Answer:
x = 5
Step-by-step explanation:
Given:
[tex]2 \frac{2}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]
Convert the mixed number into an improper fraction by multiplying the whole number with the denominator of the fraction, adding it to the numerator of the fraction, and placing it all over the denominator of the fraction:
[tex]\implies 2\frac{2}{7}=\dfrac{2 \times 7+2}{7}=\dfrac{16}{7}[/tex]
Therefore:
[tex]\implies \dfrac{16}{7}:(0.6x)=\dfrac{4}{21}:0.25[/tex]
[tex]\implies \dfrac{\frac{16}{7}}{0.6x}=\dfrac{\frac{4}{21}}{0.25}[/tex]
Cross multiply:
[tex]\implies \dfrac{16}{7} \times 0.25 = \dfrac{4}{21} \times 0.6x[/tex]
[tex]\implies \dfrac{16\times 0.25}{7} = \dfrac{4\times 0.6x}{21}[/tex]
[tex]\implies \dfrac{4}{7} = \dfrac{2.4x}{21}[/tex]
Cross multiply again:
[tex]\implies 4 \times 21=2.4x \times 7[/tex]
[tex]\implies 84=16.8x[/tex]
Divide both sides by 16.8:
[tex]\implies \dfrac{84}{16.8}=\dfrac{16.8x}{16.8}[/tex]
[tex]\implies 5=x[/tex]
[tex]\implies x=5[/tex]
Answer:
The value of x is 5.
Step-by-step explanation:
Let's solve for the value of x,
→ 2 2/7 : (0.6x) = 4/21 : 0.25
→ 16/7 : (0.6x) = 4/21 : 0.25
→ (16/7) × 0.25 = (4/21) × 0.6x
→ 4/7 = (2.4x)/21
→ 2.4x × 7 = 4 × 21
→ 16.8x = 84
→ x = 84/16.8
→ [ x = 5 ]
Hence, the value of x is 5.
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. what value of p makes the equation true? p =
When p = 0.125 the equation -3p + ( 1/8 ) = ( - 1/4 ) is true.
The given equation is:
-3p + ( 1/8 ) = ( - 1/4 )
On the left-hand side of the equation, the denominator of the two terms is not the same.
So, the LCM of 1 and 8 is 8.
Therefore,
- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )
- 24p / 8 + 1 / 8 = - 1 / 4
( - 24p + 1 ) / 8 = - 1 / 4
Now multiplying each side of the equation by 8.
We get,
[ ( - 24p + 1 ) / 8 ] × 8 = ( - 1 / 4 ) × 8
- 24p + 1 = - 8 / 4
- 24p + 1 = - 2
Subtracting 1 from each side of the equation,
- 24p + 1 - 1 = - 2 - 1
-24p = - 3
Now, divide each side of the equation by 24.
- 24p / 24 = - 3 / 24
- p = ( - 1 / 8 )
Multiplying by - 1 on each side of the equation,
( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 )
p = 1 / 8
p = 0.125
The value of p = 0.125 will make the equation true.
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PLEASE HELP
A TV show had 5.6 x 105 viewers in the first week and 4.1 x 105 viewers in the second week. Determine the average number of viewers over the two weeks and write the final answer in scientific notation.
9.7 x 1010
9.7 x 105
4.85 x 1010
4.85 x 105
The average number of viewers over the two weeks is 4. 85 x 10^5. Option D
What is average?Average is simply a number taken as the representative of a list of numbers.
It is determined by taking the sum of the numbers divided by the number of listed numbers.
Given the number of viewers as;
5.6 x 105 viewers and 4.1 x 105 viewers
Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2
Average = 9. 7 x 10^5 / 2
Average = 4. 85 x 10^5
The average number of viewers over the two weeks is 4. 85 x 10^5
Thus, the average number of viewers over the two weeks is 4. 85 x 10^5. Option D
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A CD storage rack it's sold to stores at a wholesale price of $18 if the store has a 150% markup what is the retail price of the CD rack?
The retail price of the CD rack is $45.
How to calculate the value?From the information, the storage rack it's sold to stores at a wholesale price of $18 and the store has a 150% markup.
The retail price will be:
= $18 + (150% ×$18)
= $18 + $27
= $45
Therefore, the retail price of the CD rack is $45.
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two cards are dealt at random from a standard deck of $52$ cards ($13$ hearts, $13$ clubs, $13$ spades, and $13$ diamonds). what is the probability that the first card is a $6$ and the second card is a queen?
The probability of getting a number 6 as the first card and a queen as the second card is 4/663.
Probability is mathematically defined as the ratio of the number of outcomes of a particular event or occurrence to the total number of outcomes.
For a standard deck, there are 52 total outcomes since there are 52 cards. A standard deck is divided into four suits - hearts, clubs, spades, and diamonds - with 13 cards each. Each suit has nine numbered cards from 2 to 10, three face cards (king, queen, and jack), and an ace.
The probability of having a numbered 6 card is 4/52. The probability is the same for getting a queen. Although, the probability of getting 6 as the first card and the queen as the second is different. This kind of probability requires the multiplication rule.
First card probability = 4/52
Second card probability = 4/51
The total number of outcomes for the second card is reduced since the first card is not replaced.
Probability (6 then queen) = (4/52)(4/51)
Probability (6 then queen) = 4/663
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Is the following relation a function? x y 1 4 −1 −2 3 10 5 16 a Yes b No
The relation that is represented in the table is a function. YES.
How to Determine a Relation that is a Function?For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).
In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.
Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.
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v=pi r^2 h
solve for pi
Answer: π=v/(hr^2)
Step-by-step explanation:
v=pi r^2 h solve for pi
v=πhr^2 solve for π
v/h=πhr^2/h
v/h=πr^2
1/r^2 * v/h = πr^2 * 1/r^2
v*1/(h*r^2) = πr^2/r^2
π=v/(hr^2)
in rhombus $abcd$, points $e,f,g,$ and $h$ are the midpoints of $\overline{ab},\overline{bc},\overline{cd},$ and $\overline{da},$ respectively. quadrilateral $efgh$ has area 14 and perimeter 16. find the side length for rhombus $abcd$.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
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what are the terms and coeffients 3m - 2n
Answer:
your question is did you mean why 2n is 2n 2 serve that this queston with not involved
please help with this math! giving 40 points since both are different parts of 2 different hw pieces! :)
Write the rational numbers rounded to three decimal palaces.
19/6=
And
7/18=
Richard, Allan, and Fliss share some money in the ratio 4: 8: 5.
Allan gets £9 more than Fliss.
Work out the amount of money that Richard gets.
Step-by-step explanation:
the ratio is 4:8:5 for Richard, Allan and Fliss.
the sequence is important.
the money pool between them has 4+8+5 = 17 equal units.
Richard has 4 units of these 17, Allan has 8 units, and Fliss has the remaining 5 units.
we don't know the value of such a unit yet.
this we get from the second hint :
Allan gets £9 more than Fliss.
remember, Allan has 8 units, Fliss 5.
so, Allan has 3 units more than Fliss.
that means these 3 units are worth £9.
and that means each unit is worth 9/3 = £3.
Richard has 4 units, that means he has
4×3 = £12
Find the values of x and z (please Help)
The value of x is 6° and value of z is 67°
We know that when two lines intersect then the vertically opposite angles are equal.
So according to the given figure
(11x + 47)° = (6x + 77)°
Solving the above equation for x we get
11x° + 47° = 6x° + 77°
5x° = 30°
x = 6°
Thus the value of x is 6°
Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.
Thus, ∠z + (6x + 77)° = 180°
∠z + (6*6 + 77)° = 180°
∠z + 113° = 180°
∠z = 67°
Hence the value of z is 67°
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Identify an equation in point slope form for the perpindicular to y=-3x+5 that passes through (4,-1)
Answer:
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
Step-by-step explanation:
If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)
So the slope of the line perpendicular to y = -3x + 5 will be [tex]-\dfrac{1}{3}[/tex] = + 1/3 = 1/3
So the perpendicular line equation is
y = (1/3)x + b where b is the y intercept of this line
Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b
We get
[tex]-1=\dfrac{1}{3}\cdot \:4+b[/tex]
Switch sides
[tex]\dfrac{1}{3}\cdot \:4+b=-1[/tex]
[tex]\dfrac{4}{3}+b=-1[/tex]
Subtract [tex]\dfrac{4}{3}[/tex] from both sides
[tex]b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}[/tex]
So the equation of the perpendicular line is
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]
Three squares have been used to form a right triangle. What is the area of the third square if the area of the first two squares are 8 square units and 16 square units respectively?
The area of the third square is 24 units square.
How to find the area of a square?The squares forms a right angle triangle.
The side length of a square are equal.
Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.
area of a square = l²
where
l = side lengtharea of the first square = l²
√8 = l
l = 2√2 units
area of the second square = l²
√16 = l
l = 4 units
The length of the squares are the legs and hypotenuse of the right triangle formed.
using Pythagoras theorem,
a² + b² = c²Therefore,
a = 2√2 unitsb = 4 unitsc = ?(2√2)² + 4² = c²
16 + 8 = c²
c = √24
c = 2√6 units
area of the third square = (2√6)² = 24 unit²
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What is the greatest common factor of 3 and 13?
Answer: 1
Step-by-step explanation:
In order to find GCF, take the prime factorization of 3 and 13.
3: 1*3 ==> Prime factorization of 3
13: 1*13 ==> Prime factorization of 3
The common factor is 1.
GCF of 13 and 3 is 1
if 4x + 2y = 20 what is the value of 8x+4y/5
By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.
How to determine the value associated to a linear equation
Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:
4 · x + 2 · y = 20 Given
2 · (4 · x + 2 · y) = 20 · 2 Compatibility with multiplication
8 · x + 4 · y = 40 Associative and distributive properties
(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40 Compatibility with multiplication
(8 · x + 4 · y) / 5 = 8 Multiplication of fractions / Result
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the sum of two numbers is 56 . the larger number is 16 more than the smaller number. what are the numbers?
The numbers are 20 and 36.
As per the information in question, let the smaller number x. So, according to question, large number will be (x + 16).
Now, writing the equation that will form -
x + x + 16 = 56
Performing addition of variables on Left Hand Side
2x + 16 = 56
Shifting the number from Left Hand Side to Right Hand Side
2x = 56 - 16
Performing subtraction on Right Hand Side
2x = 40
Shifting 2 to denominator on Right Hand Side
x = 40÷2
Performing division to find the value of x
x = 20
So, smaller number is 20.
Larger number = x + 16
Larger number = 20 + 16
Larger number = 36
Hence, the numbers are 20 and 36.
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Earth is approximately 5x10^9. For which of these ages could this be an approximation
If earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Given,
The age of Earth = 5×[tex]10^{9}[/tex] years old
We know,
5×[tex]10^{9}[/tex]= 5000000000 years old
From the given option the closest number to 5×[tex]10^{9}[/tex] is 4,953,000,000 years old
Hence, if earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years
Complete question is:
Earth is approximately 5x109 years old. For which of these ages could this be an approximation? Select all that apply.
A. 4.37 x 100 years
B. 4.679999999 x 10º years
C. 4,953,000,000 years
D. 4,625,800,000 years
E. 50,000,000,000 years
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30 points mathamatics
Answer:
1870
Step-by-step explanation:
Answer:
c) 1,870
Step-by-step explanation:
374 multiplied 5 times, or 374 in a group of 5, equals 1,870.
Have a good day <333
What will be the change in the temperature after 3 days?
Answer:21/2
Step-by-step explanation:
Answer:
-7/6
Step-by-step explanation:
If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.
Hope this helps!!! :)
The perimeter is 26. How much bigger is the longest side than the shortest side?
Answer:
8
Step-by-step explanation:
the perimeter is the sum of the 3 sides of the triangle.
Given perimeter = 26 , then
2a - 3 + 2a + 3a + 1 = 26 , that is
7a - 2 = 26 ( add 2 to both sides )
7a = 28 ( divide both sides by 7 )
a = 4
then
shortest side = 2a - 3 = 2(4) - 3 = 8 - 3 = 5
longest side = 3a + 1 = 3(4) + 1 = 12 + 1 = 13
the difference between the 2 sides is 13 - 5 = 8
the longer side is 8 units bigger than the shortest side
The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level. How many grams of fat are recommended daily? Round to the nearest whole number.
The daily recommended grams of fat is? ...
The daily recommended grams of fat by the nutritional label is 98 grams.
How to find the grams of fat recommended daily?The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level.
let
the recommended level = x
Therefore, the product of the percentage and the required daily recommendation level is equals to the 3 grams.
grams of fat = 3.06% × x
3 = 3.06% × x
3 = 3.06 / 100 × x
3 = 3.06x / 100
cross multiply
3 = 3.06x / 100
300 = 3.06x
300 = 3.06x
divide both sides by 3.06
300 / 3.06 = 3.06x / 3.06
x = 98.0392156863
x = 98 grams
Therefore, the daily recommended grams of fat by the nutritional label is 98 grams.
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An Internet service company earned $770 in setup fees for new homes in a neighborhood. They charged $35 for each new setup. How many new setups did they perform? Responses 19 setups 19 setups 22 setups 22 setups 25 setups 25 setups 26 setups
The number of new setups the internet service company perform in the neighborhood is 22 setups.
The correct answer is option B
Find the number of new setups the internet service company performTotal amount the internet service company earned = $770Amount the internet service company charge per new setup = $35Number of new setups the internet service company perform = Total amount the internet service company earned ÷ Amount the internet service company charge per new setup
= $770 / $35
= 22 setups
Therefore, the number of new setups the internet service company perform in the neighborhood is 22 setups.
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Monica reads 7 ½ pages of a mystery book in 5 minutes. What is her average reading rate in pages per minute?
Answer:
1.5 or 1 ½ pages per min
Step-by-step explanation:
7.5/5=1.5
She reads 1 ½ pages per min
Answer: 1.5 pages per minute
Step-by-step explanation:
Divide the total number of pages she read by 5, the amount of time it took her. So it should look like this: 7.5/5
The answer is 1.5 pages per minute.
someone pls solve this for me w support work
Answer:
Slope = - 3
Step-by-step explanation:
The function of the line:
y = - 3x + 7
=> Slope = - 3
a sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order. what is the 2021st term of this sequence?
The 2021st term of the sequence is (- n - 2017).
Given,
A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.
We need to find out what is the 2021st term of this sequence.
What is an arithmetic sequence?An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.
Example: 2, 4, 6, 8, 10
4 - 2 = 2
6 - 4 = 2
8 - 6 = 2
The nth term of an arithmetic sequence is given by:
= a + ( n - 1 ) d
Where a = the first term
d = common difference
Let the sequence that contains no digit less than 3 in ascending order be:
3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......
Where n = any real number from 1.
We see that the common difference is -1.
3 - (n+1) - (3 - n)
= 3 - n - 1 - 3 + n
= -1
3 - (n+2) - [3-(n+1)]
= 3 - n - 2 - 3 + n + 1
= -1
Find the 2021st term.
We have,
a = 3 - n
d = -1
n = 2021
= a + ( n - 1 ) d
= (3 - n) + ( 2021 - 1 ) (-1)
= 3 - n - 2020
= - n - 2017
Thus the 2021st term of the sequence is - n - 2017.
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At a football game, a vender sold a combined total of 144 sodas and hot dogs. The number of sodas sold was two times the numbers of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
4. A right cone has a surface area of 258 cm² and a base radius of 4 cm. What is
the height of the cone to the nearest tenth of a centimetre?
Answer:
64.5cmStep-by-step explanation:
I hope this answer help you
Answer:
h = 16.0 cm
Step-by-step explanation:
Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)
Total Surface Area of a right cone
= Lateral Area(L) + Base Area(B)
All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point
Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²
So Lateral Area = 258 - 50.3 = 207.7 cm²
Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]
So we get
[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm
Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]
Square both sides
[tex]16.5^2 = 16 + h^2[/tex]
==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex] rounded to 1 decimal place
So final answers is h = 16 cm
Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads, on which he can travel an average of 35 mph for a total of 1.5 hours. Sam also takes the highway, on which he travels an average of 65 mph for a total of x hours. Approximately how long does Sam travel on the highway, to the nearest tenth of an hour?
The hours travelled on the highway is 1.3 hours.
What is the time travelled?The first step is to determine the distance Sam travelled on the city road. The formula that would be used is the average speed formula. The average speed is the ratio of total distance travelled and the total time travelled.
Average speed = distance /time
average speed x time = distance
Distance = 35 x 1.5 = 52.50 miles
The second step is to determine the distance travelled on the highway.
Distance travelled on the high way = 140 - 52.50 = 87.50 miles
Now, determine the total hours travelled:
Hours travelled = distance / average speed
87.50 / 65 = 1.3 hours
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Answer: Sam traveled 1.3 hours.
Step-by-step explanation:
It takes 15 over 2 minutes to fill an empty aquarium to a depth of 3 over 5 meters. what is the unit rate in minutes per meter? write your answer as a fraction or a mixed number in simplest form.
The unit rate in minutes per meter is 25/2
We are given the time taken to fill an empty aquarium = 15/2 minutes
Also, the depth of aquarium = 3/5 meters
To find the unit rate in minutes per meter, we will simply keep the values in formula. We do not need to change the units, as they are already in required ones, which are minutes and meters.
Unit rate = minutes ÷ meter
Unit rate = 15/2 ÷ 3/5
Rewriting the fraction
Unit rate = 15×5 ÷ 3×2
Performing multiplication in both numerator and denominator
Unit rate = 75 ÷ 6
Performing division of both numerator and denominator by 3
Unit rate = 25/2
So, the unit rate in minutes per meter is 25/2.
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