Started with 54 cookies, considering fractions, removals, and distributions, ending with 15 cookies.
let's break it down:
1. **Initial Batch**: They started with an unknown number of cookies, denoted as [tex]\( x \).[/tex]
2. **Cookies for Teachers**: They took [tex]\( \frac{1}{4} \) of the cookies for their teachers, leaving \( \frac{3}{4}x \)[/tex] cookies.
3. **Burnt Cookie**: They discarded one burnt cookie, resulting in [tex]\( \frac{3}{4}x - 1 \) cookies.[/tex]
4. **Cookies for Nursing Home**: They gave [tex]\( \frac{2}{3} \) of the remaining cookies to the nursing home, keeping \( \frac{1}{3} \) of \( \frac{3}{4}x - 1 \) cookies.[/tex]
5. **Cookies for Neighborhood Kids**: They gave 3 cookies to the neighborhood kids, resulting in [tex]\( \frac{1}{3}x - 3 \) cookies.[/tex]
6. **Cookies for Friends**: They wrapped up [tex]\( \frac{2}{3} \) of the remaining cookies for their friends, keeping \( \frac{1}{3} \) of \( \frac{1}{3}x - 3 \) cookies.[/tex]
7. **Final Count**: They were left with 15 cookies, so [tex]\( \frac{1}{3}x - 3 = 15 \).[/tex]
[tex]\[ \frac{1}{3}x - 3 = 15 \]\[ \frac{1}{3}x = 15 + 3 \]\[ \frac{1}{3}x = 18 \]\[ x = 18 \times 3 \]\[ x = 54 \][/tex]
So, they initially had 54 cookies.
Which equation has both 4 and -4 as possible values
Answer:
x² - 16 = 0
Also,
|x| = 4
Step-by-step explanation:
(x-4)(x+4) = 0
x² - 16 = 0
|x| = 4
x = 4, -4
A circle with radius 9 has a sector with a central angle of 120°
What is the area of the sector?
Either enter an exact answer in terms of it or use 3.14 for it and enter your answer as a decimal
Step-by-step explanation:
[tex]radius = 9[/tex]
[tex]central \: angle = 120 \times \frac{3.14or\pi }{180} radian[/tex]
[tex]central \: angle = 2.09334 \: approximately = 2.1[/tex]
[tex]area \: of \: sector = \frac{1}{2} \times {r}^{2} \times central \: angle[/tex]
[tex]putting \: the \: values[/tex]
[tex]area \: of \: sector = \frac{1}{2} \times {9}^{2} \times 2.1[/tex][tex] = \frac{1}{2} \times 9 {}^{2} \times 2.1[/tex]
[tex]area \: of \: sector \: = 85.05 {m}^{2} [/tex]
Answer:
27π square units
Step-by-step explanation:
Note that a central angle of 120° is exactly 1/3 of a full circle.
So to find the area of this sector, find the area of the whole circle and divide your result by 3:
A = (1/3)π(9)^2 = 27π square units
What is 7,211 divided by 58?
Answer:
Approximately 124.327586
Step-by-step explanation:
Hope this helped.
Answer:
124.3275862068966
Step-by-step explanation:
I put it in my calculator
What is the edge length of 216 cubic inches?
The edge length of a cube with a volume of 216 cubic inches is 6 inches.
To find the edge length of a cube with a volume of 216 cubic inches, we can use the formula: Volume = [tex]edge length^3[/tex]. This formula tells us that the volume of a cube is equal to the edge length raised to the power of 3.
Given that the volume is 216 cubic inches, we can rearrange the formula to solve for the edge length. Let's call the edge length "x":
[tex]x^3 = 216[/tex]
To find the value of x, we need to find the cube root of 216. The cube root of a number is the number that, when multiplied by itself three times, equals the original number.
In this case, the cube root of 216 is 6, because 6 x 6 x 6 = 216.
Therefore, the edge length of a cube with a volume of 216 cubic inches is 6 inches.
To Learn more about original number here:
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The output is ten less then the input x
Y=X-10
Step-by-step explanation:
Step 1:
Let X be the input and Y be the output variable
Given: The output is 10 less than the input
Step 2:
Y=X-10 be the require function
Eg:
for X=1, Y = -9
X=2, Y=-8, etc
Solve this question
giving 5 points
Answer:
tossing two coins once
Step-by-step explanation:
i calculated.oh and my battery's About to die and i need to write the equation so if it cuts something off, it died.Ok so since it goes two ways and has headS And tai
Line M is parallel to line L. Name the angles which are congruent to angle C in the figure shown below:
A) S, Q, and B
Hope that help you!
Answer:
S, Q and B
Step-by-step explanation:
Those are the angles.
I need help with this one please do not do decimals!
I've attached the picture you need below. 1 3/4 is equal to 1 6/8 as well, so that is why the first one is placed over there.
Answer:
joja90 did it all theres no point explaining anything now lol
Step-by-step explanation:
Segments CD, AE, and BF are medians of triangle ABC. What is the value of x?
A. x = 3.7
B. x = 4.75
C. x = 5.8
D. x = 8
Step-by-step explanation:
The centroid divides the length of each median in 2:1 ratio.
The length of the part between the vertex and the centroid is twice the length between the centroid and the mid-point of the opposite side.
When CD is the median, C is the vertex and D is the midpoint of AE.
CG = 2 × DG
6.5= 2(3x- 11)
6.5 = 6x -22
6x= 6.5+22
6x= 28.5
x= 28.5/6
x= 4.75
optionB
Select the most SPECIFIC name for this shape
O Rectangle
O
Square
O
Quadrilateral
O kite
Answer: Kite
Step-by-step explanation:
(x+y)(x–y), if x=−3, y=−5
Answer: answer is -16
Step-by-step explanation:
Substitute the values of x and y into the equation to give
(3 + (-5)) (3-(-5))
(3-5) (3+5)
(-2) (8)
-16
Write the expression in simplest form.
(-11/2 x + 3)-2(-11/4 x - 5/2)
Answer:
-(11 / 2x + 3) + (11x / 2) + 5
Step-by-step explanation:
I hope this helps!
what is the perimeter of a rectangle with a height of 4 km and a length of 10 km
Perimeter is the sum of the 4 sides.
4+ 4 + 10 + 10 = 28 km
Answer:2 horizontal sides will equal 10 and The 2 Vertical side will equal 4. So add all them together to get 28.
Step-by-step explanation:Perimeter means the outside of Area so u can add all the numbers instead of mutiplying.
determine area under the standard normal curve given the z score, z less than 1.25
Answer:
0.8944
Step-by-step explanation:
Use a calculator or table.
Using a z-score table:
P(z < 1.25) = 0.8944
The perimeter of a rectangle is 18x – 24 and the width is
2x – 9. What is the length?
A: -7x + 3
B: 16x + 15
C: 7x - 3
D: 7x + 3
Answer:
C
Step-by-step explanation:
18x - 24 = 2 [length + 2x - 9]
9x - 12 = length + 2x - 9
Length = 7x - 3
Answer:
C: 7x - 3
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w) where l is the length and w is the width
We know the perimeter is 18x -24 and the width is 2x-9. Substituting these values into the equation
18x-24 = 2( l+2x-9)
Divide each side by 2
(18x-24)/2 = 2/2( l+2x-9)
9x-12 = l+2x-9
Add 9 to each side
9x-12 +9 = l+2x-9+9
9x -3 = l+2x
Subtract 2x from each side
9x-2x-3 = l+2x-2x
7x -3 = l
The length is 7x-3
Which relationships describes angles 1 and 2?
Select EACH correct answer
A. Adjacent angles
B. Vertical angles
C. Supplementary angles
D. Complementary angles
Answer:
C. Supplementary angles
Step-by-step explanation:
Supplementary angles add up to 180 degrees, making a straight line.
Answer:
Adjacent and Supplementary
Step-by-step explanation:
Adjacent: having a common vertex and a common side.
Supplementary: When two angles add up to 180 degrees.
!! How could it be s
The solution to the system of equations are (2, 5).
Solution:
The system of equations are
x + y = 7 – – – – (1)
2x – y = –1 – – – – (2)
To find x from equation (1):
x + y = 7
Subtract y from both sides of the equation, we get
⇒ x + y – y = 7 – y
⇒ x = 7 – y – – – (3)
Substitute (3) in (2) we get,
2(7 – y) – y = –1
14 – 2y – y = –1
14 – 3y = –1
Subtract 14 from both sides,
–3y = –15
Divide by –5 on both sides,
y = 5
Substitute y = 5 in equation (3)
x = 7 – 5
x = 2
The solution to the system of equations are (2, 5).
The square root of 1000 is between __________ .
A
498 and 502
B
98 and 102
C
48 and 52
D
28 and 32
The square root of 1000 is between 28 and 32. so option D is correct.
How to find the closest integer less than and greater than the square root of a number?The function is strictly increasing function for x ≥ 0.
Assuming that all the values of x are ≥ 1, whenever there is increment in the value of 'x', the value of y increases too.
That means, we've got:
[tex]x_1 < x_2 < x_3 \implies \sqrt{x_1} < \sqrt{x_2} < \sqrt{x_3} \: \text{(such that } x_1 \leq 1[/tex]
Perfect square are those integers whose square root is an integer.
Let x-a be the closest perfect square less than x and let x+b be the closest perfect square more than x, then we get: x-a < x < x+b (no perfect square in between x-a and x+b, except possibly x itself).
Then, we get:
[tex]\sqrt{x-a} < \sqrt{x} < \sqrt{x+b}[/tex]
We need to find the square root of 1000
So, the square root of 1000 is 31.6227766017
[tex]\sqrt{1000} = 31.622[/tex]
Thus, The square root of 1000 is between 28 and 32. so option D is correct.
Learn more about square root here:
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The square root of 1000 lies between 28 and 32, so the correct answer matches option D.
To determine the square root of 1000, we need to find two consecutive integers between which this value lies. We know that:
The square root of 900 (which is 30²) is 30.
The square root of 1024 (which is 32²) is 32.
Therefore, the square root of 1000 lies between 30 and 32.
This matches option D which states between 28 and 32.
solve the question of what is 2 + 3
Answer:
it's 5
Step-by-step explanation:
[tex]2 + 3 = 5[/tex]
5
Step-by-step explanation:
2 + 3 = 5
Total of answer is 5
What does z= ? I need the answer asap, help plsss !
Answer:
51
Step-by-step explanation:
tan(z) = 10/8
z = (tan^-1)(1.25)
z = 51.3401917459
Answer:
D) 51
Step-by-step explanation:
Form an equation to find z:
tan(z)=10/8
tan^-1(tan(z))=tan^-1(10/8)
z=51.34
So the correct choice is D
Before tax, and miscellaneous charges, Jason's cell phone bill is $100 per month plus $0.15 for every text message that he sends or receives. Which expression represents his cell phone bill for any given month?
A) 100 + 15t
B) 100 + 0.15t
C) 0.15 + 100t
D) 100t - 0.15
Answer:
b
Step-by-step explanation:
100 dollars month
100
plus
100+
0.15 per text
100+15t
During a 3-day event a total
of 7,458 people attended. If
the same number of people
attended each day, how
many people attended on
one day?
Divide Whole Numbers by Unit Fractions Quiz How many 1/5 s are in 9? A. 5/9 B. 9/5 C. 45 D. 4 1/2
Please answer my question Experts ASAP. Thank you in advance and remember to wash your hands with antibacterial soap for 1 minute.
The area of the given trapezoid is 60 square inches.
Step-by-step explanation:
Step 1:
The trapezoid's area is calculated by adding the base lengths and multiplying it with the trapezoid's height and [tex]\frac{1}{2} .[/tex]
The trapezoid's area, [tex]A = (sum of the lengths)(\frac{height}{2})[/tex]
Here the sum of the base lengths is given as 15 inches.
Step 2:
In the given problem, the sum of the base lengths is 15 inches and the height of the trapezoid is 8 inches.
The trapezoid's area [tex]A = (15)(\frac{8}{2} )= (15)(4) = 60.[/tex]
So the area of the given trapezoid is 60 square inches.
The ratio of pencils to pens in the drawer is 8:14. If there are actually twice as many pencils as in the ratio, how many pencils and pens are there in the drawer?
A. 8 pens, 14 pencils
B. 8 pencils, 14 pens
C. 16 pens, 28 pencils
D. 16 pencils, 28 pens
Yo sup??
let the number of pencils and pens be 8x and 14x
x=2
therefore the number of pens and pencils are
16 pencils and 28 pens
Hope this helps
As the actual no. of pencils is double than that of the given ratio it is
C. 16 pens, 28 pencils
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, The ratio of pencils to pens in the drawer is 8 : 14, so for every 14 pencils, there are 8 pens.
Given, there are actually twice as many pencils as in the ratio.
Therefore actual no. of pencils are (2×14) = 28 pencils.
learn more about proportion here :
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the sum of the digits in a two-digit number is 15. Three times the second digit equals two times the first digit. Write and solve a system of equations to represent this situation. Intepret the solution.
Answer:
3x 5
Step-by-step explanation:
Answer: 96 ordered pair form : (9, 6)
Step-by-step explanation:
x + y = 15
1x + 1y = 15
-1x
y = 15 - 1x (we did this so that it can be the in y=mx format)
3y = 2x (substitute the y for the solution above)
3 ( 15 - 1x ) = 2x
45 - 3x = 2x
+3x +3x
45 = 5x (divide 5 on both sides)
45/5 = 9 ; x = 9
now go back to the first equation and substitute the x for 9
y = 15 - 1(9)
y = 15 - 9
y = 6
hope this helped :)
The perimeter of the triangular park shown on the right is 10x - 3. What is the missing length?
Answer:
6x - 1
Step-by-step explanation:
Okay this is basically polynomial algebra:
1. Add the value of the lengths already given.
like terms: 3x + x = 4x, -4 + 2 = -2. Now you're left with, 4x - 2.
2. Find the difference between the perimeter and the sum of the lengths.
(10x -3) + (4x + 2) = 6x - 1
A grocery chain conducts a random survey of sales in stores to determine the types of juice to restock. The results are shown on the table. Which juice is MOST LIKELY to sell BEST when restocked? AN) Organic Apple Juice B) Organic Grape Juice C) Organic Pineapple Juice D) Grape Juice (from concentrate)
Answer:pineapple juice
Step-by-step explanation:
How much further up the wall does the ladder in figure 2 reach than
the ladder in figure 1 (to the nearest tenth of a foot)?
The ladder in figure 2 reaches 3.2 feet further up than the ladder in figure 1.
Step-by-step explanation:
Step 1:
In both the given figures, the ladder, the wall and the floor form a right-angled triangle. The floor is the adjacent side, the wall is the opposite side and the ladder is the hypotenuse.
According to the Pythagorean theorem,
[tex]a^{2}+b^{2}=c^{2}[/tex], where c is the length of the hypotenuse while a and b are the lengths of the other two sides.
Step 2:
For the ladder in figure 1, assume the distance from the floor to the ladder's top is x feet. So a = x, b = 8 and c = 10 (hypotenuse).
[tex]a^{2}+b^{2}=c^{2}[/tex], [tex]x^{2}+8^{2}=10^{2}[/tex], [tex]x^{2}=100-64=36, x=\sqrt{36}=6 \text { feet }[/tex].
So the distance between the floor and the ladder's top is 6 feet.
Step 3:
For the ladder in figure 2, assume the distance between the floor and the ladder's top is y feet. So a = y, b = 4 and c = 10 (hypotenuse).
[tex]a^{2}+b^{2}=c^{2}[/tex], [tex]y^{2}+4^{2}=10^{2}[/tex], [tex]y^{2}=100-16=48, x=\sqrt{84}=9.1651 \text { feet }[/tex].
So the distance between the floor and the ladder's top is 9.1651 feet.
Step 4:
The difference in heights = The wall height in figure 2 - the wall height in figure 1.
The difference in heights = 9.1651 feet - 6 feet = 3.1651 feet.
Rounding this off to the nearest tenth of a foot, we get 3.2 feet.
Answer: the answer is 3.2 when rounded
Step-by-step explanation:
if you want the explanation look at the one above
j(m) = 2m-1
What is j(4) ?
Enter your answer in the box.
Final answer:
To calculate j(4), we plug in 4 into the function j(m) = 2m - 1, which gives us j(4) = 7.
Explanation:
To determine the value of j(4) in the given function j(m) = 2m - 1, a straightforward substitution is applied. By replacing the variable m with the provided value of 4, the expression j(4) is computed as 2 × 4 - 1, yielding 8 - 1, which simplifies to 7. Therefore, the value of j(4) is unequivocally established as 7. This process exemplifies the fundamental concept of function evaluation, showcasing how input values substitute variables within a function, ultimately producing a specific numerical result for a given function and input combination.