The correct product of 27 and 600 is:
[tex]\[ \boxed{16200} \][/tex]
"The correct answer to find the product of 27 and 600 is not obtained by simply adding 27 six times and then appending zeros. The correct method to calculate 27 x 600 is as follows:
First, multiply 27 by 6 to get the hundreds place value correct:
[tex]\[ 27 \times 6 = 162 \][/tex]
Next, since we are multiplying by 600, we need to account for the additional zeros. Each zero represents a factor of 10, so we multiply 162 by 100 (since there are two zeros in 600):
[tex]\[ 162 \times 100 = 16200 \][/tex]
Therefore, the correct product of 27 and 600 is:
[tex]\[ \boxed{16200} \][/tex]
The method described in the question is incorrect because it does not properly account for the place value of the digits in the multiplication. When multiplying by a number with zeros, each zero represents a power of ten and must be considered in the multiplication process. The correct method involves multiplying the numbers and then adjusting the final product's place value by adding zeros according to the multiplier's zeros."
The weight of a body varies inversely as the square of its distance from the center of the earth. If the radius of the earth is 3500 miles, how much would a 180-pound man weigh 750 miles above the surface of the earth?
The weight of the body when the distance is 750 miles if it is inversely proportional is 3,920 pounds.
How much would a 180-pound man weigh 750 miles above the surface of the earth?w = k/d²
Where,
k = constant of proportionality
w = 180 pound
d = 3,500 miles
w = k/d²
180 = k/3500²
180 = k/12,250,000
cross product
k = 180 × 12,250,000
k = 2,205,000,000
Therefore, when d = 750 miles
w = k/d²
w = 2,205,000,000 / 750²
= 2,205,000,000 / 562,500
= 3,920 pounds
Hence, the weight of the body is 3,920 pounds.
Read more on variation:
https://brainly.com/question/6499629
#SPJ3
How do I do this using distributive property
answer: [tex]-15 - x[/tex]
work:
[tex]5-(x+4)[/tex] | distribute the negative into the parentheses, which means multiply into the parentheses.
[tex]5 - x - 20[/tex] | combine like terms
[tex]-15 - x[/tex] | final answer
correct me if anything is wrong, otherwise hope this helps! ❤ from peachimin
Hello there!
Distributive property you had to used their formula like:
↓
a(b+c)=ab+ac
5-(x+4)
First you had to distribute by the negative signs.
5+-1(x+4)
5+-1x+(-1)(4)
5+-x+-4
Then you combine like terms of
↓
5+-x+-4
(-x)+(5+-4)
Simplify
=-x+1
Answer⇒⇒⇒⇒-x+1
Hope this helps!
Thank you for posting your question at here on Brainly.
-Charlie
edward wants to have $50,000 in 10 years for college. what single deposit would he need to make snow into an account that pays 4.3% interest, compounded daily to meet his goal
Answer: Single deposit by Edward=$3594 to make it amount for college=$50,000 in 10 years.
Step-by-step explanation:
Here Compound amount =$50,000
Time=10 years
Rate of interest=4.3%
By the Daily compound interest formula ,we have
[tex]Amount=Principal(1+rate/365)^{365\times\ time}\\\Rightarrow\ Amount=Principal(1+4.3/365)^{365\times\ 10}\\\Rightarrow\ 50000=P(1+.011)^{3650}\\\Rightarrow\ 50000=P(1.011)^{3650}\\\Rightarrow\ 50000=P(13.911)...........(approx)\\\Rightarrow\ P=\frac{50000}{13.911}=3594......(approx)[/tex]
Therefore Principal amount deposited by Edward is $3594.
Answer:
$32,526.67
Step-by-step explanation:
Let the Principle be P
amount here A= $50,000
time n= 10 years n= 10*365=3650 days
rate of interest= 4.3% compounded daily= 4.3/365
let us use compound interest formula to calculate the principle
[tex]A= P(1+\frac{r}{100})^n[/tex]
putting all the values we get
[tex]50000=P(1+\frac{4.3}{100\times365})^10times365[/tex]
on solving we get P= $32,526.67
therefore he need to deposit $32,526.67
Find the measure of the indicated angle
(geometry)
The measure of the indicated angle [tex]\angle A$ is 46 degrees[/tex]
We can use the fact that the sum of the angles in a triangle is 180 degrees to solve for the missing angle.
Since we are given that [tex]\angle C = 46^\circ$,[/tex] we can write the following equation:
[tex]m\angle A + m\angle B + 46^\circ = 180^\circ[/tex]
Solving for [tex]$m\angle A[/tex] we get:
[tex]m\angle A = 180^\circ - m\angle B - 46^\circ[/tex]
Since [tex]$\angle B$[/tex] is the missing angle, we can substitute the given information into the equation to solve for its measure:
[tex]m\angle A = 180^\circ - 46^\circ - 46^\circ = 98^\circ - 92^\circ = 46^\circ[/tex]
Therefore, the measure of the indicated angle $\angle A$ is 46 degrees.
For similar question on missing angle.
https://brainly.com/question/28969239
#SPJ3
please help me!!! 60 points 2 questions and show work!!!!!!!!
[tex]1.\\\dfrac{9}{2}(8-x)+36=102-\dfrac{5}{2}(3x+24)\ \ \ \ |\text{multiply both sides by 2}\\\\\not2^1\cdot\dfrac{9}{\not2_1}(8-x)+2\cdot36=2\cdot102-\not2^2\cdot\dfrac{5}{\not2_1}(3x+24)\\\\9(8-x)+72=204-5(3x+24)\ \ \ \ |\text{use distributive property}\\\\(9)(8)+(9)(-x)+72=204+(-5)(3x)+(-5)(24)\\\\72-9x+72=204-15x-120\ \ \ \ |\text{use commutative and associative property}\\\\-9x+(72+72)=-15x+(204-120)\\\\-9x+144=-15x+84\ \ \ \ |\text{subtract 144 from both sides}[/tex]
[tex]-9x=-15x-60\ \ \ \ |\text{add 15x to both sides}\\\\6x=-60\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{x=-10}[/tex]
[tex]2.\\-12x-0.4 > 0.2(36.5x+80)-55\ \ \ \ |\text{use distributive property}\\\\-12x-0.4 > (0.2)(36.5x)+(0.2)(80)-55\\\\-12x-0.4 > 7.3x+16-55\ \ \ \ |\text{use associative property}\\\\-12x-0.4 > 7.3x+(16-55)\\\\-12x-0.4 > 7.3x-39\ \ \ \ |\text{add 0.4 to both sides}\\\\-12x > 7.3x-38.6\ \ \ \ |\text{subtract 7.3x from both sides}\\\\-19.3x > -38.6\ \ \ \ \ |\text{change the signs}\\\\19.3x < 38.6\ \ \ \ |\text{divide both sides by 19.3}\\\\\boxed{x < 2}[/tex]
2)
-12x - 0.4 > 0.2(36.5x + 80) - 55
Distributive property
-12x - 0.4 > 7.3x + 16 - 55
Combine like terms
-12x - 0.4 > 7.3x -39
Subtract both sides by 7.3x
-19.3x - 0.4 > - 39
Add 0.4 to both sides
-19.3x > -38.6
Divide both sides by -19.3 (remember when dividing a negative number, the sign will be flipped)
x < 2
1)
9/2(8 -x) + 36 = 102 - 5/2(3x+24)
Multiply both sides by 2
9(8 -x) + 72 = 204 - 5(3x+24)
Distributive propery
72 - 9x + 72 = 204 - 15x - 120
Combine like terms
- 9x + 144 = -15x + 84
Add 15x to both sides
6x + 144 = 84
Subtract 144 from both sides
6x = -60
x = -10
Hope they help.
The graph represents the cost of a subscription to a newspaper.
What is the constant of variation for the subscription cost based on the number of weeks?
A. $1.50
B. $7.50
C. $15.00
D. $30.00
what is the domain of range of y=4(1/3)^x
Answer:
Domain = R
Range =(0,infinity)
Step-by-step explanation:
Given a function as
y = 4(1/3)^x
The function does not have x or y in the denominator or any square root sign.
Hence we can assign any values to x.
Domain = R = Set of all real numbers = (-infinity, infinity)
Let us consider range.
We find that 4(1/3)^x is a multiple of 4 and powers of 1/3
Since power of 1/3 is always positive, y cannot take any negative value.
When x=0 y =4.
When x tends to -infinity, y tends to 0
So y cannot take the value 0 except at -infinity.
Range =(0,infinity)
Samara ate 1/3 of a pizza and Vyolet ate 1/5 of the pizza. How much of the pizza did they eat in all?
can you help me find length bc please!!!!
Remark
You are dealing with a right angle triangle. You can use one of Sin(x) Cos(x) or Tan(x). Since the Hypotenuse is involved and since you are given the adjacent side, Cos(71) is what you will need.
Solution
H = BC
Cos(x) = adjactent / hypotenuse
Cos(71) = 6.3 / H Multiply both sides by H
H * Cos(71) = 6.3 Divide by Cos(71)
H = 6.3 / cos(71) Cos(71) = 0.32557
H = 6.3 / 0.32557 Divide
H = BC = 19.351 Answer
The table shows partial results of a survey about students who speak foreign languages.
Choose only one option
What is the relative frequency of girls who speak German to the total number of students who speak German?
A) 31%
B) 36%
C) 40%
D) 77%
Oh this is easy.I completed the table. C) 40%
THE ANSWER IS C (◡ ‿ ◡ ✿)
Solve for x. Enter your answer in the box.
The sum of the measures of the angles of a hexagon is equal 720°.
Therefore we have the equation:
[tex]160^o+75^o+132^o+113^o+108^o+x^o=720^o\\\\588^o+x^o=720^o\ \ \ \ |-588^o\\\\x^o=132^o[/tex]
Answer: x = 132
Robert climbs 775 steps in 12 1/2 minutes what was his average steps per minute
A recipe calls for 2 cups of flour and 1 cup sugar and half cup butter how many cups of flour are needed to mix with each cup of butter
answer is equal to2:1/2=4:1
4 cups are required
Final answer:
For every cup of butter in the recipe, 4 cups of flour are needed. This is found by analyzing the ratio of flour to butter given in the recipe, which is 2 cups flour to 0.5 cup butter.
Explanation:
The question asks how many cups of flour are needed to mix with each cup of butter according to a given recipe. To determine this, we look at the provided ratios and find that the recipe calls for 2 cups of flour and 0.5 cup of butter. This results in the ratio of 4 cups of flour for every 1 cup of butter.
To calculate the amount of flour required for each cup of butter, we use a simple proportion:
0.5 cup butter : 2 cups flour
1 cup butter : x cups flour
To solve for x (the amount of flour needed for 1 cup of butter), we cross-multiply and get:
0.5x = 2
x = 2 / 0.5
x = 4
So, for every cup of butter, 4 cups of flour are needed.
You play darts with a friend. The board has several concentric circles (same center). The central part of the board is called the Bull’s Eye and it is a circle with a 1-inch radius.
Just outside of that is the “inner ring”: it is the region inside a circle with a 3-inch radius and outside of the Bull’s Eye.
How much harder is it to hit the Bull’s Eye than the Inner Ring?
Area of Bull's Eye:
A = π r²
= π (1)²
= π
Area of Inner Ring:
A = π r²
= π (3-1)²
= 4π
Ratio between Inner Ring and Bull's Eye:
[tex]\frac{InnerRing}{Bull's Eye} = \frac{4\pi }{\pi} = 4[/tex]
Answer: It is 4 times harder to hit the Bull's Eye than it is to hit the Inner Ring
Final answer:
The Inner Ring is 8 times larger than the Bull's Eye.
Explanation:
To determine how much harder it is to hit the Bull's Eye compared to the Inner Ring, we can compare their areas.
The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle.
The area of the Bull's Eye can be calculated as A = π(1)^2 = π square inches.
The area of the Inner Ring can be calculated as A = π(3)^2 - π(1)^2 = 9π - π = 8π square inches.
Therefore, the Inner Ring is 8 times larger than the Bull's Eye.
The picture below shows a portion of a river dam: A right angle triangle is shown with acute angle on base equal to 40 degrees and length of base equal to 100 meters. Which of the following can be used to calculate the height of the river dam? 100 divided by sin 40 degrees 100 sin 40° 100 divided by tan 40 degrees 100 tan 40°
Using the base and the acute angle on the base, to find the height of the dam, you would need to multiply the base by the tangent of the angle.
Height = 100 * tan(40)
Jane and sali cycled along the same 63 km route.
Jane took 3.5 hours to cycle the 63 km.
Sali started to cycle 4 minutes after Jane started to cycle.
Sali caught up with Jane when they had both cycled 30 km.
Jane and sali both cycled at a constant speeds.
Work out sali's speed in km/h.
Answer:
Sali's speed was 18.75 km/h.
Step-by-step explanation:
Jane took 3.5 hours to cycle the 63 km.
As, [tex]Speed= \frac{Distance}{Time}[/tex] , so the speed of Jane will be: [tex]\frac{63}{3.5} km/h = 18 km/h[/tex]
Suppose, the speed of Sali is [tex]x[/tex] km/h
Sali caught up with Jane when they had both cycled 30 km.
So, the time required for Jane to cycle 30 km [tex]= \frac{30}{18}=\frac{5}{3} hours[/tex] and the time required for Sali to cycle 30 km [tex]=\frac{30}{x} hours[/tex]
Given that, Sali started to cycle 4 minutes or [tex](\frac{4}{60}) or (\frac{1}{15}) hours[/tex] after Jane started to cycle. So, the equation will be.......
[tex]\frac{5}{3}-\frac{30}{x}= \frac{1}{15}\\ \\ \frac{30}{x}= \frac{5}{3}-\frac{1}{15}\\ \\ \frac{30}{x}= \frac{24}{15}\\ \\ 24x=450\\ \\ x= \frac{450}{24}= 18.75[/tex]
Thus, the speed of Sali was 18.75 km/h.
Answer:Thus, the speed of Sali was 18.75 km/h.
Step-by-step explanation:
Sali's speed was 18.75 km/h.
help!! what is 4 3/4 divided by 2 3/4?
i THINK its 2 1/2 ?????
How many solutions are there for the system of equations shown on the graph?
A coordinate plane is shown with two lines graphed. One line crosses the y axis at 3 and has a slope of negative 1. The other line crosses the y axis at 3 and has a slope of two thirds.
Answer:
Only one solution
Step-by-step explanation:
Given that there is a coordinate plane (say xy)
Two lines are given.
One line crosses the y axis at 3 and has a slope of negative 1.
hence equation of I line is y = -x+3
The other line crosses the y axis at 3 and has a slope of two thirds.
So equation is y = 2x/3 +3
Since the two lines lie in the same plane and are having different slopes, they intersect at one point.
Eliminate y to get
-x+3=2x/3+3
Or x=0
y=3
Hence solutionis (0,3) for the system.
Answer:
One solution
Step-by-step explanation:
we know that
The solution of the system of equations is equal to the intersection point both graphs
we have
[tex]y=-x+3[/tex] ------> equation A
[tex]y=-(2/3)x+3[/tex] ------> equation B
Using a graphing tool
see the attached figure to better understand the problem
In this problem the intersection point is only one
therefore
The system of equations has one solution
The solution is the point [tex](0,3)[/tex]
simplify both sides of the equation
Answer: Solve by combining like terms.
Solve for x by simplifying both sides of the equation, then isolating the variable.
x > [tex]-\frac{99}{4}[/tex]
As a decimal is: x > −24.75
On simplify both sides of the inequality the solution for the inequality -2/5x - 9 < 9/10 is x > -247.5.
To simplify both sides of the inequality, we'll perform the necessary mathematical operations step by step:
-2/5x - 9 < 9/10
Step 1: Add 9 to both sides of the inequality to isolate the term with "x":
-2/5x - 9 + 9 < 9/10 + 9
Simplify:
-2/5x < 9/10 + 90/10
Step 2: Combine the fractions on the right side:
-2/5x < (9 + 90)/10
-2/5x < 99/10
Step 3: To eliminate the fraction, multiply both sides by the reciprocal of (-2/5), which is (-5/2). When you multiply an inequality by a negative number, remember to flip the inequality sign:
(-5/2) * (-2/5x) > (-5/2) * (99/10)
Simplify:
x > -5/2 * (99/10)
x > -495/20
Step 4: Reduce the fraction on the right side:
x > -247.5
Now, the simplified inequality is:
x > -247.5
So, the solution for the inequality is "x > -247.5."
To know more about inequality click here :
https://brainly.com/question/29731212
#SPJ2
6. Which type of angle pair are LSM and OSN?
A. Adjacent angles
B. Linear pair
C. Complementary angles
D. Vertical angles
7. Which of the following statements are false?
A. LSM and MSN are adjacent angles
B. LSM and MSN form a linear pair of angles
C. LSM and MSN are vertical angles
D. M
8. Which angle is supplementary to LSM?
A. OSN
B. SLM
C. LMS
D. MSN
6. vertical
7. LSM and MSN are vertical angles
8. MSN
Answer:
6. Which type of angle pair are LSM and OSN?
Answer - D. Vertical angles
Vertical angles are pairs of opposite angles made by two intersecting lines.
7. Which of the following statements are false?
Answer - C. LSM and MSN are vertical angles.
Vertical angles are pairs of opposite angles made by two intersecting lines.
8. Which angle is supplementary to LSM?
Answer - D. MSN
Two angles are supplementary when they add up to become 180 degrees.
Here adding both we will get angle S as 180 degrees.
Emerson runs 2 miles to her friend's house and 2 miles back to her house 5 times each month. How many miles does she run?
Essica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80. How many more cookies will Jessica have Martha? If x represents the number of cookies Jessica started with, complete the statements below. The inequality that describes the relationship between the number of cookies each one of them has is x2 - x + 224 ≥ 0. Jessica has at least cookies more than Martha.
I just took the test. For PLATO the first blank is 30 and the second blank is 2.
Answer:
Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]
Part 2) Jessica has at least 2 cookies more than Martha.
Explanation:
Let Jessica has x cookies.
Let Martha has y cookies.
Total cookies they have = 30
Equation forms:
[tex]x+y=30[/tex] or [tex]y = 30-x[/tex] .....(1)
Each of them ate 6 cookies from their bag.
Cookies left with Jessica = [tex]x-6[/tex]
Cookies left with Martha = [tex]y-6[/tex]
The product of the number of cookies left in each bag is not more than 80.
[tex](x-6)(y-6) \leq 80[/tex] ....(2)
Substituting [tex]y = 30-x[/tex] in equation (2)
[tex](x-6)(30-x-6) \leq 80[/tex]
=> [tex](x-6)(24-x) \leq 80[/tex]
=> [tex]24x-x^{2}-144+6x \leq 80[/tex]
=> [tex]-x^{2}+30x-144 \leq 80[/tex]
=> [tex]-x^{2}+30x-224 \leq 0[/tex]
Multiplying both sides by -1.
[tex]x^{2} -30x+224 \geq 0[/tex]
Solving this quadratic equation, we get
[tex]x\leq 14[/tex] or [tex]x\geq 16[/tex]
We will take x = 16 (bigger value as Jessica has more cookies)
And y = [tex]30-16=14[/tex]
y = 14
So, Jessica has 16 cookies.
Martha has 14 cookies.
Cookies left in the bag :
Jessica : [tex]16-6=10[/tex] cookies
Martha : [tex]14-6=8[/tex] cookies
Therefore, Jessica has at least 2 cookies more than Martha.
Pencils come in cartons of 24 boxes. A school bought 50 cartons of pencils for the start school. Each box of pencils cost 2 dollars.How much did the school spend on pencils?
Write the prime factorization of 675 using exponent
675 : 5 = 135
135 : 5 = 27
27 : 3 = 9
9 : 3 = 3
3 : 3 = 1
675 = 5 · 5 · 3 · 3 · 3 = 5² · 3³
What best describes the number 5 write prime composite neither prime non composite or both prime and composite
Answer:
it is PRIME
Step-by-step explanation:
It has 2 factors: 1 and 5
Determine the solution x^2 - 3x -28 ≥ 0
Final answer:
The solution to the inequality [tex]x^2 - 3x - 28[/tex]≥ 0 is found by factoring the quadratic equation to find its roots, which are x = 7 and x = -4. The solution to the inequality is x ≤ -4 or x ≥ 7.
Explanation:
To determine the solution to the quadratic inequality [tex]x^2 - 3x - 28[/tex] ≥ 0, we first need to find the roots of the equation [tex]x^2 - 3x - 28 = 0.[/tex]We can do this by factoring the quadratic expression.
We look for two numbers that multiply to give -28 and add to give -3. These numbers are -7 and +4. So we can rewrite the equation as (x-7)(x+4) = 0. Setting each factor equal to zero gives us the roots x = 7 and x = -4.
Now, we test intervals that are determined by these roots to see where the inequality holds true. The intervals are (-infinity, -4), (-4, 7), and (7, infinity). If we test a number from each interval in the inequality [tex]x^2 - 3x - 28[/tex] ≥ 0, we find that the inequality is true for x ≤ -4 and x ≥ 7. Therefore, the solution to the inequality is x ≤ -4 or x ≥ 7.
Avery predicts that the number of horses, HHH, on her farm ttt years from now will be modeled by the function H(t)=25(2)^tH(t)=25(2) t H, left parenthesis, t, right parenthesis, equals, 25, left parenthesis, 2, right parenthesis, start superscript, t, end superscript, and that the amount of hay, AAA, in tons, that she produces on her farm ttt years from now will be modeled by the function A(t)=150(1.5)^tA(t)=150(1.5) t A, left parenthesis, t, right parenthesis, equals, 150, left parenthesis, 1, point, 5, right parenthesis, start superscript, t, end superscript. Let FFF be the predicted yearly supply of hay, in tons, available to each horse in Avery's farm ttt years from now. Note that the hay produced on Avery's farm is used exclusively to feed her horses. Write a formula for F(t)F(t)F, left parenthesis, t, right parenthesis in terms of H(t)H(t)H, left parenthesis, t, right parenthesis and A(t)A(t)A, left parenthesis, t, right parenthesis.
Number of Horses in Avery's farm, after t years from now is given by function H(t); where [tex]H(t) = 25(2)^{t}[/tex]
The amount of hay, in tons, that is produced on her farm t years from now is given by function A(t); where [tex]A(t) = 150(1.5)^{t}[/tex]
The predicted yearly supply of hay, in tons, available to each horse in Avery's farm t years from now is given by function F(t); where F(t) = A(t)/H(t)
So, F(t) = [tex]\frac{150(1.5)^{t}}{25(2)^{t}}[/tex] = [tex]6 (\frac{1.5}{2}) ^{t}[/tex] = [tex]6 (0.75)^{t}[/tex] tons/horse
The formula for F(t) in terms of H(t) and A(t) is F(t) = (150(1.5)^t) / (25(2)^t).
Explanation:To find the formula for F(t), we need to divide the amount of hay produced, A(t), by the number of horses, H(t). So, the formula for F(t) is F(t) = A(t) / H(t). Substituting the given functions, we have F(t) = (150(1.5)^t) / (25(2)^t).
Learn more about Writing a formula for F(t) in terms of H(t) and A(t) here:https://brainly.com/question/33937440
#SPJ3
How can u divide whole numbers and decimals?
Mr. Fink's economy car can travel 420 miles on a 12 gallon tank of gas. How many miles can he travel on 8 gallons?
Distance covered in 12 gallons tank of gas = 420 miles
So, distance covered in 1 gallon tank of gas = [tex]\frac{420}{12}[/tex] miles
Now, distance covered in 8 gallons will be =
[tex]8*\frac{420}{12}[/tex] =280 miles
Hence, distance covered by Mr.Fink's economy car in 8 gallons tank of gas is 280 miles.
Sam ran 40 yards in 5 seconds. What was her rate of speed in miles per hour? A) 2 mph B) 5 mph C) 16 mph D) 22 mph
B) 5 mph
hope this helped
Answer:
Its 16
100% Correct
Step-by-step explanation:
USA TEST PREP