A rectangle has a perimeter of 48 inches. If twice the length decreased by three is equal to three times the width, the find the length and the width
Answer:
Length= 15, width= 9Step-by-step explanation:
perimeter of a rectangle P= 2(L+W)
L= length
W= width
48=2(L+W)---------------(1)
twice the length= 2×L= 3L
decreased by three= 2L-3
three times the width= 3×W= 3W
twice the length decreased by three is equal to three times the width
2L-3= 3W-------------------(2)
solving equation one and two simultaneously
from equation (2)
3W= 2L-3
W=2L/3-3/3
W= 2L/3 - 1----------(3)
substitute equation (3) into equation (1)
48=2(L+2L/3-1)
48=2L+4L/3-2
48×3=6L+4L-6
144=10L-6
10L=144+6
10L=150
dividing bothsides by 10
L= 15
substitute L= 15 into equation (2)
2L-3=3W
2(15)-3=3W
30-3 = 3W
27= 3W
3W= 27
dividing bothsides sides 3
3W=27/3
W=9
therefore, Length= 15, width= 9please answer question below asap!!
Answer:
175000
Step-by-step explanation:
If the 1 is centimeters, then you would take 7 centimeters and multiply it by 25000 to get 175000.
Identify the growth factor for the following exponential function: y= 2.3(1.32)*
A. 2.3
B. 1.32
C. X
D 32%
A shirt is on sale for 40% off. The sale price is $12. How much was the discount?
Let p = the original price
p - .4p = 12
.96p = 12
p = 12.5
The original price was $12.50
12.5 - 12 = .5
The amount of the discount was $.50
Evaluate. (3/8+3/4)−(1/3+1/6)
Answer:
0.625
Step-by-step explanation:
You must first calculcate what is in between the parentheses. Firstly, you add 3/8 + 3/4 (as shown in the beginning) to get 1.125. Second, you add 1/3 plus 1/6 (shown in the second part of the equation) to get 0.5. Lastly, you're left with 0.625 after subtracting 0.5 from 1.125.
A bag of colored paper clips contains 3 red clips
and 6 green clips. What's the probability of
pulling out a red clip and then a green clip?
(Assume that you don't put the first red paper
clip back in the bag.) Write your answer as a
fraction.
Answer:
1/5
Step-by-step explanation:
solution [ calculation of probability ]
P= (3/3+6) × (6/3+6-1)
=3/9×6/10
=1/5
Evaluate the integral, please help!!!
[tex]\int_{0}^{\pi}(1+cosx) dx[/tex]
Answer:
pi
Step-by-step explanation:
First solve the integral
[tex]\int\ {(1+ cos x} )\, dx[/tex]
[tex]\int\ {1} \, dx +\int\ {cos x} \, dx[/tex]
[tex]\int\ {1} \, dx = x[/tex] and [tex]\int\ {cos x} \, dx = sin x[/tex]
x + sin x
Now consider the limit from 0 to π
[tex]\lim_{0 \to \\pi } (x+sin x)[/tex]
(π +sin π) -(0 +sin 0)
sin π = 0 and sin 0 = 0
π-0
π
Answer:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx=\pi[/tex]
Step-by-step explanation:
[tex]\displaystyle \int\limits^\pi_0 {(1+\cos x)} \, dx\\\\=x+\sin x\biggr|^{\pi}_0\\\\=[\pi+\sin\pi]-[0+\sin0]\\\\=\pi[/tex]
Remember your antiderivatives!
What is the variance of the data set? round to the nearest hundredths. 0.40 0.72 1.15 2.14
The variance of the data set is 0.43.
What is the variance?The variance is used to measure the spread or the dispersion of a dataset using all the data points in the dataset. The variance is the sum of the squared difference between the data point and the mean.
The first step is to determine the mean: (0.40 + 0.72 + 1.15 + 2.14) / 4
= 4.41 / 4= 1.10
The second step is to subtract the mean from each of the data point and square the difference:
(0.40 - 1.10) ² = 0.49(0.72 - 1.10)² = 0.14(1.15 - 1.10)² = 0.0025(2.14 - 1.10)² = 1.08Add the sum of the squared differences and divide by 4 : 1.7125/4 = 0.43
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You roll a number cube twenty times and it lands on a 3 five times. What is the
experimental probability that it ends on a 3 the next time you roll?
Answer:
Hence, a fair dice has a probability of 16 to land on any predetermined number 1 through 6. Therefore, to land on 3 the probability is 16
Step-by-step explanation:
Explain how the arc BX, central angle BCX, and inscribed BNX are connected. You can compare two or three at a time. B АХ C Z
Answer:
arc BX = central angle BCX
inscribed BNX = 1/2 of central angle BCX
inscribed BNX = 1/2 of arc BX
Step-by-step explanation:
arc BX = central angle BCX
inscribed BNX = 1/2 of central angle BCX
inscribed BNX = 1/2 of arc BX
5
——
——
i need help!!
————-
math geniuses pls help me!
Answer:
C
Step-by-step explanation:
x = 7 cos (2pi/3) y = 7 sin (2pi/3)
x = -7/2 y = 7 sqrt(3) /2
Cube: Find the surface area of a cube with side 5 inches.
Answer:
We are given the dimension of the side being 5 inches and it states that we need to determine the surface area. The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.
[tex]A = s^2[/tex]
[tex]A = (5\ in)^2[/tex]
[tex]A = 25\ in^2[/tex]
Now that we have the area of one side we can multiply it by 6 to get the total surface area.
[tex]A = 25\ in^2 * 6[/tex]
[tex]A = 150\ in^2[/tex]
Therefore, our final answer is that the surface area is 150 inches squared
Hope this helps!
Answer:
150 square inches
Step-by-step explanation:
find the area of 1 square face
5*5=25
multiply by 6 faces
25*6=150
Pls answer
THe question below in the image
Answer:
Question 1: D.Question 2: C.Step-by-step explanation:
Question 1:
Franco made 36 invitations and gave out 14. How many invitations does he have left?
Simple. Solve for the bottom:
Bottom (Total): 36Right (Blue grid): 14Left (Red grid): ?That is the answer D.
Question 2:
Ebba gave out 36 invitations and still has 14 left. How many invitations does she have in all?
Complicated (a bit). Solve:
Bottom (Total): ?Left (Red grid): 14Right (Blue grid): 36That is the answer C.
8 There are a combined 33 students who play a spring sport of track or
baseball. There are 3 more students on the track team than the baseball
team. How many students are on the track team? How many are on the
baseball team?
30
The number of students that are on the track team are 18.
The number of students that are on the baseball team are 15.
What are the linear equations that represent the question?a + b = 33 equation 1
a - b = 3 equation 2
Where:
a = number of students that are on the track teamb = number of students that are on the baseball teamHow many students that are on the baseball team?
Subtract equation 2 from equation 1
2b = 30
Divide both sides by 2
b = 30/2 = 15
How many students that are on the track team?
Subtract 15 from 33: 33 - 15 = 18
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Rowan bought a bag of jelly beans that
contained 54 ounces of jelly beans. She
divided the jelly beans into bags that
contained 6.75 ounces each. Write a division
equation that could be used to find the
number of bags she made.
Answer:
[tex]\sf y=\dfrac{54}{6.75}[/tex] or [tex]\sf y=54 \div 6.75[/tex]
(where y is the number of bags made)
Step-by-step explanation:
If Rowan bought a 54 oz bag of jelly beans and divided them into bags that each contained 6.75 oz, to find how many bags were made, divide the total weight of jelly beans by the weight of each bag.
⇒ Number of bags = Total weight ÷ bag weight
= 54 ÷ 6.75
= 8
Therefore, Rowen made 8 bags.
Total weight of jelly beans initially
54ozEach bag contains
6.75ozSo the equation should be
Bags=54/6.75Or
B=54/6.75If we solve we get total bags as 8
If h = 3.5u, what is the value of h when u = 17?
Give any decimal answers to 1 d.p.
Put u=17
h=3.5(17)h=51+8.5h=59.5Answer:
59.5.
Step-by-step explanation:
h = 3.5u
When u = 17,
h = 3.5*17
= 59.5
a triangle ABC like the one below suppose that a=40, B = 62 and c= 23 (the figure is not drawn to scale) solve the triangle carry your intermediate computations to at least four decimal places , and round your answers to the nearest tenth . if there is more than one solution , use the button labeled "or"
Answer:
Answer:
A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
∴ A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Im not sure if it is right. But hope it helps
How many dots are in 1/2 of this group?
Answer:
the answer is 9, the total number of dots is 18. which divided into three is 6 in a column.
and the 1/2 of this in the group Is 9
Solve for x and find the length of GH (show work)
Answer:
A. How are GH and GI related?
They are tangents.B. Write an equation to solve for x.
GH = GIC. Let's solve the equation...
GH : 2x
GI : x + 12
2x = x + 122x - x = 12x = 12D. Now, that we solve for x, let's find the length of GH....
GH = 2x where, x = 12
2(12)24Therefore, the length of GH is 24.
Consider the cone with slant height of 13 m and perpendicular height of 12 m: a) Find the length of the radius, r. b) Find the length of the diameter of the cone's base.
Answer:
Step-by-step explanation:
Ruth ann wants to research two different careers, medical doctor and astronaut. what is a good first step ruth ann could take? if she went to a bookstore to research her careers, which section would she search?
Ruth can visit US Bureau of Labor Statistics website so that she could know more about those careers.
What is a career?career can be regarded as a profession that individuals choose to follow in his lifetime and this his occupation.
Therefore, in choosing a career , one needs to equip himself with information about it, he can visit Bureau of Labor Statistics.
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Answer:
visit the US. Bureau of Labor Statistics website to find information on both careers and the career section
Step-by-step explanation: well i know it right because i just answered it correct
A bag of flour weighs 90 grams. If the weight of the bag increases by 15% find the new weight of the bag.
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
weight of bag = 90 grams
According to Question ,
weight of the bag increases by 15%
therefore ,
the new weight of bag ,
[tex] \frac{\cancel{15}}{\cancel{10}\cancel0} \times 9\cancel0 \\ \\ \dashrightarrow \: \frac{3}{2} \times 9 \\ \\ \dashrightarrow \: \frac{27}{2} \\ \\ \dashrightarrow \: 13.5[/tex]
so ,
new weight = 90 + 13.5 kg
= 103.5 kg
hope helpful ~
Instructions
For this activity, you will need two different coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events.
Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:
Result
Frequency
Two heads 30
Two tails 40
One head, one tail 70
Answer the following questions based on the data you gathered. You must show your work to receive credit.
What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?
The experimental probability that a coin toss results in two heads showing is 3/14
The theoretical probability of two headsThe sample space of two coins is:
S = {HH, HT, TH, TT}
In the above sample space, we have:
n(HH) = 1 i.e. number of two headsTotal = 4 i.e. the sample sizeThe theoretical probability of two heads is calculated as:
P = n(HH)/Total
This gives
P = 1/4
Hence, the theoretical probability of two heads is 1/4
The experimental probability of two heads?To do this, we make use of the table in the question
The table is given as:
Result Frequency
Two heads (HH) 30
Two tails (TT) 40
One head, one tail (HT) 70
Total 140
The experimental probability of two heads is calculated as:
P = n(HH)/Total
This gives
P = 30/140
Simplify
P = 3/14
Hence, the experimental probability of two heads is 3/14
The theoretical probability of two tailsUsing the sample space in (a), we have:
n(TT) = 1 i.e. number of two tailsTotal = 4 i.e. the sample sizeThe theoretical probability of two tails is calculated as:
P = n(TT)/Total
This gives
P = 1/4
Hence, the theoretical probability of two tails is 1/4
The experimental probability of two tailsFrom the table in the question, we have:
Two tails (TT) =40
Total = 140
The experimental probability of two tails is calculated as:
P = n(TT)/Total
This gives
P = 40/140
Simplify
P = 2/7
Hence, the experimental probability of two tails is 2/7
The theoretical probability of one head and one tailUsing the sample space in (a), we have:
n(HT) = 2 i.e. number of one head and one tailTotal = 4 i.e. the sample sizeThe theoretical probability of one head and one tail is calculated as:
P = n(HT)/Total
This gives
P = 2/4
Simplify
P = 1/2
Hence, the theoretical probability of one head and one tail is 1/2
The experimental probability of one head and one tailFrom the table in the question, we have:
One head one tail (HT) = 70
Total = 140
The experimental probability of one head one tail is calculated as:
P = n(HT)/Total
This gives
P = 70/140
Simplify
P = 1/2
Hence, the experimental probability of one head one tail is 1/2
Why are there difference between the theoretical probabilities and the experimental probabilities?The reason for the difference between the probability types is because one is as a result of an actual experiment, while the other is an estimate of the experiment.
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Help pls
Two digits of the 6-digit number X = 345 * 8* are missing. Fill in the missing digits
so that the number obtained is the smallest possible number that is divisible by 45.
Find X.
The smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.
What is the divisible rule of 9 and 5?The divisible rule of 9 and 5 are:
Divisible rule of 9- When the addition of all number is divisible by 9, then that number also divisible by 9.Divisible rule of 5- When a number has a digit 0 or 5 in the last of it, then that number also divisible by 5.Two digits of the 6-digit number are missing.
[tex]X = 345 * 8*[/tex]
The smallest possible number from this is divisible by 45. The factors of 45 are 9 and 5.
[tex]45=9\times5[/tex]
Thus, the 6-digit number which is divisible by 45, must be divisible by 9 and 5.
To be divisible with 5, the number has 0 or 5 in last. So the numbers can be,
[tex]X = 345 * 85\\X=345 * 80[/tex]
For first number, when the blank is filled with number 2 to make sum 9 and for second the blank number should be 7. Thus, the numbers,
[tex]X = 345 285\\X=3457 80[/tex]
Thus, the smallest possible number that is divisible by 45 when the blanked place of the number is filled is 345285.
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The annual fundraising goal of a college is $100,000. so far $58,743 has been raised. how much more money is needed to reach the goal?
Answer:
41,257
Step-by-step explanation:
100,000
-
58,743
-------------
41,257
The amount that is needed to reach the goal is $41257 if the annual fundraising goal of a college is $100,000. so far $58,743 has been raised.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The annual fundraising goal of a college is $100,000.
Let x be the amount that is needed to reach the goal.
The linear equation in one variable can be framed as follows:
x + 58,743 = 100,000
x = 100,000 - 58,743
x = $41257
Thus, the amount that is needed to reach the goal is $41257 if the annual fundraising goal of a college is $100,000. so far $58,743 has been raised.
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You work for a cereal company that is looking to design some new boxes for their cereal. The cereal is sold in the size of 512 cubic units
You will be designing three rectangular prisms with unique dimensions. Find the surface area of each of your prisms, showing your work.
Dimensions and Surface Area
1)
2)
3)
If the dimension of the rectangular prism will be (4, 8, 16), (2, 8, 32), and (2, 4, 64). Then the surface area will be 448, 672, and 784 square units respectively.
What is a rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
You work for a cereal company that is looking to design some new boxes for their cereal.
The cereal is sold in the size of 512 cubic units.
You will be designing three rectangular prisms with unique dimensions.
The possible dimension of the rectangular prism will be
Volume = 512
Volume = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Then we have
{(4, 8, 16), (2, 8, 32), (2, 4, 64)}
Then the surface area will be
If the dimension is (4, 8, 16). Then the surface area will be
Surface area = 2(4x8 + 8x16 + 16x4)
Surface area = 448 square units
If the dimension is (2, 8, 32). Then the surface area will be
Surface area = 2(2x8 + 8x32 + 32x2)
Surface area = 672 square units
If the dimension is (2, 4, 64). Then the surface area will be
Surface area = 2(2x4 + 4x64 + 64x2)
Surface area = 784 square units
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which statement about a parallelogram is true?
some parallelograms have side lengths that are all different
all parallelograms have opposite sides that are parallel.
all parallelograms have 4 square corners
some parallelograms have more than 4 sides
giving brainiest
Step-by-step explanation:
all parallelograms have opposite sides that are parallel.
that is the only true statement.
Find the lcd of the given rational equation
The LCD of the rational equation [tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex] is (x + 2) (x -1)(x - 2)
How to determine the LCD?The rational equation is given as:
[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{x^2 -3x + 2}[/tex]
Factorize the quadratic denominator
[tex]-\frac{3}{x + 2} + \frac{5x}{x - 1} = \frac{x + 2}{(x -1)(x - 2)}[/tex]
Write out the denominators
(x + 2), (x - 1) and (x -1)(x - 2)
Remove the repetition
(x + 2) (x -1)(x - 2)
Hence, the LCD of the rational equation is (x + 2) (x -1)(x - 2)
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2 of 8
=
Given that y = 10 cm and 0 = 19°, work out x rounded to 1 DP.
у
х
oo
Answer:
x = 3.255 cm
Step-by-step explanation:
Given:
⇒ y = 10cm
⇒ θ = 19
To find:
⇒ Value of "n"
Solution
⇒ By Pythagoras theorem
⇒ Δ Sin θ = n/y
⇒ sin 19° = n/10
⇒ 0.3255 = n/10
⇒ n = 0.3255 × 10
⇒ n = 3.255 cm
Hence, the answer is = n = 3.255 cm.
Which of the following is a true statement?
6/16 > 7/24
3/5 <5/16
6/16 > 4/10
4/8 < 5/16
The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24. Then the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The expressions are 6/16 and 7/24.
Then the LCM of the 16 and 24 will be 48.
Then the expressions will be 18/48 and 14/48.
The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24.
Thus, the correct option is A.
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