Answer:
D
Step-by-step explanation:
[tex]P(1+r\%)^t[/tex]
[tex]700 \times (1+0.8\%)^5[/tex]
[tex]700 \times (1+0.8/100)^5[/tex]
[tex]700 \times (1+0.008)^5[/tex]
[tex]700 \times (1.008)^5[/tex]
The value expresses the population five years later is (700)(1.008)^5.
We have given that in 1997 the population of a small town was 700.
The annual rate of increase is about 0.8%.
We have to find the population for 5 years
What is the formula for future value?
[tex]F=P(1+r)^t\\\\[/tex]
Here p=700
r=0.8/100=0.008
t=5
Use the above value in the formula so we get,
[tex]F=700(1+0.008)^5[/tex]
[tex]F=700(1.008)^5[/tex]
Therefore option D is correct.
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please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
C. Multiply 3 by 18
Step-by-step explanation:
Susan reads:
1 page in 3 mins
So,
1 page = 3 mins
If we want the time for 18 pages, we would multiply both sides by 18
So,
18 pages = 3×18 mins
18 pages = 54 mins
Answer:
C
Step-by-step explanation:
1 page every 3 minutes
18 pages will take 3 × 18 = 54 minutes to read.
The number of cards in a deck of playing cards is numbered in the tens.
O A. True
B. False
The amount of money, in dollars, Sarah has in her savings account is modeled as a function of time in months. This function is represented by the graph below. What is the average rate of change for the amount of money, in dollars per month, from month 0 to month 12? A $25 per month B $50 per month C $300 per month D $500 per month
Answer:
The average rate of change for the amount of money is A) $25 per month
Step-by-step explanation:
From the graph we can see Sarah earn $50 every two months, 50/2 = 25/1 so we can determine Sarah's average rate of change from month 0 to month 12 is $25 dollars per month. Hope this helped, let me know if you have any questions! :)
Can u please help me , I’m stuck on this .
Answer:
Use this website it gives you the answer and show the work
math
way
dot
com
Step-by-step explanation:
Answer:
24a: n = 5/14
24b: p = 18
25a: (x + 11) (x - 12)
25b: x (x + 2) (x - 2)
Step-by-step explanation:
I hope this helps
5) A recipe for cookies calls for 2 cups of milk for 3 cups of Flour. You decide that you want to make more cookies than the recipe calls for. You have enough to use 9 cups of flour. How many cups of milk is needed if you use 9 cups of flour?
Answer: If you want to make more cookies then what is called for in this situation then you would need 6 cups of milk.
Step-by-step explanation: You have 2 cups of milk and 3 cups of flour of course. In order to make a complete batch you need 2 cups of milk and 3 cups of flour. In order to make a second batch you need the same things as you did for the first batch. Therefore two batches of cookies requires 4 cups of milk and 6 cups of flour. In this situation you want to make 3 batches of cookies. The required items are 6 cups of milk and 9 cups of flour.
4.
Here is the proof of (sin x - cos x)2 = sec2 x - tan2 x - 2sin x cos x.
What is the missing line
Answer:
See Explanation Below
Step-by-step explanation:
Given
[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.[/tex]
Required
Prove
To start with; we open the bracket on the left hand side
[tex](sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)[/tex]
[tex](sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)[/tex]
[tex](sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x[/tex]
[tex](sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x[/tex]
Reorder
[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]
From trigonometry;
[tex]sin^2x + cos^2x = 1[/tex]
So;
[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]
becomes
[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]
Also from trigonometry;
[tex]sec^2x - tan^2x = 1[/tex]
So,
[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]
becomes
[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x[/tex]
Proved
8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How
much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?
The amount of pure gold that should be added is
grams.
(Type an integer or a decimal.)
Answer: 65 grams
Step-by-step explanation:
If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, you should first calculate the amount of gold that makes up this percentage.
That is, 85% of 130 grams.
85/100 × 130 = 110.5
Then, let X be what will be added to the above value to make 90%. So,
(110.5 + X) / ( 130 + X ) × 100 = 90
Divide both sides by 100
(110.5 + X) / ( 130 + X ) = 90/100
(110.5 + X) / ( 130 + X ) = 0.9
Cross multiply and open the bracket
110.5 + X = 117 + 0.9X
Collect the like terms
X - 0.9X = 117 - 110.5
0.1X = 6.5
Divide both sides by 0.1
X = 6.5/0.1
X = 65 grams
Therefore, the amount of pure gold that should be added is 65 grams
The weight of a body above sea level varies inversely with the square of the distance from the center of Earth. If a woman weighs 123 pounds when she is at sea level, 3960 miles from the center of Earth, how much will she weigh when she is at the top of a mountain, 3.2 miles above sea level?
Answer:
Her weight is approximately 122.8lb
Step-by-step explanation:
Given
Inverse proportion;
Weight = 123lb when distance = 3960 miles from center of earth
Required
Calculate the weight when distance is 3.2 miles above sea level
Let weight be represented by W and distance by D
From the question, we understand that;
Weight is inversely proportional to square of distance;
Mathematically; this is
[tex]W \alpha \ \frac{1}{D^2}[/tex]
Convert proportion to equation
[tex]W = \frac{k}{D^2}[/tex]
Where k is the constant of proportionality
When W = 123; D = 3960.
This implies that
[tex]123 = \frac{k}{3960^2}[/tex]
Make k the subject of formula
[tex]k = 123 * 3960^2[/tex]
[tex]k = 1928836800[/tex]
Calculating her weight when she's at the top of mountain, 3.2 miles above sea level
First, her distance from center of earth has to be calculated
Distance = Previous distance + 3.2
Distance = 3960 + 3.2
Distance = 3963.2
Now, her weight can be calculated using [tex]W = \frac{k}{D^2}[/tex]
Substitute for k and D
[tex]W = \frac{1928836800}{3963.2^2}[/tex]
[tex]W = \frac{1928836800}{15706954.24}[/tex]
[tex]W = 122.801452817[/tex]
[tex]W = 122.8\ (Approximated)[/tex]
Translate the following into an expression: m% of n
Answer:
n(m%)
Step-by-step explanation:
By Translate the following into an expression: m% of n. Thus, the expression is 0.01mn.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
We have to Translate the following into an expression:
m% of n
m x 1/100 x n = 0.01mn
Thus, the expression is 0.01mn.
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DF is the angle bisector of ADE. Determine the value of x. ANSWERS: A) – 8 B) 8 C) – 4 D) 4
Answer:
D) [tex]x=4 \textdegree[/tex]
Step-by-step explanation:
Before answering this question, we must first understand what an angle bisector is. An angle bisector is any ray, line, or line segment that splits an angle into two congruent, smaller angles.
That being said, since [tex]DF[/tex] bisects [tex]\angle ADE[/tex], we can say that [tex]\angle ADF \cong \angle FDE[/tex]. If you'll remember, congruent angles have equal measures, so [tex]m\angle ADF = m\angle FDE[/tex].
Substituting the given values of the angle measures into the equation and solving, we get:
[tex]9x-1=8x+3[/tex]
[tex]9x=8x+4[/tex] (Add 1 to both sides)
[tex]\bf x = 4 \textdegree[/tex] (Subtract 8x from both sides)
Hope this helps!
Answer:
[tex]x = 4[/tex]
Answer D is correct.
Step-by-step explanation:
( ADF angle = FDE angle)
[Because DF is the angle bisector]
[tex]9x - 1 = 8x + 3[/tex]
[tex]9x - 8x = 1 + 3 \\ x = 4[/tex]
hope this helps you.
can someone help me with this pleaseee
Answer:
The real part is -1
Step-by-step explanation:
The real axis is the horizontal axis
The value on the horizontal axis is -1
Alex drives at an average speed that is 1/4 of the average speed that Roy's train travels. Alex takes 20 minutes to travel 12 km in her car. Roy travels for 2 hours and 20 minutes on his train. How far does Roy travel to 2 dp?
Answer:
336.00 km distance of train
Step-by-step explanation:
Alex = 20mins =12km We distribute to 1hr to find 60mins = 36km p/h.
Roy = 2hrs 20 mins and is 4x the speed of the car.
So 36km x 4 p/h = 144km p/h
2hrs and 20 = 144 x 2.3333 = 335.9952 = 336km
Answer:
336 km
Step-by-step explanation:
"Alex takes 20 minutes to travel 12 km in her car."
Alex's speed = (12 km)/(20 min) = 0.6 km/min
"Alex drives at an average speed that is 1/4 of the average speed that Roy's train travels."
Therefore, Roy's speed is 4 times Alex's speed.
Roy's speed = 4 * 0.6 km/min = 2.4 km/min
Roy travels for 2 hours and 20 minutes = 2 * 60 min + 20 min = 140 min
speed = distance/time
distance = speed * time = 2.4 km/min * 140 min = 336 km
The radius of a circle is 9.7 m. Find the circumference to the nearest tenth?(help its urgent)
Answer:
Step-by-step explanation:
Circumference C=2πr r=radius [tex]\pi =3.14[/tex]
C=2(3.14)9.7
C=60.9
7. The function ƒ(x) = sqrt x is reflected across the x-axis and vertically stretched by a factor of 2. Select the correct graph for the resulting function.
Answer:
the answer is NOT b, i got that wrong on the quiz
Step-by-step explanation:
Answer:
The correct answer is C.
Step-by-step explanation:
(1,-2) (4,-4) (9,-6)
i need help pleaseeee ASAP!!!!!!
Answer:
180 degrees
Step-by-step explanation:
I need help please :)))
Answer:
[tex]\mathrm {7.1 \: inches}[/tex]
Step-by-step explanation:
Circumference of a circle is [tex]\pi d[/tex]
The diameter is [tex]2.25[/tex] inches as shown in the readings of the scale.
[tex]2.25\pi[/tex]
[tex]\approx 7.06858347058[/tex]
IMAGE 1: Find the value of the indicated trigonometric ratio cos α
IMAGE 2: Find the value of the indicated trigonometric ratio sin β
IMAGE 3: Find the value of the indicated trigonometric ratio cot γ
IMAGE 4: Find the value of the indicated trigonometric ratio tan α (WORTH 30 POINTS!) Thanks!
Answer:
28.07° ; 70.53° ; 53.13° ; 36.87°
Step-by-step explanation:
Using PYTHAGORAS RULE :
IMAGE 1:
value of cos α equals :
cos α = Adjacent / Hypotenus
cos α = 15 / 17
cos α = 0.88235
α = cos^-1 (0.88235)
α = 28.07°
IMAGE 2:
sin β = Opposite / Hypotenus
sin β = 14√2 / 21
sin β = 0.9428
β = sin^-1(0.9428)
β = 70.53°
IMAGE 3:
From trigonometry :
cot = 1 / tan
Tan = Opposite / Adjacent
Therefore, Cot = Adjacent / Opposite
cot γ = 3/4
cot γ = 0.75
γ = cot^-1 (0.75)
γ = 53.13°
IMAGE 4:
tan α = Opposite / Adjacent
tan α = 15 / 20
tan α = 0.75
α = tan^-1 (0.75)
α = 36.87°
Answer:
15
Step-by-step explanation:
At a profit of 8% a shopkeeper sold a calculator for Rs 1,382.40. If he wants to increase his profit by 2%, at what price should he sell the calculator?
Answer:
Step-by-step explanation:
Bud's cheeseburger and fries contained 1310 milligrams and 350 milligrams of sodium, respectively. Together they contained 66.4% of the recommended daily intake of sodium for
diet. What is the daily recommended intake of sodium for a 2,000 calorie diet?
Answer:
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Step-by-step explanation:
In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.
[tex]\text{total sodium} = 1310 + 350 = 1660 \text{ mg}[/tex]
We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:
[tex]\frac{1660}{x} \frac{mg}{mg} = \frac{66.4\%}{100\%}[/tex]
[tex]66.4*x = 1660*100\\x = \frac{166000}{66.4} = 2500 \text{ mg}[/tex]
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Answer:
2,500 mg
1,310 + 350 = 1,660
1,660 is 66.4% of 2,500
what are the steps and answer
Answer:
Trust me it’s I disagree
Step-by-step explanation:
So you have to use the Pythagorean Theorum which is [tex]a^2+b^2=c^2[/tex] and in this case a is 70 and b is 40.
So if we plug those numbers in we have to square a and b and add them which is 6,500 and to find c we have to find the square root of 6500 which is about 80 so lines PR and QR are different
Answer:
It's I disagree
Step-by-step explanation:
what’s the solution of y=x-4 and y=1/3x
Answer:
(6, 2)
Step-by-step explanation:
Step 1: Use substitution
x - 4 = 1/3x
Step 2: Isolate x
2/3x = 4
x = 6
Step 3: Plug back into original equation(s)
y = 6 - 4
y = 2
Answer:
(6,2)
Step-by-step explanation:
Let's use the substitution method.
x-4=1/3x
3x-12=x
3x=x+12
2x=12
x=6
y=6-4
y=2
Can someone help me please!!!
Answer:
65°
Step-by-step explanation:
180°-50°:130°
130°÷2:65°
130° divide by 2 because the shape was isosceles triangle
A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Traveled (miles) Gasoline Used (gallons) 22 1 44 2 x 3 88 4 Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown? StartFraction 1 over 22 EndFraction = StartFraction x over 2 EndFraction StartFraction 22 over 1 EndFraction = StartFraction x over 2 EndFraction StartFraction 1 over 22 EndFraction = StartFraction x over 3 EndFraction StartFraction 22 over 1 EndFraction = StartFraction x over 3 EndFraction
Answer: The answer is the second one/b.
Answer:
D. 22/1=x/3
Step-by-step explanation:
Well what you multiply by the top you must do the bottom and opposite way also goes, sometimes so to get three as shown in (x/3) you must use the 1 from (22/1) times something to equal 3. In this it would be 1*3=3 so I multiplied three to the bottom and what I do the the bottom I haft to do to the top so 22*3=x and x is equal to 66 witch makes (D. 22/1=x/3) the correct option. If you want or need to check a good way to is to use a calculator to multiply 22*3 just as a small check up.
Which represents the solution set of 5(x+5) < 85?
X<12
x>12
x<16
x>16
Answer:
x<12
Step-by-step explanation:
Divide both sides by 5
5(x+5) < 85
5 5
then simply
Answer:
x < 12
Step-by-step explanation:
[tex]5(x+5)<85\\\\5 * x = 5x\\\\5 * 5 = 25\\\\5x+25<85\\\\5x+25-25<85-25\\\\5x<60\\\\\frac{5x}{5}<\frac{60}{5}\\ \boxed{x<12}[/tex]
Help please I don’t understand the concept
Answer:
B
Step-by-step explanation:
The question is asking for what y would be when x is 2.
So, look on the graph where x = 2.
When x = 2, y = 6.
This means after 2 hours, the cost is $6
For the equations given below, which statement is true?
-21 = 14
6.1 = -42
A. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -3.
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by 3.
C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first
equation by -4.
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value.
Answer:
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value
Step-by-step explanation:
-21=14 Equ(1)
6.1=-42 Equ(2)
Multiplying the first equation by -3 will give
-63= -42
Which is not equivalent to the second equation
Multiplying the first equation by 3, we have
-63=42
Not equivalent to the second equation
Multiplying both sides of the first equation by -4, we have
84=56
Not equivalent to the second equation
D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first
equation by any value
Shruthi has a total of ₹590 as currency notes in the denominations of ₹50, ₹20 and ₹10. The ratio of the number of ₹50 notes and ₹20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination she has?
Answer:
50 = 6 notes
20 = 10 notes
10 = 9 notes
Step-by-step explanation:
to check whether it is correct :
50×6 + 20×10 + 10×9 = 590 (total money of Shruti)
Answer:
What does this mean
Step-by-step explanation:
What is the measure of ∠E? Enter the correct value. Do not enter the degree symbol.
Answer:
To find < E we use tan
tan E = opposite / adjacent
DF is the opposite
EF is the adjacent
DF = 11
EF = 11
tan E = 11/11
tan E = 1
E = 45
Hope this helps
Answer:
45 degrees
Step-by-step explanation:
Since this triangle is isosceles, we know that the other angles, D and E, are both 45 degrees because of the sum of interior angles of a triangle always equaling 180 degrees.
The number of 90° angles formed by the intersections of and the two parallel lines and is
.
Answer:
4.
Step-by-step explanation:
What is the value of x? answers: A) 90° B) 65° C) 50° D) 80°
Answer:
Please mark be brainliest and I hoped this helped!
x = 80°
Step-by-step explanation:
These are both isosceles triangles, so the top 2 angles are both 65°. The last angle of that triangle is 180° - (65° + 65°) which is 50°. Then, the opposite of that angle is in the next traingle. It is also 50°. So the 2 base angles are both 50°, so x is 180° - (50° + 50°) which is 80°.
The measure of angle 'x' is 65 degrees and this can be determined by using the properties of the isosceles triangle.
Given :
Angles --- [tex]65^\circ[/tex] and x
The following steps can be used in order to determine the measure of angle 'x':
Step 1 - Both the triangles are isosceles triangles because in both the triangles two sides are similar.
Step 2 - Let the upper triangle be ABC and the lower triangle be DBE.
Step 3 - The angle B of the triangles can be calculated as:
[tex]\angle A + \angle B + \angle C = 180[/tex]
[tex]65+65+\angle B = 180[/tex]
[tex]\angle B = 50^\circ[/tex]
Step 4 - Now, angle 'x' can be calculated as:
[tex]\begin{aligned}\\\angle D + \angle B + \angle E &= 180\\x+x + 50 &= 180\\2x &= 130\\x &= 65^\circ\\\end{aligned}[/tex]
The measure of angle 'x' is 65 degrees. Therefore, the correct option is B).
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