Since there is no number line below I’m going to do this.
_________ __________ __________
Just split it into three ,’:b
PLEASE HELP!!!!
Mike says that if he doubles each dimension of any rectangular prism, the surface area also doubles. Is Mike correct? Give an example to support your answer.
Answer:
Mike is not right
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z----> the scale factor
x----> surface area of the enlarged rectangular prism
y-----> surface area of the original rectangular prism
[tex]z^{2}=\frac{x}{y}[/tex]
so
In this problem we have
[tex]z=2[/tex]
substitute
[tex]2^{2}=\frac{x}{y}[/tex]
[tex]4=\frac{x}{y}[/tex]
[tex]x=4y[/tex]
so
The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism
therefore
Mike is not right
Verify with an example
we have a rectangular prism
[tex]L=5\ m[/tex]
[tex]W=2\ m[/tex]
[tex]H=3\ m[/tex]
The surface area of the prism is equal to
[tex]SA=2(LW)+(2L+2W)H[/tex]
substitute the values
[tex]SA=2*(5*2)+(2*5+2*2)*3=62\ m^{2}[/tex]
If he doubles each dimension of any rectangular prism
then
the new dimensions will be
[tex]L=5*2=10\ m[/tex]
[tex]W=2*2=4\ m[/tex]
[tex]H=3*2=6\ m[/tex]
The new surface area will be
[tex]SA=2*(10*4)+(2*10+2*4)*6=248\ m^{2}[/tex]
[tex]248/62=4[/tex]
therefore
The surface area of the enlarged rectangular prism is 4 times the surface area of the original rectangular prism
I don’t understand it
So first you have to find the volume of the entire tank using the height of 6cm. Then you have to find the volume of just the water using the height of 4 cm. Then you subtract both of your volumes and that will represent the volume of the part of the tank that isn't filled with water
Answer:
432cm³
Step-by-step explanation:
First we need to find the volume.
Use the volume formula.
[tex]V=l*w*h[/tex]
Plug in the values.
[tex]V=18*12*6\\ \\ V=1296[/tex]
Now find the volume of water we filled up.
[tex]V=18*12*4\\ \\ \\V=864[/tex]
Now we can subtract to find how much more water we need.
[tex]V=1296-864\\ \\ \\V=432[/tex]
432cm³ of water is needed to fill up the tank completely.
What is the equation of the line that passes through the points (2,-1) and (6,1)?
The answer is y=1/2x-2
Which of the following statements are true? Select all that apply. This is Algebra Nation
Answer:
241
Step-by-step explanation:
What is the probability that a vehicle is white?
Answer:
B. 0.22
Step-by-step explanation:
8/36 = 0.2222
B is the correct answer
The product of 43 x 6 can be broken down into expanded
form.
What is the missing expression?
43 x 6
= (40 6) + (?)
3x6
6x6
40 x 1
40 x 3
Answer:3*6
Step-by-step explanation: It is (40*6)+(3*6) you have to break it down
Find the value of x.
Answer:
x=60
Step-by-step explanation:
As the sides of the triangle are doubled (21 to 42 and 44 to 88) that means that the side of 30 is doubled to 60
Answer:
x=60
Step-by-step explanation:
The graph below shows three different normal distributions which statement must be true
Answer:
4th option is correct; Each distribution has a different mean and a different standard deviation
Step-by-step explanation:
For the mean to be same in all three distributions, all graphs must be centered around the same number, so mean is not same.
The width of each graph shows how much data deviate from the mean. Since the width is different in all three distributions, standard deviation is different in all three distributions
Answer:
D
Step-by-step explanation:
E2020
Devon made a scale drawing of a triangle. He used a scale factor 1/4 to draw the new triangle. How does each side of the new triangle compare to the original?
Answer:
The sides of the new triangle compared to the original are 4 times smaller.
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor
Let
z-----> the scale factor
x----> the corresponding side of new triangle
y----> the corresponding side of the original triangle
[tex]z=\frac{x}{y}[/tex]
we have
[tex]z=\frac{1}{4}[/tex]
substitute
[tex]\frac{1}{4}=\frac{x}{y}[/tex]
[tex]x=\frac{1}{4}y[/tex]
therefore
The sides of the new triangle compared to the original are 4 times smaller.
Answer:
C
Step-by-step explanation:
Sara has a circular fence around her dog house. Each day when she comes home from
school the dog runs exactly three laps around his pen before he is calm enough to be
petted. If the radius of his pen is 12 meters, how far does her dog run?
Answer needs to be explained
WILL GIVE BRAINLYIST
Answer:
226.2 feet
Step-by-step explanation:
The fence around the dog's house is a circle, with a radius of 12 meters.
To calculate the distance the dog runs, we need to find the circumference of that circle, which is given by the formula:
C = 2 π r, since we know r, the calculation is easy:
C = 2 π 12 = 24 π = 75.4 feet.
The dog makes three laps around the circle before calming down... so he runs 3 times 75.4 feet.
Dogs run = 3 x 75.4 ft = 226.2 feet
Which set of fractions is ordered from least to greatest?
A) 5/8, 8/12, 3/4
B) 8/12, 5/8, 3/4
C) 3/4, 5/8, 8/12
D) 5/8, 3/4, 8/12
Answer:
a
Step-by-step explanation:
math
5/8, 8/12, and 3/4 are ordered from least to greatest.
What is ascending order of fractions?Write all the fractions so that they have a common denominator in order to arrange them in ascending order. By comparing the numerators and sorting the fractions, determine which fraction is the smallest. Rewrite the numbers in the order of size that they appear in the question.
Given
5/8, 8/12, 3/4
Least common multiple of 8, 4, and 12 is 24
[tex]\frac{5*3}{8*3} , \frac{8*2}{12*2} ,\frac{3*6}{4*6} \\\\\frac{15}{24} , \frac{16}{24} .\frac{18}{24}[/tex]
therefore, 5/8, 8/12, and 3/4 are ordered from least to greatest
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A rectangular prism has a length of 8 in., a width of 4 in., and a height of 2 1/4 in. The prism is filled with cubes that have edge lengths of 14 in. How many cubes are needed to fill the rectangular prism? Enter your answer in the box. To fill the rectangular prism, cubes are needed.
It is not possible to fill a smaller rectangular prism with larger 14-inch cubes.
However, there is a typo in the question because the cubes with an edge length of 14 inches cannot fit inside a rectangular prism of smaller dimensions.
Hence, it is impossible to fill the rectangular prism with cubes of 14-inch edge lengths.
Sue danced for 15.5 minutes.Allie danced for 23.25 minutes. Carol danced for 8 minutes and 12 seconds less than Sue and Allie combined. How much time in minutes and seconds fed the girls dance altogether
Answer:69.38
Step-by-step explanation: Sue = 15.5 allie = 23.25 carol = 15.5+32.25 - 8.12 2. 15.5+32.25=38.75-8.12= 30.63 now all together 23.25+15.5+30.63= 69.38
The girls danced for a total of 30 minutes and 33 seconds.
First, we need to calculate the total time Sue and Allie danced combined:
Sue danced for 15.5 minutes, which can be written as [tex]\(\frac{155}{10}\)[/tex] minutes.
Allie danced for 23.25 minutes, which can be written as [tex]\(\frac{2325}{100}\)[/tex] minutes.
To combine these times, we need a common denominator, which is 100:
Sue's time in minutes: [tex]\(\frac{155 \times 10}{100} = \frac{1550}{100}\)[/tex]
Allie's time in minutes: [tex]\(\frac{2325}{100}\)[/tex]
Now we add Sue's and Allie's times:
[tex]\(\frac{1550}{100} + \frac{2325}{100} = \frac{3875}{100}\)[/tex]
Converting this back to mixed numbers:
[tex]\(\frac{3875}{100} = 38\)[/tex] minutes and [tex]\(\frac{75}{100}\)[/tex] minutes, which is 45 seconds.
Now, Carol danced for 8 minutes and 12 seconds less than the combined time of Sue and Allie. We need to subtract this time from the total time Sue and Allie danced:
[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds.
Subtracting the minutes:
[tex]\(38 - 8 = 30\)[/tex] minutes.
Subtracting the seconds:
[tex]\(45 - 12 = 33\)[/tex] seconds.
Therefore, Carol danced for 30 minutes and 33 seconds. Since Sue and Allie's combined time was 38 minutes and 45 seconds, and Carol danced for 8 minutes and 12 seconds less, the total time the girls danced altogether is:
[tex]\(38\)[/tex] minutes and [tex]\(45\)[/tex] seconds [tex]\(-\) \(8\)[/tex] minutes and [tex]\(12\)[/tex] seconds [tex]\(=\) \(30\)[/tex] minutes and [tex]\(33\)[/tex] seconds.
Thus, the girls danced for a total of 30 minutes and 33 seconds.
find the slope of the line that passes through -2 -2 and 2 -4
Answer:
-1/2
Step-by-step explanation:
To find the slope we know that:
Slope = (Y2-Y1)/(X2-X1)
Then, given the two points, we have that:
(X1, Y1) = (-2,-2)
(X2, Y2) = (2, -4)
Then:
m= (Y2-Y1)/(X2-X1) = (-4-(-2))/(2-(-2)) = -4+2/2+2 = -2/4 = -1/2
So the slope of the function that passes through those points is: -1/2
what is perfect square trinomials
(x+4)^2=
Answer:
x² + 8x + 16
Step-by-step explanation:
(x + 4)² = (x + 4)(x + 4)
Each term in the second parenthesis is multiplied by each term in the first parenthesis, that is
x(x + 4) + 4(x + 4) ← distribute both parenthesis
= x² + 4x + 4x + 16 ← collect like terms
= x² + 8x + 16 ← perfect square trinomial
Chuck puts $900,000 into an account that earns 5% APR compounded annually how much money will chuck earn each year in interest
Answer:
45,000
Step-by-step explanation:
Apex is the source
Answer: the answer is $ 45,000 APEX
Which of the following arcs are congruent in the circle below?
D) Arc wx and arc yz is the correct answer because both arcs are equal to 27
Answer:
Option D is correct.
Step-by-step explanation:
Arcs are said to be equal if it subtends equal angles at the center
here we can see that arcs WX and ZY subtends equal angle and its measure is 27 degrees.
therefore option D is correct answer
Since we are not given the angles subtended by WY and XZ in the center
so we cannot say for option A
Likewise we cannot say for rest of the option.
use the quadratic formula to solve the equation 4x²-x+3=0
Answer:
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]4x^2-x+3=0[/tex].
Compare with [tex]ax^2+bx+c=0[/tex], we get:
a=4, b=-1, c=3
Now plug these values into quadratic formula :
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\frac{-\left(-1\right) \pm \sqrt{\left(-1\right)^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}[/tex]
[tex]x=\frac{1 \pm \sqrt{1-48}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{-47}}{8}[/tex]
[tex]x=\frac{1 \pm \sqrt{47}i}{8}[/tex]
Hence final answer is
[tex]x=\frac{1+ \sqrt{47}i}{8}[/tex] and [tex]x=\frac{1 -\sqrt{47}i}{8}[/tex]
Answer:
Solution of given quadratic equation,
x = [1 + 6.86i]/8 or x = [1 - 6.86i]/8
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + c = 0
x = [-b ± √(b² - 4ac)]/2a
It is given a quadratic equation, 4x²-x+3=0
To find the solution using quadratic formula
Here a = 4, b = -1 and c = 3
We have,
x = [-b ± √(b² - 4ac)]/2a
x = [--1 ± √((-1)² - 4*4*3)]/2*4
= [1 ± √(1 - 48)]/8
= [1 ± √(-47)]/8
= [1 ± 6.86i]/8
x = [1 + 6.86i]/8 or
x = [1 - 6.86i]/8
What's the least amount 0.146, 2.0102, 0.45, 1.09, 2.001
The least amount would be 0.146 because the tenths digits is the smallest.
The least amount among the given different amounts is 0.146
What is least amount of something?Least amount of something means the smallest amount or number.
How to find the least number or amount among the list of numbers?To find the least number or amount among the list of numbers we first go through the whole list of numbers and compare their values one after the other. And we arrange these numbers or amount in ascending order and find the least one.
According to the given question
We have different amounts
0.146, 2.0102, 0.45, 1.09, 2.001
For finding the least amount, arrange all the given amount in the ascending order.
So, the required ascending order is
0.146, 0.45, 1.09, 2.001, 2.0102
Hence, the least amount among the given different amounts is 0.146.
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If you are going to use the SAS postulate to prove these two triangles congruent what additional information do you need
Answer:
Option D. ET=IT
Step-by-step explanation:
we know that
The Side Angle Side postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent
In this problem
the included angle ∠ETK of triangle TEK is congruent with the included angle ∠KTI of triangle TIK
the side KT is a common side both triangles
therefore
ET must be equal to IT to prove that triangles TEK and TIK are congruent by SAS postulate
Two groups of workers are painting a bridge in the bay. The first group is responsible for painting the north side of the bridge, and the second group is responsible for painting the south side of the bridge. The first group has already painted 2 kilometers of the bridge and is painting 2 additional kilometers per day. The second group has already painted 5 kilometers of the bridge and is painting 1 additional kilometer per day. When the two groups have painted the same amount of the bridge, how much of the bridge will they each have painted?
Answer:
They will each have painted 8 km. This goal will be met on Day 4.
Step-by-step explanation:
Group A | Group B
Start: 2 | Start: 5 Day 1
2 + 2 = 4 | 5 + 1 = 6 Day 2
4 + 2 = 6 | 6 + 1 = 7 Day 3
6 + 2 = 8 | 7 + 1 = 8 Day 4
The first group and second group of workers will each have painted 8 kilometers of the bridge after 3 days.
Explanation:This question is related to the concept of linear equation in one variable. To solve such a problem, we typically set up an equation that relates the two groups and the amount they have painted to find out when they have painted an equal amount.
The equation representing the painting work of the first group is: 2 + 2d = x, where d is the number of days and x is the total distance painted. For the second group, the equation is 5 + d = x. We can set up these equations because each new day adds certain kilometers to the existing painted distance.
To find when these two equations are equal, we can simply equate them: 2 + 2d = 5 + d. Solving this equation, we get d = 3 days. Substituting d = 3 into either of the group's equations, we get x = 8 kilometers.
So, after 3 days, both groups would have painted 8 kilometers each.
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Linda Young opened up a computer service company. To pay for start up cost Linda borrowed $79,000 from a bank at 15% for 1 year. Find the interest for the year
Interest=Principal×Rate×Time
I=PRT/100
I= 79000×15×1
100
I= 1185000
100
I= $11850
To confirm
11850/79000 ÷ 100
= 0.5 ×100
= 15% (rate)
The interest of one year is $11850.
What is simple interest?
easy interest is based on the essential amount of a loan or the primary deposit in a savings account.
calculation:-
Amount of money borrowed by Linda = $79000
rate of interest =15%
Interest amount= $79000*15/100
The interest of the year =$11850
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Express the difference in the simplest form; 3t^2/5-4t^2/15
Answer:
t^2/3
Step-by-step explanation:
At the Rolling Ridge School spelling bee, 75% of the
contestants advanced to the second round and 60% advanced
to the third round. What is the probability that a randomly
selected contestant advanced to the third round given the same
contestant advanced to the second round?
A. 3/20
B. 9/20
c. 7/15
D. 4/5
Answer: Option D
[tex]P (B | A) =\frac{4}{5}[/tex]
Step-by-step explanation:
Call A to the event in which a student advances to the second round.
We know that:
[tex]P (A) = 75\% = 0.75[/tex]
Call B the event in which a student advances to the third round.
We know that:
[tex]P (B) = 60\% = 0.6[/tex]
We then look for the probability of B given A. This is:
[tex]P (B | A) =\frac{P(B\ and\ A)}{P(A)}[/tex]
In this case, the probability of B and A is equal to the probability of B, since the students who advance to the third round also advanced to the second round before
[tex]P (B | A) =\frac{P(B)}{P(A)}[/tex]
[tex]P (B | A) =\frac{0.6}{0.75}[/tex]
[tex]P (B | A) =\frac{4}{5}[/tex]
Solve -2(2x+5) -3(x-1)
The answer is:
[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]
Why?To solve the problem, we need to perform the operations and then, add like terms.
We need to apply the distributive property, which is defined by the following way:
[tex]a(b+c)=ab+ac[/tex]
Also, we need to remember how to add like terms. Like terms are terms that share the same exponent and the same variable, for example:
[tex]3x+5x+x^{2}=8x+x^{2}[/tex]
We were able to add only the first two terms since they are like terms, both are sharing the same exponent and the same variable.
So, we are given the expression:
[tex]-2(2x+5)-3(x-1)[/tex]
Then, solving we have:
[tex]-2(2x+5)-3(x-1)=-4x-10-(3x-3)\\\\-4x-10-(3x-3)=-4x-10-3x+3\\\\-4x-10-3x+3=-4x-3x-10+3\\\\-4x-3x-10+3=-7x-7[/tex]
Hence, we have that the answer is:
[tex]-2(2x+5)-3(x-1)=-7x-7\\[/tex]
Have a nice day!
factor z^2 - 3z - 18
Answer:
(z-6)(z+3)
Step-by-step explanation:
Answer:
The factored form of the given expression is (z-6)(z+3).
Step-by-step explanation:
The given expression is
[tex]z^2-3z-18[/tex]
The middle term can by written a -6z+3z.
[tex]z^2-6z+3z-18[/tex]
[tex]z(z-6)+3(z-6)[/tex]
[tex](z-6)(z+3)[/tex]
Therefore the factored form of the given expression is (z-6)(z+3).
What is the sum of 1/9, 2/3, and 5/18?
A. 4/15
B. 19/18
C. 8/30
D. 12/9
The correct answer is B.
1/9 can be converted into 2/18. 2/3 can be converted into 12/18. 2/18 + 12/18 + 5/18 = 19/18. The answer is B
please help me i’m very confused
The ratio of dry rice to water is 1 to 2. This means that water is two times more than dry rice. Since the chef uses 9.5 cups of dry rice, the chef needs 19 cups of water.
You can check by using fractions. 9.5 / 19 in simplified form is 1/2, which is 1:2 in ratio.
It would be 9.5:19 just multiply 9.5 by 2
solve for X
(5x-2)^2=17
Answer:
hello : x = 2 +√17 or x = 2 -√17
Step-by-step explanation:
(5x-2)^2=17
5x-2 = √17 or 5x-2 = - √17
x = 2 +√17 or x = 2 -√17
Apex Help!!!! At the beginning of year 1, Gracie invest $350 at annual simple interest rate of 4%. She makes no deposits to or withdrawals from the account
It's B A(n)= 350 + (n - 1) (0.04 · 350); $504.00
Answer:
Option B.
Step-by-step explanation:
Gracie invest $350 at the beginning of the year 1 at annual simple interest rate of 4%.
the balance at the beginning of the year 12. Interest will be calculated for 11 years.
Formula for simple interest : A = P(1 + rt)
By putting the value : A = 350(1 + 0.04 × 11)
A = 350 ( 1.44 ) = $504.00
So the best answer would be option B.