Answer:
Length: 9 inches.
Width: 6 inches.
Step-by-step explanation:
Find the dimensions of the floor of the doll house.
Apply the formula:
[tex]A=lw[/tex]
Where A is the area, l is the lenght and w is the width.
You know that:
[tex]A=864\\w=\frac{2}{3}l[/tex]
Then you can solve for l:
[tex]864=l(\frac{2}{3}l)\\\\864=\frac{2}{3}l^2\\\\l=\sqrt{\frac{864*3}{2}}\\\\l=36in[/tex]
Then the width is:
[tex]w=\frac{2}{3}(36)=24in[/tex]
Therefore, the dimensions of the floor on the blueprint of the doll house are:
[tex]l'=\frac{1}{4}(36in)=9in\\\\w'=\frac{1}{4}(24in)=6in[/tex]
Answer:
Step-by-step explanation:
The actual dollhouse floor measurements were figured out to be 24 by 36.
24x36 = 864 square inches for the area, which matches to the problem.
The blueprint measurements are to be 1/4 of the actual measurements, so 1/4 of 24 is 6, and 1/4 of 36 is 9. Therefore, the scaled down measurements of the dollhouse floor are 6x9, which supposedly solves the problem.
But my family and I wondering -- if the actual floor area is 864, and the scaled down drawing is supposed to be 1/4 the size of the actual, then shouldn't the scaled down blueprint area be 1/4 of 864, so 216??
And 6x9 equals 54, not 216!
What are we missing??
two models are shown. Each model has been shaded grey to represent a fraction. wgucj statement is true about the fractions 3/4 and 6/8
The fractions 3/4 and 6/8 are equivalent. They are essentially the same when reduced to their lowest terms, both representing the same part of a whole.
Explanation:The statement that is true about the fractions 3/4 and 6/8 is that they are equivalent fractions. The student's question is about the comparison of the fractions 3/4 and 6/8. When these two fractions are examined, it becomes clear that they are, in fact, equivalent.
This is because when you divide the numerator and the denominator of 6/8 by their highest common factor, which is 2, you get 3/4. Therefore, 3/4 and 6/8 are equivalent fractions and represent the same part of the whole.
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Meg buys 12 bags of sunflower seeds. Each bag has 58 seeds. How many seeds dose meg have??
Answer: 696
Step-by-step explanation:
58 times 12
Answer:
696 seeds
Step-by-step explanation:
12*58
if you borrow $400 for 2 years at an annual interest rate of 15%, how much will u pay altogether?
Answer:
$520
Step-by-step explanation:
We first find the interest;
400*2*15/100=4*2*15
=$120
Total=$120+$400
=$520
Answer:520
Step-by-step explanation:
above correct
Amanda teaches the art of quilling to four students these students each teach the art of quilling to four other students if this process continues for five generations blank people will know the art of quilling
In the fifth generation 1024 people learnt the art of quilling.
What is a geometric series?A geometric series is a series for which the ratio of each two consecutive terms is a constant and called the common ratio.Nth term of the Geometric series is given as [tex]t_{n} = ar^{n-1}[/tex] where a is the first term of the series and r is the common ratio.How to find how many people will know the art of quilling?In the first generation , 4 people learnt the art of quilling.In second generation (4 x 4) = 16 people learnt the art of quilling.In the third generation (16 x 4) = 64 people learnt the art of quilling.In the fourth generation (64 x 4) = 256 people learnt the art of quilling.In the fifth generation ( 256 x 4) = 1025 people learnt the art of quilling.In the fifth generation 1024 people learnt the art of quilling.
The series is going as a geometric pattern.In total 5 generations total (16+ 64 + 256 + 1024) = 1364 people learnt the art of quilling.
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Using the exponential growth formula, it is determined that by the end of five generations, 4096 people will know the art of quilling, starting with one teacher teaching four students, and each subsequent student teaching four others.
Explanation:The question involves an exponential growth scenario where Amanda teaches the art of quilling to four students, and then these students each teach four others, and so on for five generations. To find out how many people will know the art of quilling by the fifth generation, we use the formula for exponential growth: Total = a(1 + r)^n, where a is the initial amount (number of people who know the art at the beginning), r is the rate of increase (each person teaches 4 others means the rate is 4), and n is the number of generations.
The initial teacher, Amanda, is not counted in the first generation of students she teaches, so we begin with 4 students as our initial amount (a=4). Thus, the calculation for five generations becomes: Total = 4(4)^5. The formula simplifies to 4 * 1024 = 4096 people. Therefore, by the end of five generations, 4096 people will know the art of quilling.
Plz help needed to graduate!!
I hope the answer is 7/4
4. The MAD of a set of six data values is 10. The mean is 20. What could the data values be? Show that the mean is 20 and the MAD is 20.
Answer:
15
Step-by-step explanation:
The data values could be 10, 10, 10, 25, 25, 40.
What is mean Absolute Deviation?Mean absolute deviation is defined as the average value of the absolute deviations from the mean.
Given that,
Mean absolute deviation of a set of 6 data values = 10
Let x1, x2, x3, x4, x5 and x6 be the data values.
Mean = 20
x1 + x2 + x3 + x4 + x5 + x6 / 6 = 20
x1 + x2 + x3 + x4 + x5 + x6 = 120
Also we have mean absolute deviation = 10
Data values could be 10, 10, 10, 25, 25, 40.
Mean = 20 and MAD = 10
Hence the data values could be 10, 10, 10, 25, 25, 40.
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what is the coefficient of the variable in the expression 1/2 + v - 3
The coefficient of the variable is equal to 1
What is a coefficient
A coefficient is a value that is attached to a variable. It is the number always in front for a variable eg x, y or v in this case.
Data given;
[tex]\frac{1}{2} + v - 3 = v - \frac{5}{2} [/tex]The coefficient of the variable (v) is 1 because if it is greater than 1, or less than one and cannot be equal to zero, it would be attached.
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what is the lateral area of this regular octagonal pyramid?
149.3 cm
182.9 cm
211.2 cm
298.7 cm
Answer:
The lateral area is [tex]298.7\ units^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the regular octagonal pyramid is equal to the area of its eight triangular lateral faces
The lateral area is equal to
[tex]LA=8[\frac{1}{2}(b)(l)][/tex]
we have
[tex]b=6.6\ cm[/tex]
To find the slant height apply the Pythagoras Theorem
[tex]l^{2}=8^{2} +8^{2}\\l^{2}=128\\l=\sqrt{128}\ units[/tex]
Find the lateral area
substitute the values
[tex]LA=8[\frac{1}{2}(6.6)(\sqrt{128})]=298.7\ units^{2}[/tex]
The answer is 298.7 cm²
Which method is most efficient method to use to solve 2x^2+4x-7=0
Answer:
Use the quadratic formula
Step-by-step explanation:
Use the quadratic formula
For a quadratic function of the form:
[tex]ax ^ 2 + bx + c[/tex]
Where a, b and c are the real coefficients of the polynomial
Then, for
[tex]2x^2+4x-7=0\\a = 2\\b = 4\\c = -7[/tex]
The solutions are:
[tex]x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_2 = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]
[tex]x_1 = \frac{-4+\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_2 = \frac{-4-\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_1 = \frac{-2+3\sqrt{2}}{2}\\\\x_2 = \frac{-2-3\sqrt{2}}{2}[/tex]
Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)
Which of them factored 14y3 correctly ?
Answer:
Hiro factored them correctly.
Step-by-step explanation:
The factors of 14 are 1, 2, 7, and 14.
7 * 2 = 14
10 and 4 make the product of 14.
10 + 4 = 14
Bilial factored 14y3 correctly.
Explanation:Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)
To determine which one factored 14y3 correctly, we need to compare their factorizations to the original expression: 14y3. Hiro's factorization (7y2)(2y) does not match the original expression, as it is missing a y term. On the other hand, Bilial's factorization (10y)(4y2) matches the original expression.
Therefore, "Bilial factored 14y3 correctly."
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Find the volume of a sphere with a diameter 40 cm in length. Approximate pi as 3.14 and round your answer to the nearest tenth. A. 5,026.5 cm3 B. 33,493.3 cm3 C. 42,090.0 cm3 D. 268,082.6 cm3
Answer:
Option B. [tex]33,493.3\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=40/2=20\ cm[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{4}{3}(3.14)(20)^{3}=33,493.3\ cm^{3}[/tex]
What's the value of x? x=
Answer:
x = 2
Step-by-step explanation:
These are 2 secant lines intersecting a circle. This problem can be solved using secant-theorem.
Simply put, the secant theorem tells us that the outer segment (outside the circle) times the total length of secant line (outer and inner segment) is equal to that of the other secant line's product of outer and total.
For this diagram, according to the theorem, it should be:
DE * CE = AE * BE
Hence we have:
[tex]DE * CE = AE * BE\\(1+x+4)*(x+4)=(11+x+1)*(x+1)\\(x+5)*(x+4)=(x+12)*(x+1)\\x^2+9x+20=x^2+13x+12\\20-12=13x-9x\\8=4x\\x=\frac{8}{4}=2[/tex]
The value of x is 2
If a man weighs 198 pounds on earth, his mass on earth is 90 kilograms. If you can answer A & B
It is 5892 and i know it has to be or I guess I am wrong (i don’t care) hahahaha
Can anyone help please?
Answer:
- 9 1/4
Step-by-step explanation:
Get a common denominator for the fractions
-5 3/4 - 3 1/2 *2/2
-5 3/4 - 3 2/4
-5 3/4 + -3 2/4
Add them together
-8 5/4
We have an improper fraction
-( 8 + 1 1/4)
- (9 1/4)
- 9 1/4
I need help please???
I need help to please?
Answer:
x = 15
Step-by-step explanation:
Which expressions are equivalent to (a^2-16(a+4)? Select the three equivalent expressions
A.) a^3-64
B.) (a-4)^3
C.) (a+4)^3
D.) (a+4)^2(a-4)
E.) (a-4)^2(a+4)
F.) [(a)^2-(4^2)](a+4)
G.) (a-4)(a+4)(a+4)
Answer:
F
Step-by-step explanation:
Final answer:
The three equivalent expressions to (a^2-16(a+4)) are: (a-4)^3, (a+4)^2(a-4), and (a-4)(a+4)(a+4).
Explanation:
The expression (a^2-16(a+4)) can be simplified by expanding the terms and combining like terms. First, apply the distributive property by multiplying -16 by (a+4), giving -16a-64. Then, multiply a^2 by -16 to get -16a^2. Finally, combine like terms to get -16a^2 - 16a - 64.
Therefore, the three equivalent expressions to (a^2-16(a+4)) are:
(a-4)^3
(a+4)^2(a-4)
(a-4)(a+4)(a+4)
how much empty space is inside the can of tennis balls? the radius of each tennis ball is 1.5 inches. The radius of the can is 1.75 inches and the height is 9 inches. Use 3.14 for pi, and round your answers to the nearest hundredth.
Final answer:
To find the empty space in the can of tennis balls, calculate the volume of one tennis ball and multiply by three (since there are typically three balls per can), then subtract from the volume of the can. There are 43.54 inches³ of empty space in the can, after rounding to the nearest hundredth.
Explanation:
To calculate the empty space inside the can of tennis balls, we first need to determine the volume of one tennis ball and then the volume of the can. Given the radius of each tennis ball is 1.5 inches, we use the formula for the volume of a sphere:
V_ball = 4/3 π r³
Substitute with r = 1.5 inches and π = 3.14:
V_ball = 4/3 × 3.14 × (1.5 inches)³
V_ball = 4/3 × 3.14 × 3.375 inches³
V_ball = 14.13 inches³ (rounded to the nearest hundredth)
Next, we calculate the volume of the can, using the formula for the volume of a cylinder:
V_can = π r² h
Substitute with r = 1.75 inches and h = 9 inches:
V_can = 3.14 × (1.75 inches)² × 9 inches
V_can = 3.14 × 3.0625 inches² × 9 inches
V_can = 85.93 inches³ (rounded to the nearest hundredth)
The empty space within the can is therefore the volume of the can minus the volume of three tennis balls (assuming the can holds three balls):
Empty space = V_can - 3 × V_ball
Empty space = 85.93 inches³ - 3 × 14.13 inches³
Empty space = 85.93 inches³ - 42.39 inches³
Empty space = 43.54 inches³ (rounded to the nearest hundredth)
Therefore, there are approximately 43.54 inches³ of empty space inside the can.
Which ordered pair is a solution of the inequality?
Y-1<2x
a. (3,7)
b. (1,8)
c. (2,7)
d. (3,-11)
Answer:
d. (3, -11)Step-by-step explanation:
[tex]y-1<2x\qquad\text{add 1 to both sides}\\\\y<2x+1\\\\\text{Substitute the coordinates of the points and check the inequality:}\\\\a.\ (3,\ 7)\\7<2(3)+1=6+1=7\qquad\text{FALSE}\\\\b.\ (1,\ 8)\\8<2(1)+1=2+1=3\qquad\text{FALSE}\\\\c.\ (2,\ 7)\\7<2(2)+1=2+1=5\qquad\text{FALSE}\\\\d.\ (3,\ -11)\\-11<2(3)+1=6+1=7\qquad\text{TRUE}[/tex]
how long can the run be made?
Answer:
[tex]L=15\ m[/tex]
Step-by-step explanation:
we know that
The perimeter of rectangle is equal to
[tex]P=2L+2W[/tex]
In this problem we have
[tex]P=42\ m[/tex]
[tex]W=6\ m[/tex]
substitute in the formula and solve for L
[tex]42=2L+2(6)[/tex]
simplify
[tex]21=L+(6)[/tex]
[tex]L=21-6=15\ m[/tex]
If y varies inversely with x and y=8 when x=40, what is the constant of variation
Answer:
Step-by-step explanation:
Inverse Variation. Since k is constant, we can find k given any point by multiplying the x-coordinate by the y-coordinate. For example, if y varies inversely as x, and x = 5 when y = 2, then the constant of variation is k = xy = 5(2) = 10.
In 1998 the population of a city was 100,000. Then each year for the next five years the population increases by 3%. Write and exponential growth model to represent this situation.
➷ population = 100,000 x 1.03^5
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ANSWERRRR<3 5. It took 12 reams of paper to produce 500 pamphlets. How many reams can produce 48
pamplets?
(A)0.096 (B)2000 (C)125 (D) 1 19/125
Answer:6
Step-by-step explanation:
500/12 is 41 so therefore you do 48/12 is 6.
Answer:
1 19/125
Step-by-step explanation:
1.) 12/500 = 0.024
2.) 0.024 * 48 = 1.152
3.) 1.152 converted to a fraction is 144/125, or 1 19/125
Need help QUICK!!! #3
A=f(18)=110(.8855)^18=12.3mg
===========================================================
Explanation:
Plug in t = 18 to get
f(t) = 110*(0.8855)^t
f(18) = 110*(0.8855)^18
f(18) = 110*(0.112045)
f(18) = 12.32495
f(18) = 12.32
The answer is approximate. I rounded to two decimal places (aka to the nearest hundredth).
The half-life of a radioactive kind of europium is 9 years. How much will be left after 18 years, if you start with 40 grams of it ?
Answer:There will be 10 grams left because you subtract half of the current amount from it every 9 years.
Step-by-step explanation:
Starting with 40 grams of europium which has a half-life of 9 years, after the first half-life, there would be 20 grams left, and after the second half-life (a total of 18 years), there would be 10 grams remaining.
The question is about calculating the amount of a radioactive substance that remains after a certain period of time has passed, which is based on the substance's half-life. Given that the half-life of europium is 9 years, after one half-life (9 years) 50% of the substance would remain, and after two half-lives (18 years) only 25% would remain. Since we started with 40 grams of europium, we apply this decay process step by step:
After the first half-life (9 years), 40 grams become 20 grams.After the second half-life (another 9 years, total of 18 years), the remaining 20 grams become 10 grams.Therefore, after 18 years, there will be 10 grams of the radioactive europium left.
Rewrite as a simplified fraction.
0.482=?
Answer: [tex]\bold{\dfrac{241}{500}}[/tex]
Step-by-step explanation:
[tex]0.482 = \dfrac{482}{1000}\\\\\\\dfrac{482}{1000}\div \dfrac{2}{2}=\dfrac{241}{500}[/tex]
Answer:
241/500 is The answer
Step-by-step explanation:
1) 0.482 = 482/1000
2) Divide by 2 on both side
0.482 = (482/2)/(1000/2) = 241/500
Hopes this helps!
What is the value of angle x rounded to the nearest whole number
Answer:
x ≈ 42°
Step-by-step explanation:
Label the vertices of the quadrilateral shown at the upper left in you diagram A, B, C, and D, starting at the lower left. Label the center point X. Then the red line is CX and the lower two line segments are CD and DA. (A, C, D, and X are not coplanar.)
Angle D of triangle ACD is the interior angle of a regular pentagon, so measures 108°. That means angle ACD measures (180° -108°)/2 = 36°. If we label the midpoint of segment AC point Y, then the length of segment CY is ...
CY = CD·cos(36°)
Now triangle BCD is an equilateral triangle, so segment CX will have a length corresponding to the altitude of that triangle, CD·√3/2. Shifting our focus to the triangle AXC, we find that angle XCY will satisfy the relation ...
cos(XCY) = CY/CX = CD·cos(36°)/(CD·√3/2) = (2/)√3·cos(36°)
Angle x is the exterior angle of triangle AXC that is opposite the two equal interior angles XCY and XAY. Hence its value is double that of angle XCY.
angle x = 2·arccos((2/√3)·cos(36°)) ≈ 2·20.905° ≈ 41.81°
angle x ≈ 42°
_____
Comment on the angle
The icosahedron is the only Platonic solid with a dihedral angle more than 120°. It is about 138.19°, the supplement to angle x.
Comment on point labels
It may help to label the points in the 3-d version of the figure. Then you can see that segment AC is a line through the interior space of the icosahedron.
4 lb of bananas for $2.76 is the same as
1 lb of bananas for $.69
A triangular window pane has a base of 30 inches and a height of 24 inches.What is the area of the window pane?
54 or it 180 i got 54 by adding 30 and 24in and got 180 by multiplying
Answer: 360 sq inches
Step-by-step explanation: The formula for finding the area of a triangle is 1/2*bh. So, plug-in your numbers: 1/2*(30*24). Then multiply the value in the perentheses which is 720 and then you multiply that by 1/2 (0.5) or you can divide it by 2. When you divide it by 2 or multiply it you would get 360.
Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. How long did it take Lucy to bike the trail?
Plz explain your awnser
Answer:
3.75 hours
Step-by-step explanation:
Using the relation
Distance = speed × time
Change Jasmine's speed into an improper fraction
9 [tex]\frac{3}{10}[/tex] = [tex]\frac{93}{10}[/tex], then
distance = [tex]\frac{93}{10}[/tex] × [tex]\frac{5}{2}[/tex] = [tex]\frac{93}{4}[/tex] miles
To calculate Lucy's time over the same distance use
Time = [tex]\frac{distance}{speed}[/tex]
Change speed to an improper fraction
6 [tex]\frac{1}{5}[/tex] = [tex]\frac{31}{5}[/tex], hence
time = [tex]\frac{\frac{93}{4} }{\frac{31}{5} }[/tex]
= [tex]\frac{93}{4}[/tex] × [tex]\frac{5}{31}[/tex] ( cancel 93 and 31 )
= [tex]\frac{3(5)}{4}[/tex]
= [tex]\frac{15}{4}[/tex] = 3.75 hours
Final answer:
It took Lucy approximately 160.17 minutes to bike the trail.
Explanation:
Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. To find out how long it took Lucy to bike the trail, we can use the formula:
Time = Distance / Rate
Since the distance is the same for both Jasmine and Lucy, we can set up an equation:
2.5 = Distance / 6 1/5
To solve this equation, we first need to convert 2.5 into a fraction. 2.5 is the same as 2 1/2. So, the equation becomes:
2 1/2 = Distance / 6 1/5
To make the equation easier to work with, we can convert 2 1/2 into an improper fraction: 2 1/2 = 5/2. The equation now becomes:
5/2 = Distance / 6 1/5
To solve for Distance, we can use cross-multiplication:
(5/2)(6 1/5) = Distance
Simplifying the right side of the equation:
(5/2)(31/5) = Distance
(5/1)(31/5) = Distance
31 = Distance
So, the distance of the bike trail is 31 miles. Now, we can find out how long it took Lucy to bike the trail by using the formula Time = Distance / Rate:
Time = 31 / 6 1/5
Once again, let's convert 31 into a fraction: 31 = 31/1. The equation now becomes:
Time = 31/1 / 6 1/5
To divide fractions, we can multiply by the reciprocal of the second fraction. So, the equation becomes:
Time = 31/1 * 5 1/6
Now, we can convert 5 1/6 into an improper fraction: 5 1/6 = 31/6. The equation now becomes:
Time = 31/1 * 31/6
To multiply fractions, we can multiply the numerators together and the denominators together. So, the equation becomes:
Time = (31*31) / (1*6)
Calculating the numerator and denominator separately:
Time = 961 / 6
So, it took Lucy approximately 160.17 minutes to bike the trail.
Simplify 4/16 to lowest terms and find and equivalent fraction that has a denominator of 32
8/32 is the answer to your problem
The equivalent fraction of given fraction is [tex]\frac{8}{32}[/tex].
Given fraction is, [tex]\frac{4}{16}[/tex]
It is observed that both numerator and denominator of given fraction is divisible by 4.
Simplest form of [tex]\frac{4}{16}[/tex] is,
[tex]\frac{4}{16}=\frac{4*1}{4*4} =\frac{1}{4}[/tex]
Equivalent fraction that has a denominator of 32 is,
[tex]\frac{1}{4}=\frac{1*8}{4*8}=\frac{8}{32}[/tex]
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