Answer:
[tex]\frac{1}{2}[/tex] is a rational number
Step-by-step explanation:
Given
[tex]Real\ Number = \frac{1}{5}[/tex]
Required
Determine which set of numbers it belongs to
Analyzing the options one after the other;
1. Whole numbers: 0, 1, 2, 3....
2. Natural numbers: 1, 2, 3, 4... 3.
3. Irrational numbers are numbers that can't be expressed as fractions
The option that answers this question is rational numbers because [tex]\frac{1}{2}[/tex] can be expressed as decimal and fraction interchangeable.
Hence;
[tex]\frac{1}{2}[/tex] is a rational number
PLEASE HELP!!!!! 1. −2=6/7p P=?
Answer:
p = -7/3
Step-by-step explanation:
-2 = 6/7p
multiply each side by (7/6)
-2(7/6) = 6/7p(7/6)
-7/3 = p
Answer:
[tex]-\frac{7}{3}[/tex]
Step-by-step explanation:
Divide each side by 6/7, so it now looks like this: [tex]-\frac{7}{3} = p[/tex]What is the gcf of 100 and 48
Answer: 4
Step-by-step explanation:
Factor of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factor of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
4 appears in both factors, so the GCF (Greatest Common Factor) will be 4
Hope this helps!! :)
Please let me know if you have any question
Forgot what I do next.
Answer:
you do subtraction than the plus and you got your answer!
Hope this helps :)
Answer:
7h - 15h + 40 = -72
-8h + 40 = -72
take +40 on the other side of equation
-8h = -72-40
-8h = -112
h = -112/-8
h = 14
Step-by-step explanation:
1. The subsets of the real numbers can be represented in a Venn diagram as shown. To which subsets of real numbers does 12 belong?
A) Integers and Whole Numbers only
B) Rational Numbers, Integers, and Whole Numbers
C) Rational Numbers and Integers only
D) Irrational Numbers, Integers, and Whole Numbers
2. Which statement BEST describes the relationship between whole numbers and natural numbers shown in the diagram?
A) The diagram shows that whole numbers are a subset of natural numbers, because all whole numbers are natural numbers.
B) The diagram shows that natural numbers are a subset of whole numbers, because all natural numbers are whole numbers.
C) The diagram shows that whole numbers are a subset of natural numbers, because some whole numbers are not natural numbers.
D) The diagram shows that natural numbers are a subset of whole numbers, because all whole numbers and natural numbers have no numbers in common.
Answer:
The answer to number 1 is b and number 2 is also b
Answer:
A.
Step-by-step explanation:
Every integer is a rational number but a rational number does NOT need to be a integer, therefore meaning that integers are a subset of rational numbers. Not the other way around.
ou live in the building on the left in the drawing, and a friend lives in the other building. the two of you are having a discussion about the heights of the buildings, and your friend claims that the height of his building is more than 1.50 times the height of yours. to resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, whereas your line of sight to the base of the other building makes an angle of 52° below the horizontal. determine the ratio of the height of the taller building to the height of the shorter building. state whether your friend is right or wrong.
Answer:
1.3
Friend is wrong
Step-by-step explanation:
Given:
friend's claim: height of his building is more than 1.50 times the height of yours
line of sight to the top edge of the other building makes an angle of 21° above the horizontal
line of sight to the base of the other building makes an angle of 52° below the horizontal
Solution:
Let A be the height of your building is A
Let B+A his building is B higher than yours.
Let the distance between the buildings is x.
then
tan 52 = A/x
tan 21 = B/x
A/B = tan 52 / tan 21
= 1.27994 / 0.38386
A/B = 3.33
(A + B) / A = 1.5 0
A/A + B/A = 1.50
1 + B/A = 1.50
B/A is basically (B/x) / (A/x)
So
1+ 3.33 / 3.33
= 4.33/3.33
= 1.3
Since 1.3 is not equal to 1.5
Hence the friend's claim is wrong.
The height of the taller building can be given in relation to the height of
the other building using trigonometric ratios.
Correct response:
The claim is wrongReasons for the above responseThe given parameters are;
Angle of elevation to the top of the other building = 21°
Angle of depression to the base of the other building = 52°
The claim of the friend = The height of his building > 1.5 × The height of the other building
Required:
To state whether the claim is right or wrong.
Solution:
Let h represent the height of the smaller building, let l represent the
distance between the two buildings, and let d represent the height by
which one building is taller than the other, we have;
[tex]tan\left(21^{\circ} \right) = \mathbf{ \dfrac{d}{l} }[/tex]l·tan(21°) = d
[tex]tan \left(52^{\circ} \right) = \mathbf{\dfrac{h}{l} }[/tex]l·tan(52°) = h
Height of the taller building, H = h + d = l·tan(52°) + l·tan(21°)
Height of the other building = h = l·tan(52°)
Therefore;
[tex]\dfrac{H}{h} = \mathbf{ \dfrac{l \cdot tan \left(52^{\circ} \right) + l \cdot tan \left(21^{\circ} \right)}{l \cdot tan \left(52 ^{\circ} \right)}} = 1 + \dfrac{tan \left(21^{\circ} \right)}{tan \left( 52^{\circ} \right)} \approx 1.3[/tex]H ≈ 1.3·h
Which gives that the taller building, H, is approximately 1.3 times the other building.
Therefore;
The claim is incorrectLearn more about trigonometric ratios here:
https://brainly.com/question/14692278
A manufacturer determines that the cost of making a computer component is4.161616 $. Write the repeating decimal cost as a fraction and as a mixed number.
Answer:
$4.161616 =
As a fraction
= $[(4 × 62500) + 10101]/62500
= $(260101/62500)
As a mixed number =
$[tex]4\frac{10101}{62500}[/tex]
Step-by-step explanation:
Cost of making a computer component = $4.161616
= $4 + $0.161616
6 numbers after the decimal , hence
0.161616 × 1000000/1000000
= 161616/1000000
= 10101/62500
We are told in the question to write the repetiting decimal cost as a fraction and as a mixed number
$4 + $0.161616 = $4 + 10101/62500
As a fraction
= $[(4 × 62500) + 10101]/62500
=$260101/62500
As a mixed number = [tex]$4\frac{10101}{62500}[/tex]
perform the indicated operation (3 - 5i) - (-2 +11i)
Answer:
5 - 16i
Step-by-step explanation:
combine like terms:
3 - (-2) = 5
(-5i) - 11i = -16i
5 - 16i
Simplify these algebraic expressions: (12x + 3 − 4x + 7) (8 − 7x − 13 + 2x) (−3x − 18 + 5x − 2) These are three separate equations.
Answer:
(2 (4 x + 5), -(3 x + 25))
Step-by-step explanation:
Simplify the following:
(12 x - 4 x + 3 + 7, 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8)
Grouping like terms, 12 x - 4 x + 3 + 7 = (12 x - 4 x) + (3 + 7):
((12 x - 4 x) + (3 + 7), 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8)
12 x - 4 x = 8 x:
(8 x + (3 + 7), 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8)
3 + 7 = 10:
(8 x + 10, 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8)
Factor 2 out of 8 x + 10:
(2 (4 x + 5), 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8)
Grouping like terms, 5 x + 2 x - 3 x - 7 x - 18 - 13 - 2 + 8 = (-7 x + 2 x - 3 x + 5 x) + (8 - 13 - 18 - 2):
(2 (4 x + 5), (-7 x + 2 x - 3 x + 5 x) + (8 - 13 - 18 - 2))
-7 x + 2 x - 3 x + 5 x = -3 x:
(2 (4 x + 5), -3 x + (8 - 13 - 18 - 2))
8 - 13 - 18 - 2 = -25:
(2 (4 x + 5), -25 - 3 x)
Factor -1 out of -3 x - 25:
Answer: (2 (4 x + 5), -(3 x + 25))
Gomez has 30 cans of regular soda and 18 cans of diet soda. He wants to create some identical refreshment tables that will operate during the football game. He also doesn’t want to have any sodas left over. What is the greatest number of refreshment tables that Gomez can stock?
Answer: 6
Step-by-step explanation:
Given: Gomez has 30 cans of regular soda and 18 cans of diet soda.
He wants to create some identical refreshment tables that will operate during the football game and doesn't want any sodas left over.
Then, the greatest number of refreshment tables that Gomez can stock = GCD (30,18).
Since, 30= 2 x 5 x x 3
18= 2 x 3 x 3
GCD (30,18) = 2 x 3 = 6
Hence, the greatest number of refreshment tables that Gomez can stock is 6.
Find h(-2) if h (x) = x3 + 1
Solve for the indicated variable: 2p+5r=q for p
Answer:
p = [tex]\frac{q-5r}{2}[/tex]
Step-by-step explanation:
Given
2p + 5r = q ( subtract 5r from both sides )
2p = q - 5r ( divide both sides by 2 )
p = [tex]\frac{q-5r}{2}[/tex]
-1, 5, 15, 29, 41,
What is the next terms
Answer:
63
Step-by-step explanation:
-1,5,15,29,41,63
between the 2nd term and first term, we add 6
between the 3rd and 2nd, we add 10
between 4th and 3rd, we add 14
between 5th and 4th, we add 12
to get the next term, we add 22 to the fifth tern which is 63
this is how to get the 4th term 6 interval was added to 8 making 14 and to get the fifth, then add 2 to the difference of 10 making 12. 29+12=41..so to get the last term 14 was added to 8 making 22 and therefore 41+22=63
HELP!!! 35 POINTS Solve the equation. −7.8x=−1.56. x=?
Answer:
x = 0.2
Step-by-step explanation:
-7.8x = -1.56
-1.56/-7.8 = 0.2
x = 0.2
Answer:
[tex]x =\frac{1}{5}[/tex] or [tex]0.2[/tex] (they're the same)
Step-by-step explanation:
Divide each side by -7.8, so it now looks like this: x = 0.2can anyone answer this question. A) How many scarves can be made from 7 1/2m of fabric, if each scarf requires 1 3/8m of fabric? B) will any fabric be left over? If so, how much? Will mark brainliest for the answers.
Answer:
A) 2
B) 13/16
A) If 1 3/8 = 1 scarf
7 1/2 = 7 1/2 ÷ 1 3/8
= 2.8125
so 7 1/2 can make 2 scarfs
B) remaining fabric is 0.8125
= 13/16
Write an equation of the line that passes through the points. Use the slope-intercept form (if possible). If not possible, explain why and use the general form. Use a graphing utility to graph the line (if possible).
Answer:
y = 7/8x -1/2 y = mx+bm = slopeSlope = 7/8Step-by-step explanation:
[tex](4,3)=(x_1,y_1)\\(-4,-4)=(x_2,y_2)\\\\\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}\\ \\\frac{y-3}{x-4}= \frac{-4-3}{-4-4}\\\\\frac{y-3}{x-4}=\frac{-7}{-8} \\-8(y-3) =-7(x-4)\\-8y +24=-7x +28\\-8y =-7x +28-24\\-8y = -7x +4\\Divde\:both\:sides\:of\:the\:equation\:by\: -8\\\\\frac{-8y}{-8} = \frac{-7x}{-8} +\frac{4}{-8}\\\\y = \frac{7}{8}x -\frac{1}{2}[/tex]
Identify the following pairs of angles as complementary, supplementary, adjacent, and/or vertical angles.
5. ABH and HBC
6. ABE and FBG
7. ABE and EBG
8. HBF and FBG
Please show all work and not just the answer.
Answer:
ABH and HBC ---- Complementary angles ( Sum of complementary anfges = 90 degrees )
ABE and FBG------Vertical angles (they are vertically opposite to each other and sum of the vertical angles =180
ABE and EBG-------Supplementary angles ( Sum of supplementary angles =180 degrees)
HBF and FBG----------Adjacent Angles(These two angles are next to each other/adjacent to each other )
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Past
Prim
What is the prime factorization of 10?
Answer: Prime factorization: 10 = 2 x 5.
Step-by-step explanation:10 is a composite number. 10 = 1 x 10 or 2 x 5. Factors of 10: 1, 2, 5, 10.
The prime factorization of 10 is 2 and 5
5)
Below is a data table that shows the growth of a plant in a garden. Use the data table to create a graph
that shows the height of the plant for each day recorded. Make sure you label your x and y-axis with a
correct scale. Use a scatter plot to create your graph.
Day # (days)
Plant Height (cm)
0
0
1
0.2
2
0.4
3
0.6
Plant Height
(cm)
I
4
0.8
5
1.0
6
1.2
0
Day #
Answer:
is number one ka matalab hindi me janiye to the meeting ko join date puchhrahai hai ki tum mere ko bohot achhi lagi aur attitude to nahin hai ki tum mere ko bohot achhi lagi aur attitude to nahin hai ki tum mere ko bohot achhi lagi aur attitude to nahin hai ki tum mere ko bohot achhi lagi aur attitude to nahin hai ki tum mere ko bohot achhi lagi aur attitude to nahin hai ki tum mere ko bohot achhi lagi aur attitude to
Thanks for the help, question below :)
Answer:
a: [tex]40h+75f=800,h+f=13[/tex]
b: 5
c: 8
Step-by-step explanation:
Explanation for a: Making the equations
Assuming h is the amount of half-page ads and f is the amount of full page ads, we can create the equations [tex]40h+75f=800,h+f=13[/tex] since the total cost will be 800$, and we have a total of 13 ads.
Explanation for b: Solving for h
We can now solve for one of the variables using elimination. Let’s multiply the expression [tex]h+f=13[/tex] by -75.
[tex]-75h - 75f = -975[/tex]
Great! Now let’s add the equations.
[tex]40h + 75f = 800\\\\-75h - 75f = -975[/tex]
Adding these equations, we get
[tex]-35h = -175[/tex]
Divide both sides by -35, and we get [tex]h = 5[/tex].
Explanation for c: Solving for f
We can now substitute h inside the equation [tex]h + f = 13[/tex].
[tex]5 + f = 13\\\\f = 13-5\\\\f = 8[/tex]
Hope this helped!
(a) Let's say that h = half-page advertisement, and f = full-page advertisement.
Now It is given that there is a total of 13 advertisements present, and hence we have the first equation h + f = 13. Respectively we have the equation 40h + 75f = 800. This is represented by the following system of equations,
[tex]\begin{bmatrix}h+f=13\\ 40h+75f=800\end{bmatrix}[/tex]
(c) From here on let's solve this system for h and f. Isolating h in the first equation would give us h = 13 - f, which then can be substituted into the second equation to receive 40(13 - f) + 75f = 800. Let's solve for f --- (1)
40(13 - f) + 75f = 800,
520 - 40f + 75f = 800,
520 + 35f = 800,
35f = 280,
f = 280 / 35 = 8 full advertisements
(b) Now let's substitute this value of f back into the first equation to solve for the value of h --- (2)
h + 8 = 13,
h = 13 - 8 = 5 half advertisements
help please idk how to do this
-2.5 hope this helps you
Help please!!! Thank you
Answer: ∠ABE=20°
Step-by-step explanation:
∵ AB=BC
∴ ΔABC is a isosceles triangle
∵ ∠A=30
∴ ∠C=30
∵ The interior angle sum of triangle is 180°
∵ ∠A+∠B+∠C=180
30+∠B+30=180
∠B+60=180
∠B=120 (∠ABC)
∵ ∠EBD+∠ABE+∠ABC=linear pair
∴∠EBD+∠ABE+∠ABC=180°
4x+2x+120=180
6x+120=180
6x=60
x=10
∠ABE=2x=2(10)=20°
Hope this helps!! :)
Please let me know if you have any question
I really need help with this please
Answer: Answer is in steps
Step-by-step explanation:
A) To find p(46) input the 46 into the equation and solve
p(46) = 61.41 + 2.32(46)
p(46) = 168.13
B) This means that if the female's femur is 46 in length then that female will be 168.13 centimeters tall.
Sam and Mary are picking a topping for the ice cream. Their choices are strawberries, chocolate chips, gummi bears, caramel sauce, and whip cream. What is the probability that they both pick gummi bears as their topping?
Answer:
2/5
Step-by-step explanation: Total outcomes=5
favourable outcomes=2
Therefore ,P(E)=2/5
how to do this question plz answer me step by step plzz
Answer:
Adult ticket= 7£
Child ticket= 2£
Step-by-step explanation:
Let the cost of an adult ticket be £A and the cost of a child ticket be £C.
2A +3C= 20 -----(1)
A +4C= 15 -----(2)
From (2):
A= 15 -4C -----(3)
Susbt. (3) into (1):
2(15 -4C) +3C= 20
30 -8C +3C= 20 (expand)
30 -5C= 20 (simplify)
5C= 30 -20
5C= 10
C= 10 ÷5
C= 2
Subst. C=2 into (3):
A= 15 -4(2)
A= 15 -8
A= 7
Thus, the cost of an adult ticket and a child ticket is 7£ and 2£ respectively.
Find the length of the hypotenuse of QPO
Answer:
The answer is option DStep-by-step explanation:
To find the length of the hypotenuse of QPO we must first find the value of x
Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x
Using Pythagoras theorem we have
QO² = QP² + OP²
That's
( x + 6)² = 5² + ( x + 5)²
x² + 12x + 36 = 25 + x² + 10x + 25
Group like terms
x² - x² + 12x - 10x = 50 - 36
2x = 14
Divide both sides by 2
x = 7
The hypotenuse of QPO is (x + 6)
Substitute the value of x into the expression
That's
7 + 6= 13Hope this helps you
Answer:
[tex]\Huge \boxed{\mathrm{D.} \ 13}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use Pythagorean theorem to solve for the value of x.
[tex]OP^2 +PQ^2 =OQ^2[/tex]
[tex](x+5)^2 +5^2 =(x+6)^2[/tex]
Simplifying both sides.
[tex]x^2 +10x+50=x^2 +12x+36[/tex]
Subtracting x², 10x and 36 from both sides.
[tex]14=2x[/tex]
Dividing both sides by 2.
[tex]7=x[/tex]
Letting x = 7 for the length of the hypotenuse.
[tex]\Longrightarrow \ 7+6 \\\\\\ \Longrightarrow \ 13[/tex]
[tex]\rule[225]{225}{2}[/tex]
Apply the Distributive Property first to solve the equation below. What operation will you need to use last? If instead, you divide first to solve the equation what operation would you need to use last? 24(d/4 -5)=156
Step-by-step explanation:
The distributive property is as follows :
[tex]a(b+c)=ab+ac[/tex] ....(1)
We need to solve [tex]24(\dfrac{d}{4}-5)=156[/tex] using distributive property
Applying property (1) on the LHS of given equation
Taking a = 24, b = d/4 and c = -5
So,
[tex]24(\dfrac{d}{4}+(-5))=156\\\\24\times \dfrac{d}{4}+24\times (-5)=156\\\\6d-120=156\\\\6d=156+120\\\\6d=276\\\\d=\dfrac{276}{6}\\\\d=46[/tex]
So, we get the value of d as 6 using distributive property.
a gardener spends half an hour to mow and weed the lawn which has a measurement of 24 m × 15 m. He is paid $25 per hour. how much is he paid for a lawn which has a measurement of 48m × 30m?
Answer:
$100
Step-by-step explanation:
Half - a - hour = (24*15) =360 m
one hour payment $25
hour(?) =(48*30) = 1440 m
1440/ 360 = 4 hours
So, 25*4 =$100
NEED HELP ALGEBRA 1
Which fraction has the least value?
A. 4/10
B. 12/25
C. 14/20
D. 28/50
E. 1/5
========================================================
Method 1
Use your calculator to find the decimal version of each fraction
4/10 = 0.4012/25 = 0.4814/20 = 0.7028/50 = 0.561/5 = 0.20We see that 0.20 is the smallest decimal of the list, so 1/5 is the smallest fraction of the list.
----------------------------
Method 2
To compare fractions, we need to get all of the denominators to the same value. A good target is the lowest common denominator (LCD)
In this case, the LCD is 100
4/10 = 40/100 .... multiply top and bottom by 1012/25 = 48/100 .... multiply top and bottom by 414/20 = 70/100 .... multiply top and bottom by 528/50 = 56/100 .... multiply top and bottom by 21/5 = 20/100 .... multiply top and bottom by 20The last fraction has the smallest denominator, so 1/5 is the smallest.
To pass an Examination consisting of four papers, candidates MUST score a mean mark of 40% or above and NOT less than 33% in each paper. The table below shows the marks for 3 students. Using the tables, which students passed the examination? Give reason(s).
Answer:
Josephine
Step-by-step explanation:
2 criteria was given to pass an exam:
1. At least, a mean mark of 40% must be achieved in the exam consisting of 4 papers
2. Score at least, 33% in each paper.
From the table given, and considering these two criteria, James definitely didn't pass the examination. He scored below 33% in one of the 4 papers. James scored 30% in Maths
Calculated the mean score for John and Josephine to determine if they meet the first criteria of having at least a mean score of 40%.
Mean score of John = (35 + 36 + 42 + 44) ÷ 4 = 39.25%
Mean score for Josephine = (60 + 55 + 38 + 75) ÷ 4 = 57%
Josephine passed the examination because she had a mean score of 57%, and also scored 33% and above in each test.
Emily is three years older than twice her sister Mary's age. The sum of their ages is less than 30. Let x represent Mary's age. Which inequality represents Mary's possible age?
Answer:
0 < x < 9
Step-by-step explanation:
Mary's age = x
Twice of Mary's age = 2x
Emily's age = (2x + 3) (we are told Emily is 3 years older than twice of Mary's age)
Given that the sum of their ages is > 30, we have the following expression:
[tex] (2x + 3) + x [/tex] > 30
Let's simply:
[tex] 2x + 3 + x [/tex] > 30
[tex] 3x + 3 [/tex] > 30
Subtract 3 from both sides
[tex] 3x + 3 - 3 [/tex] > [tex] 30 - 3 [/tex]
[tex] 3x [/tex] > [tex] 27 [/tex]
Divide both sides by 3
[tex] \frac{3x}{3} [/tex] > [tex] \frac{27}{3} [/tex]
[tex] x [/tex] > [tex] 9 [/tex]
Therefore, the inequality that represents Mary's possible age is: 0 < x < 9