down an inclined plane is √(2a/g•sin(theta)•cos(theta)), where a is the horizontal distance defined by the inclined plane, g is the acceleration due to gravity and theta is the angle of the inclined plane. For what values of theta is the expression undefined?
A. 0°
B. 90°
C. Both A and B
D. None
An expression is said to be undefined when its value doesnt take on a real number value, e.g., its value goes to infinity.
And the value of a fractional expression goes to infinity when the denominator is equal to 0.
In the given expression for time,
√(2a/g•sin(theta)•cos(theta)),
The denominator of the expression is
g•sin(theta)•cos(theta)
Since g (acceleration due to gravity) cannot be zero, this expression will go to zero if either
Sin (theta) = 0
or
Cos (theta) = 0
Sin (theta) = 0 when (theta) = 0°
Cos (theta) = 0 when (theta) = 90°
Hence, it is easy to see that the expression given for the amount of time required for a box to slide down an inclined plane becomes undefined when (theta) = 0° or 90°.
Hope this Helps!!!
Please help!!
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 kilograms and gained weight at a constant rate of 8 lbs. a week.
a. Write a function to represent this situation. Use x and y as your variables.
b. What would his weight be after 8 weeks?
Answer:
A. y=90+8x
B. After 8 weeks he would be 154 pounds.
Step-by-step explanation:
You use the equation and plug in your x variable as 8 and you get 154 as the y.
A drone is flown, with constant acceleration, in a horizontal plane.
When initially observed, at a point P, it has a velocity of (2i − 7j) ms−1
Four seconds later the drone is at a point Q and has a velocity of (14i + j) ms−1
(i) Find the acceleration of the drone in terms of i and j.
Answer:
3i + 2j
Step-by-step explanation:
Acceleration = change in velocity/time
Change in velocity
(14i + j) - (2i - 7j)
= 12i + 8j
Divide by time (t = 4)
3i + 2j
The acceleration of the drone in terms of i and j is 3i+2j.
What is the average acceleration?Acceleration is the amount by which the velocity of something changes over a set period of time.
The formula to find the acceleration is a=(v-v₀)/t, where a=average acceleration, v=final velocity, v₀=initial velocity and t=time.
Given that, a drone is flown, with constant acceleration, in a horizontal plane. When initially observed, at a point P, it has a velocity of (2i-7j) ms⁻¹.
Four seconds later the drone is at a point Q and has a velocity of (14i+j) ms⁻¹.
Acceleration = change in velocity/time
Change in velocity
(14i + j) - (2i - 7j)
= 12i + 8j
Divide by time (t = 4)
= 4(3i+2j)/4
= 3i+2j
Therefore, the acceleration of the drone in terms of i and j is 3i+2j.
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