Answer:
Each value has been identified below.
Step-by-step explanation:
(1) We have to describe two ways the numbers in each proportion are related;
(a) 5 : 20 = 125 : 500
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
20 [tex]\times[/tex] 125 = 5 [tex]\times[/tex] 500
2500 = 2500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 5 : 20 = 125 : 500
We will check that; [tex]\frac{5}{125}[/tex] is equal to [tex]\frac{20}{500}[/tex] or not.
[tex]\frac{5}{125} = \frac{20}{500}[/tex]
[tex]\frac{1}{25} = \frac{1}{25}[/tex]
This shows that the given proportion is related.
(b) 10 : 1 = 120 : 12
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
1 [tex]\times[/tex] 120 = 10 [tex]\times[/tex] 12
120 = 120
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 10 : 1 = 120 : 12
We will check that; [tex]\frac{10}{120}[/tex] is equal to [tex]\frac{1}{12}[/tex] or not.
[tex]\frac{10}{120} = \frac{1}{12}[/tex]
[tex]\frac{1}{12} = \frac{1}{12}[/tex]
This shows that the given proportion is related.
(c) 75 : 25 = 300 : 100
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
25 [tex]\times[/tex] 300 = 75 [tex]\times[/tex] 100
7500 = 7500
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 75 : 25 = 300 : 100
We will check that; [tex]\frac{75}{300}[/tex] is equal to [tex]\frac{25}{100}[/tex] or not.
[tex]\frac{75}{300} = \frac{25}{100}[/tex]
[tex]\frac{1}{4} = \frac{1}{4}[/tex]
This shows that the given proportion is related.
(d) 1 : 3 = 16 : 48
One way of describing that the given ratios are in proportion is;
Product of means = Product of extremes
3 [tex]\times[/tex] 16 = 1 [tex]\times[/tex] 48
48 = 48
This shows that the given proportion is related.
Another way of describing that the given ratios are in proportion is;
As 1 : 3 = 16 : 48
We will check that; [tex]\frac{1}{16}[/tex] is equal to [tex]\frac{3}{48}[/tex] or not.
[tex]\frac{1}{16} = \frac{3}{48}[/tex]
[tex]\frac{1}{16} = \frac{1}{16}[/tex]
This shows that the given proportion is related.
(2) Now we have to determine each value of n in the following given ratios;
(a) 2 : 5 = 8 : n
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 8 = 2 [tex]\times[/tex] n
40 = 2n
[tex]n=\frac{40}{2}[/tex] = 20
Hence, the value of n is 20.
(b) 2 : n = 6 : 9
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 6 = 2 [tex]\times[/tex] 9
6n = 18
[tex]n=\frac{18}{6}[/tex] = 3
Hence, the value of n is 3.
(c) n : 5 = 12 : 20
As we know that Product of means = Product of extremes
5 [tex]\times[/tex] 12 = n [tex]\times[/tex] 20
60 = 20n
[tex]n=\frac{60}{20}[/tex] = 3
Hence, the value of n is 3.
(d) 8 : n = 4 : 15
As we know that Product of means = Product of extremes
n [tex]\times[/tex] 4 = 8 [tex]\times[/tex] 15
4n = 120
[tex]n=\frac{120}{4}[/tex] = 30
Hence, the value of n is 30.
(3) Now we have to determine each value of z in the following given ratios;
(a) 4 : 8 = 3 : z
As we know that Product of means = Product of extremes
8 [tex]\times[/tex] 3 = 4 [tex]\times[/tex] z
24 = 4z
[tex]z=\frac{24}{4}[/tex] = 6
Hence, the value of z is 6.
(b) 5 : z = 6 : 18
As we know that Product of means = Product of extremes
z [tex]\times[/tex] 6 = 5 [tex]\times[/tex] 18
6z = 90
[tex]z=\frac{90}{6}[/tex] = 15
Hence, the value of z is 15.
(c) z : 14 = 10 : 20
As we know that Product of means = Product of extremes
14 [tex]\times[/tex] 10 = z [tex]\times[/tex] 20
140 = 20z
[tex]z=\frac{140}{20}[/tex] = 7
Hence, the value of z is 7.
(d) 3 : 21 = z : 56
As we know that Product of means = Product of extremes
21 [tex]\times[/tex] z = 3 [tex]\times[/tex] 56
21z = 168
[tex]z=\frac{168}{21}[/tex] = 8
Hence, the value of z is 8.
Find the 7th term in the
sequence
-4, -8,-16,
Answer:
-256
Step-by-step explanation:
Given:
a₁ = -4 (First term) r = -8 ÷ -4 = 2 (Common ratio) n = 7 (Number of term)Find:
a₇ = ?Formula:
aₙ = a₁ · rⁿ⁻¹Solve:
a₇ = -4 · 2⁷⁻¹a₇ = -4 · 2⁶a₇ = -4 · 64a₇ = -256Please help!!
Darrel’s baby sister was 8 pounds at birth. She gained 4 pounds each year. She now weighs 32 pounds. How old is she?
Subtract to find the weight she gained since birth.
32 - 8 = 24
Divide to see how many years passed.
24 / 4 = 6
Therefore, Darrel's baby sister is 6 years old.
Best of Luck!
on a ship, the price of a gift is 24 euros or $ 30. what is the difference in the price on a day when the exchange rate is 1 euro=$ 1.2378? Give your answer in dollars, correct to the nearest cent
Answer:
The price would be $29.7072
Step-by-step explanation:
Since the original price in euros is 24, you need to multiply $ 1.2378 by 24.
1.2378 × 24 = $29.7072
The new price would be $29.7072.
Hope this helps!
Bo is buying a board game that usually costs B dollars. The game is on sale, and the price has been reduced by 18%. Which of the following expressions could represent how much Bo pays for the game? Choose 2 answers: A 0.82B B 1.18B C B - 0.18 D B - 18 E B - 0.18B
Answer:
a and b
Step-by-step explanation:
Find the slope of the line passing through (3,5) and (-4,-10)
Answer:
[tex] \frac{15}{7} [/tex]
Step-by-step explanation:
Please see attached picture for full solution.
Multiply your answer should be a monomial in standard form (-4x^2)(7x^3)
answer: -28x^5
exlaningtion:I used my brain dhdhdishdhdhdhdhdh
3(a-7b)+2(4a+3b)+23(a-b)
Answer:
3a-21b+8a+6b+23a-23b.
3a+8a+23a-21b+6b-23b.
34a-38b.
Answer:
34a-38b
Step-by-step explanation:
3a-21b+8a+6b+23a-23b
=34a-38b
−13 = 5(1 + 4m) − 2m multi step equation show all steps pls
Answer:
m = -1
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
-13 = 5(1 + 4m) - 2m
Step 2: Parenthesis (distribute)
-13 = 5 + 20m - 2m
Step 3: Combine like terms (m)
-13 = 5 + 18m
Step 4: Subtract 5 on both sides
-18 = 18m
Step 5: Divide both sides by 18
-1 = m
Step 6: Rewrite
m = -1
Answer:
m = -1
Step-by-step explanation:
-13 = 5(1 + 4m) - 2m
Step 1 : Distributive Property
-13 = 5 + 20m - 2m
Add like terms
-13 = 5 + 18m
Subtract 5 on both sides
-18 = 18m
Divide
[tex]\frac{-18}{18}[/tex] = [tex]\frac{18m}{18}[/tex]
m = -1
Under which conditions does the commutative property apply to compositions of f(x) and g(x)?
A) when f(g(x)) and g(f(x) are inverse functions
B) when f(g(x)) and g(f(x) are equal for at least one value of x
C) when f(g(x)) and g(f(x) are equal for all values of x
D) when f(g(x)) and g(f(x) are not inverse functions
Answer:
The correct option is;
C) When f(g(x)) and g(f(x)) are equal for all values of x
Step-by-step explanation:
To have commutative property is to have the property to move around or change position, as such the commutative property is the property concerns the changing of the positioning of items
The commutative property for addition is a + b = b + a while the commutative property for multiplication is a×b = b×a
For functions , the commutative property can therefore, be expressed as follows;
Commutative property of f(x) and g(x) gives f(g(x)) = g(f(x)) for all values of x.
Answer:
c
Step-by-step explanation:
I need help on b. and c.
Answer:
Step-by-step explanation:
1. 8a = -2
a = -2/8 =-1/4
2. -11b = -6
b = 6/11
3. -2c = 16
c = -8
Need help ASAP not sure how to simplify this could someone pleade comment answer
Answer:
8 (3/4)
Step-by-step explanation:
convert everything into improper frantions
-3 1/2 = -7/2
-12 1/4 = -49/4
common denominators
-7/2 = -14/4
solve
-(14/4)-(-49/9)
two negative cancel out to make a positive
-(14/4)+(49/9)
35/4
35 divided by 4 = 8.75 = 8 3/4
Is the function even or odd?
Answer:
[tex]f(\theta)=\cos(\theta)[/tex] is an even function.
Step-by-step explanation:
Recall when it means when a function is even or odd. An even function has the following property:
[tex]f(-x)=f(x)[/tex]
And an odd function has the following property:
[tex]f(-x)=-f(x)[/tex]
So, let's test some values for cos(x).
Let's use π/3:
[tex]f(\pi/3)=\cos(\pi/3)[/tex]
From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).
Now, let's find -π/3. This is the same as 5π/3. Thus:
[tex]f(-\pi/3)=\cos(-\pi/3)[/tex]
And again from the unit circle, we can see that this is 1/2.
Therefore, despite the negative, the function outputs the same value.
Cosine is an even function.
Notes:
Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!
Josie hikes a trail that is 2574 meters long at the same rate of speed. She completes the trail in exactly 33 minutes.
How many meters did Josie travel each minute?
O A. 43 m/min
OB. 78 m/min
C. 594 m/min
OD. 1287 m/min
o
E
1980 m/min
Answer:
B. 78 meters
Step-by-step explanation:
2574 divided by 33 equal 78
hope this helps you :)
rewrite 3/4x - 5 = 7/12 so it does not have fractions .
Answer:
Answer
Step-by-step explanation:
0.75x -5 = 0.583333333333...
Answer:
x = 7.4444
Step-by-step explanation:
3/4 x - 5 = 7/12
3x/4 - 5 = 7/12
3x/4 = 7/12 + 5
3x/4 = 7/12 + 60/12
3x/4 = 67/12
3x = 4*67/12
3x = 268/12
3x = 22.3333
x = 22.3333/3
x = 7.4444
Check:
3*7.4444/4 - 5 = 7/12
5.58333 - 5 = 0.58333
In city A, the temperature rises 9° F from 8am then the temperature drops 8°F from 9am to 10am in city B the temperature drops 1°F from 8am to 9am then the temperature drops 3°F from 9am to 10am write an expression that represents the change In temperature from 8am to 10am for each city. Simplify and interpret each sum. Which expression represents the change in temperature for city A?
Answer:
For City A, the expression for temperature change is 9 + (-8)
The amount the temperature changes for City A = 1°F
For City B, the expression for temperature change is -1 + (-3) = -4°F
The amount the temperature changes for City B = -4°F
Step-by-step explanation:
The given information are;
In City A, the temperature rise from 8 am to 9 am = 9°F
In City A, the temperature drop from 9 am to 10 am = 8°F
In City B, the temperature drop from 8 am to 9 am = 1°F
In City B, the temperature drop from 9 am to 10 am = 3°F
The expression for that represents the temperature change from 8 am to 10 am is therefore;
For City A
Temperature change from 8 am to 10 am are
8 am to 9 am = +9°F
9 am to 10 am = -8°F
Sum, change from 8 am to 10 am = 9 + (-8) = 1°F
For City B
Temperature change from 8 am to 10 am are
8 am to 9 am = -1°F
9 am to 10 am = -3°F
Sum, change from 8 am to 10 am = -1 + (-3) = -4°F
A 37-ft ladder leans against a building so that the angle between the ground and the ladder is 73°. How high does the ladder reach up the side of the building?
Answer:
35.4 ft
Step-by-step explanation:
To solve this problem, we need to represent the statement in the question in a diagram.
Please see attached photo.
In the attached photo, x is the height of the building.
Thus, we can calculate the value of x as shown below:
Angle θ = 73°
Opposite = x
Hypothenus = 37 ft
Using the Sine ratio, the value of x can be obtained as follow:
Sine θ = Opposite /Hypothenus
Sine 73 = x /37
Cross multiply
x = 37 × Sine 73
x = 35.4 ft
Therefore, the ladder reached up to 35.4 ft of building.
Choose the best description of the ratio:
220 seventh grade students
630 middle school students
is a
DRAG & DROP THE ANSWER
<
part-to-part ratio
part-to-whole ratio
rate
unit rate
If $17,000 is invested in an account for 25 years. Calculate the total interest earned at the end of 25 years if the interest is: (a) 7% simple interest: $ (b) 7% compounded annually: $ (c) 7% compounded quarterly: $ (d) 7% compounded monthly: $
Answer:
a.) $29,750.00 simple interest
b.) $75,266.35 Compounded annually
c.) $79,358.65 compunded quarterly
d.) $80,332.11 compounded monthly
Step-by-step explanation:
a.) Formula: I = p x r x t
Where:
P is the principal amount, $17000.00.
r is the interest rate, 7% per year, or in decimal form, 7/100=0.07.
t is the time involved, 25....year(s) time periods.
So, t is 25....year time periods.
To find the simple interest, we multiply 17000 × 0.07 × 25 to get that:
The interest is: $29750.00
______________________________
b.) $75,266.35
c.) $79,358.65
d.) $80,332.11
which number is greater 0.31 or 0.03
Answer:
The number bigger is 0.31.
Step-by-step explanation:
Answer:
0.31 is greater than 0.03
Step-by-step explanation:
0.31 - 0.03 = 0.28
So, 0.31 is 0.28 greater than 0.03
Hope it helps :)
remove parentheses by applying the distributive property 10x(4 - 3x)
Answer:
40x - 30 x²
Step-by-step explanation:
When x is multiplied by x it become x².
10x(4 - 3x)
10x times 4 = 40x
10x times -3x = -30x
40x - 30 x²
Can anyone help me understand this question
We need to find an equation that's in the form of: y = kx
k = constant of proportionality
Since it has to equal 9, this will be the value of k (y = 9x).
The correct answer is B.
Best of Luck!
find the value of h
Answer: The value of h is -1.
Step-by-step explanation:
The function F(x) = ║x║ has been shifted 1 unit to the right. H in this case represents if the function has been shifted to the right or to the left. If the function is being shifted to the right then H is negative and if the function is shifted to the left, x is positive. In this case the value of h is -1.
10t+50=100
Use the subtraction property of equality first.
This will help so much, thank you!
The third angle of an isosceles triangle is 16 o less than the sum of two equal angles. Find
three angles of the triangle.
Answer: 49°, 49°, 82°
Step-by-step explanation:
Let x represent the base angles
then 2x - 16 is the vertex angle.
Triangle Sum Theorem states that the sum of the angles is 180°
(x) + (x) + (2x - 16) = 180
4x - 16 = 180
4x = 196
x = 49
Base angles: x = 49
Vertex angle: 2(49) - 16 = 82
An is climbing down a ladder. Each time he descends four rungs on the ladder, he stops to see how much farther he has to go. Which word in the problem indicates that a negative integer should be used?
Answer:
Descends
Step-by-step explanation:
The word descend is what indicates that a negative integer should be used.
When we talk about height we should be regarding it in increments which makes its integers positive, that is something that increases. But the question says descends, descends means a reduction in height. which is a way of describing height in an opposite or negative direction.
decendsStep-by-step explanation:
Rewrite the division problem using improper fractions. 3 and three-fourths divided by negative five-eighths Negative StartFraction 5 over 8 EndFraction divided by StartFraction 15 over 4 EndFraction StartFraction 15 over 4 EndFraction divided by (negative StartFraction 5 over 8 EndFraction) StartFraction 15 over 4 EndFraction divided by StartFraction 5 over 8 EndFraction Negative StartFraction 15 over 4 EndFraction divided by (negative StartFraction 5 over 8 EndFraction
Answer:
the answer is 15/4 divided by (-5/8)
Step-by-step explanation:
just did the assignment hope this helps. <3
The division problem using improper fractions can be written as (15 / 4) ÷ (- 5 / 8).
What is division?The division is the basic arithmetic operation, in which you are separating the number into some parts. In division, we distribute the total numbers.
Given:
3 and three-fourths divided by negative five-eighths Negative Start Fraction 5 over 8 End Fraction divided by Start Fraction 15 over 4 End Fraction,
The above statement can be written as
3 3/4 ÷ (- 5 / 8)
Solve the mixed fraction = 3 3/4 = 4 × 3 + 3 /4
3 3/4 = 15 / 4
Therefore, the division problem using improper fractions can be written as (15 / 4) ÷ (- 5 / 8).
To know more about division:
https://brainly.com/question/27566440
#SPJ6
If a=3, b= -5
then who has
2b + a
Answer:
-7
Step-by-step explanation:
2b+a
2(-5)+3
-10+3
-7
Answer:-7
Step-by-step explanation:
2b+a
2×-5=-10
-10+3=-7
Can someone help please
Answer:
13.2
Step-by-step explanation:
11/5=x/6
66/5=×
13.2
Find the difference of 18.6 and 5.24.*
Answer:
13.36
Step-by-step explanation:
18.60 - 5.24
=>13.36
There are 72 boys and 28 girls. What percent are girls? I'm not sure if it is 28% or 18%?
Answer:
28%
Step-by-step explanation:
do 28/28+72=28/100
then multiply 28/100 by 100 which equals 28%