Answer:
1: 75
Step-by-step explanation:
20cm : 15m
Convert meters to cm
1 meter = 100 cm
15m = 15 x 100 = 1500 cm
20cm:1500cm
Divide both sides of the ratio by 20
=> 1 : 1500/20 = 1: 75
The ratio of 20cm to 15m in the form 1:n is 1:75.
What is a ratio?A ratio is a mathematical comparison of two or more quantities expressed in terms of the number of times one quantity contains another quantity.
It is used to express the relationship between two or more numbers or variables and is usually written as a fraction or with a colon between the two numbers.
We have,
First, we need to convert both measurements to the same unit.
Let's convert 20cm to meters:
20 cm = 20/100 m = 0.2 m
Now we can express the ratio of 20cm to 15m as:
0.2m : 15m
To simplify this ratio, we can divide both sides by the greatest common factor of the two numbers, which is 0.1m:
0.2m/0.1m : 15m/0.1m
2 : 150
Finally, we can simplify the ratio by dividing both sides by 2:
1 : 75
Therefore,
The ratio of 20cm to 15m in the form 1:n is 1:75.
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Find the value of x so that the function has the given value.
m(x)=4x+15 ; m(x)=7
this is the question
Using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ a=\sqrt[]{c^2-b^2} \\ a=\sqrt[]{25^2-17^2} \\ a=\sqrt[]{336} \\ a=4\sqrt[]{21}\approx18.3 \end{gathered}[/tex]When Elizabeth left her phone in her house this morning
Cole is investing the relationship between the number of hours he tutors and the amount he is paid in dollars.He made the graph shown to model the relationshipChoose the incorrect statement based on the data shown in Cole’s graph.A) If Cole tutors 5 hours,he will be paid $40B) If Cole tutors 3 hours he will be paid $24C) If Cole tutors 7 hours he will be paid $64D) If Cole tutors 4 hours he will be paid $32
Verify each statement
A) If Cole tutors 5 hours,he will be paid $40------>
B) If Cole tutors 3 hours he will be paid $24
C) If Cole tutors 7 hours he will be paid $64
D) If Cole tutors 4 hours he will be paid $32
If α and β are the roots of the equation ax2+bx+c=0,αβ=4ax2+bx+c=0,αβ=4 and a,b,,c are in A. P then α+β=
Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:
[tex]\alpha + \beta = -2.5[/tex]
What are the sum and the product of the roots of a quadratic equation?A quadratic equation is defined as follows:
[tex]y = ax^2 + bx + c, a \neq 0[/tex]
The roots of the equation are given as follows:
[tex]\alpha, \beta[/tex]
The sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a}[/tex]
The product of the roots is given as follows:
[tex]\alpha\beta = \frac{c}{a}[/tex]
In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:
c/a = 4
c = 4a.
The coefficients are in an arithmetic progression, hence:
b = a + d. (d is the common difference of the sequence).c = a + 2d.We have that c = 4a, hence:
4a = a + 2d
2d = 3a
d = 1.5a.
Hence coefficient b is calculated as follows:
b = a + d = a + 1.5a = 2.5a.
Then the sum of the roots is given as follows:
[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]
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write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -5
Remember the slope-intercept of a line is
[tex]y=mx+b[/tex]where:
• m ,is the slope of the line
,• b, is the y-intercept of the line
Now, let's substitute the data we're given. Thereby, the equation would be
[tex]y=\frac{4}{3}x-5[/tex]Help me with this please
Answer: say can't help
Step-by-step explanation:
Elena is making a grape drink. the recipe calls for 5 parts strawberry juice to 3 parts water. elena would like to make 80 fluid ounces of the grape drink. how many fluid ounces of grape juice concentrate and water does elena need?
Answer:
50:30
Step-by-step explanation:
1.Tanisha solved the equation below by graphing a system of equations.log: (5x) = log5 (2x + 8)What are the two equations in the system of equations that could be used to approximate her solution?(Do your best to type out the two equations for the system.)Yi =Y2 =2. What is the approximate solution (x -value) for her system of equations? And where on the graph can tanisha find her solution to the system?
Part 1.
Since we have the equation
[tex]\log _3(5x)=\log _5(2x+8)[/tex]the equations which can be used to approximate the solutions are:
[tex]\begin{gathered} y_1=\log _3(5x) \\ y_2=\log _5(2x+8) \end{gathered}[/tex]Part 2.
Let's make the graph of the 2 equations. The graph is
The approximate solution is given by the intersection point of the 2 graphs, which is the point ( 0.957 , 1.425). Then x-value corresponding to the solution is x= 0.957.
The size of a monitor is determined by the length of its diagonal. You want to buy a 19 inch monitor with a height of 11inches. What is the width of this monitor? Express your answer to the nearest tenth.XSubmINTL1217K
In this problem the diagonal of the Tv is 19 and the hight is 11 so we can use the pythagorical theorem to find the width (w) so:
[tex]19^2=11^2+w^2[/tex]and we solve for w so
[tex]\begin{gathered} w^2=19^2-11^2 \\ w=\sqrt[]{361-121} \\ w=\sqrt[]{240} \\ w=15.5 \end{gathered}[/tex]
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car. What is the angle between the beam and the
Road?
The most appropriate choice for trigonometry will be given by -
Angle between beam and road is 0.33°
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\[/tex]
Trigonometry is a very important tool in mathematics.
Here,
The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.
According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle
Let the angle be [tex]\theta[/tex]. Now trigonometry is applied here
[tex]tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}[/tex]
Angle between beam and road is 0.33°
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4. Write the sentence as an inequality. Graph the inequality. A number d is more than 0
and less than 10.
The required inequality is 0 < d < 10 and the graph given below.
What is inequality?
Inequality, When two integers or algebraic expressions are stated to be greater than, greater than or equal to, less than, or less than or equal to each other in order.
Given two conditions,
The variable d is greater than 0 and the second condition is
The variable d is less than 10.
From the first condition we get 0 < d ..................(1)
From the second condition we get d < 10 ...........(2)
Combining both the inequalities (1) and (2), we get
0 < d < 10
Therefore, the required inequality is 0 < d < 10.
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Simplify: 15.4 + 3.02
Answer:
18.42
Explanation:
15+3=18
0.4+0.02=0.42
18+0.42=18.42
The area of Eh Kri's rectangular backyard, in square feet, can be found using the expression 2(4x + 5y). Use the distributive property to write an equivalent expression for the area of Eh Kri's backyard.
The area of a rectangular backyard = 2(4x - 5y)
The algebraic expression has a equivalent expression as = 2 x 4x + 2 x 5y
= 8x + 10y
The baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base? Round your answer to the nearest tenth.
160 feet
113.1 feet
80 feet
12,800 feet
If the baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base is: B.113.1 feet.
Determining the distanceGiven data
Sides measure in feet = 80 feet.
Since the diagonal tend to forms the hypotenuse of a right triangle with both sides of 80 feet
Hence,
Using the Pythagoreans theorem to determine the distance
(80)² + (80)² = x²
6400 + 6400 = x²
x² = 12,800
x = √ 12,800
x = 113.1 feet
Therefore the correct option is B.
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For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).If it does, find the constant of variation and write it in simplest form.-Click on Picture for the questions! More understandable-
(a) 2y=8x
[tex]\begin{gathered} 2y=8x \\ y=\frac{8x}{2} \\ y=4x\Rightarrow y=kx\Rightarrow y\propto x\text{ \lbrack}direct\text{ }variation] \\ k=4 \end{gathered}[/tex](b) 7x=-2y-7 [ not direct variation ]
[tex]\begin{gathered} 7x=-2y-7 \\ 7x+7=-2y \\ 7(x+1)=-2y \\ (x+1)=\frac{-2y}{7} \\ x=\frac{-2y}{7}-1 \end{gathered}[/tex]We couldn't express in the form x=ky , hence variation is not direct. OR we can say we couldn't express in the form y=kx ....hence variation is not direct
CAN Someone pleasde help me !!!!!
Answer: It will take 3.5-4 months
Step-by-step explanation:
A student simplifies 5(x+3) - 3x by distributing and combining all the terms.
1. 5(x+3)-3x This is what is given
2. 5x +15-3x After applying the Distributive Property
3. 2x+15
Adding Like Terms
4. 17x
Combining non like terms.
Which step contains the error?
O Step 4
O Step 1
O Step 2
Step 3
Answer:
Step 4
Step-by-step explanation:
You cannot combine non-like terms like 2x and 15
They have to be left as is
Steps would be:
2. 5x +15-3x → Distributive property
3. 2x+15 → Combining like terms
And that's it. You cannot go any further
a rope passing through a capstan on a dock is attached to a boat offshore. the rope is pulled in at a constant rate of 6 ft/s and the capstan is 5 ft vertically above the water. how fast is the boat traveling when it is 12 ft from the dock?
Answer:The boat is traveling at a rate of 3 ft/s.
Step-by-step explanation:
What is the average rate of change of the function x increases from -3 to 5
The average rate of change when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:
b - a = 5 - (-3) = 5 + 3 = 8.
The change in the output is given as follows:
f(b) - f(a).
(the problem is incomplete hence the answer is given in general terms).
Then the average rate of change of the function when x increases from -3 to 5 is given as follows:
r = (f(5) - f(-3))/8.
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Stanley runs, swims, and bikes every day. During these workouts, he runs at 9 mph, bikes at 16 mph, and swims at 2.5 mph. Yesterday, he ran for half an hour longer than he swam, and his biking time was twice his running time. How long did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles?
(a
If Stanley swam for t hours yesterday, what was his running time?
Answer:He biked for 3 hours (48 miles)
He ran for 1.5 hours (13.5 miles)
He swam for 1 hour (2.5 miles)
He covered 62 miles in 5.5 hours of activity
Step-by-step explanation:
Answer:
1.5h
Step-by-step explanation:
Please help me out with this!
Answer:
10
Step-by-step explanation:
I am not absolutely sure but i think that is correct
what is the advantage of reducing process variation, thereby causing process control limits to be at a greater number of standard deviations from the mean? reducing the process standard deviation causes a - select your answer - in the number of defects.
A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
What is meant by standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists more dispersed.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.
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Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance.
If they both save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
Enter your answer in the box
Answer:
3 months
Step-by-step explanation:
120 + 40m = 180 + 20m
Collect like terms
40m - 20m = 180 - 120
20m = 60
Divide
m = 60/20
m = 3
It will take them 3 months before Jaclyn and Pedro have saved the same amount of money.
Solve this system of linear equations. Separate
the x- and y-values with a comma.
8x + 8y = -56
4x + 10y = -46
The value of x is -4 and the value of y is -3.
What is linear equations?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
The linear equation's graph is a straight line.
The given system of linear equations is,
8x + 8y = -56 ...(1)
4x + 10y = -46 ...(2)
Divide equation (1) by 2, we get
4x + 4y = -28 ...(3)
Multiply equation (3) by -1
-4x - 4y = 28 ...(4)
Adding equations (2) and (4),
4x + 10y = -46
+ -4x - 4y = 28
____________________
6y = -18
y = -3
Substitute y = -3 in equation (1) and simplify, we get
x = -4.
Therefore, the value of x is -4 and the value of y is -3.
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iodinated (i 125) albumin injection contains 0.5 millicuries (18.5 mbq) of radioactivity per milliliter. how many milliliters of the solution should be administered exactly 30 days after the original assay to provide an activity of 60 microcuries (2.22 mbq) if the half life of i 125 is 60 days? round answer to the nearest hundredth (i.e. 0.xx). do not include units in your answer.
The decay constant of a radioactive nuclide exists its probability of decay per unit time.
The half life of i 125 is 60 days exists 0.169 ml.
What is meant by Decay constant?The decay constant of a radioactive nuclide exists its probability of decay per unit time. The number of parent nuclides P therefore decreases with time t as dP/P dt = −λ.
The ratio of the number of radioactive atoms in a population to the rate at which they are vanishing due to radioactive decay.
The rate of decay is determined by the decay constant. The symbol for the decay constant is "lambda," or. The many diverse decay rates that have been seen may be caused by large variations in this constant probability among various types of nuclei.
Decay constant: [tex]$& \lambda=\frac{0.693}{t_{1 / 2}}[/tex]
Decay constant expressed in any unit of time
Such as reciprocal seconds, minutes, hours etc.
[tex]$\mathbf{N}=\mathrm{N}_o \mathrm{e}^{-\lambda t} \quad \lambda=\frac{0.693}{\mathrm{t}_{1 / 2}}$[/tex]
Half Life: [tex]$\quad t_{1 / 2}=\frac{0.693}{\lambda}$[/tex]
The half life of i 125 is 60 days exists 0.169 ml.
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Ben walked for 8 1/2 minutes and
covered
3/4 of a mile.
The unit rate of Ben is 8.5 minutes.
What is Unit Rate?An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.A ratio that compares two amounts of DIFFERENT types of UNITS is called a rate. When a rate is expressed as a fraction, the denominator is 1 unit. Divide the numerator and denominator of the rate by the denominator to represent a rate as a unit rate.Unit rates may seem difficult to understand, but it explains a specific unit of measurement based on a rate of time (usually).
For this problem, we are looking for how many miles Ben walked per minute — so the goal is miles per minute
We know Ben walked a total of 3/4 of a mile (or .75 miles) and it took him 8 1/2 minutes to do it (or 8.5 minutes)Since we want miles per minute we need to divide the miles by the minutes.So, calculate:
.75 miles. = 0.088 miles per minute8.5 minutesTherefore, the unit rate for Ben is 8.5 minutes.
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Complete question:
Ben walked 3/4 of a mile in 8 1/2 minutes. Find the Unit Rate.
Malik's car used \frac{1}{48}
48
1
of a gallon to travel \frac{1}{4}
4
1
of a mile. How many miles can the car go on one gallon of gas?
On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, mixed numbers, or whole numbers.
The number of miles that the car can go on one gallon of gas is:
12 miles.
How to calculate the rate of miles per gallon?The rate of miles per gallon is given by the number of miles divided by the number of gallons, according to the equation presented as follows:
miles per gallon = miles / gallon.
In the context of this problem, the measures are found as follows:
Miles = 1/4 = distance traveled.Gallon = 1/48 = amount of fuel used to travel the given distance.Hence the rate is given as follows:
miles per gallon = (1/4) / (1/48)
For a division of fractions, we multiply the inverse of the denominator by the numerator, hence:
miles per gallon = 48 x 1/4 = 48/4 = 12 miles.
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find the missing fraction 1/2+ blank=7/8
To solve this problem we change the structure from
1/2 + ? = 7/8
to
7/8 - 1/2 = ?
Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.
1/2 = 4/8
then subtracts the numerator
7/8 - 4/8 = 3/8
there is your answer... 3/8
PLEASE HELP ASAP (QUICK MATH QUESTION)
Verify the identity: sin(x+y)-sin(x-y)= 2cosxsiny
Please show all work! Thank you so much!!!!!! <3
The given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
The identity is
sin(x+ y) - sin (x- y) = 2 cos x sin y
Here we have to use the trigonometric function
Consider the right hand side of the equation
We know
sin (x+ y) = sin x cos y + cos x sin y
sin (x-y) = sin x cos y - cos x sin y
Then
sin(x+ y) - sin (x- y) = sin x cos y + cos x sin y - (sin x cos y - cos x sin y)
= sin x cos y + cos x sin y - sin x cos y + cos x sin y
Eliminate the terms
= cos x sin y + cos x sin y
= 2 cos x sin y
Hence, the given identity sin(x+ y) - sin (x- y) = 2 cos x sin y has been verified
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