Daniel's unit rate in minutes per mile of running is 12
What is unit rate?The amount per unit of an item is represented by the unit rate.
To determine the unit rate of an item, we divide
How to find the rate in minute per mileIf Nicholas Daniel ran 5 miles in 1 hour
5 miles = 1 hour = 60 minutes
1 miles = ? minute
cross multiplying
60 * 1 = 5 * ?
? = 60 / 5
? = 12 minutes per mile
Daniel will take 12 minutes to run 1 mile
Learn about unit rate at:
https://brainly.com/question/4895463
#SPJ1
What is sin(60) in degrees?
Answer:
(sqrt3)/2
Step-by-step explanation:
Sin(x)=opposite/hypotenuse
30, 60, 90 right triangle.
ratio of sides are 1, sqrt3, and 2.
Locate the 60 degree angle on the triangle
The opposite side is sqrt3
The hypotenuse is 2
so its (sqrt3)/2
Answer:
√3/2 or 0.866
Step-by-step explanation:
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle. Explanation is given.
What are angle bisectors?Lines that cross the angle under investigation are known as angle bisectors. To "bisect" is to split into two sections of equal size. Therefore, the bisected halves divide the considered angle in half.
According to the angle bisector theorem;
An angle bisector divides the opposing side of a triangle into two portions that are proportionate to the other two sides, according to the angle bisector theorem.
a point is equally far from both sides of an angle if it is on the angle's bisector.
According to the inverse of the angle bisector theorem, a point is on the angle's bisector if it is both in the interior of the angle and equally far from its sides.
The explanation with diagram is given in the image.
Therefore, If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.
Learn more about angle bisector here;
https://brainly.com/question/12896755
#SPJ1
find X giving Brainly show work
Answer:
[tex]b = 6\sqrt{2}[/tex]
Step-by-step explanation:
Don't say giving brainiest for work, I will still help you.
Use the Pythagorean Theorem to solve:
[tex]a^2+b^2=c^2[/tex]
A and B refers to the legs, or the shorter sides. C refers to the hypotenuse, or the longest side.
Plug in what you know:
[tex](7)^2+b^2=(11)^2[/tex]
[tex]49 + b^2 = 121[/tex]
Subtract 49 on both sides.
[tex]49 - 49 + b^2 = 121-49[/tex]
[tex]b^2=72[/tex]
Find the square root of both sides.
[tex]\sqrt{b^2} = \sqrt{72}[/tex]
b = [tex]6\sqrt{2}[/tex]
need help now i need to finish this delta
Observing the provided figure and using the transformation rule of geometry, The required transformation to map figure H onto figure I is reflection along y=x axis.
What do you mean by transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
What is reflection in mathematics?In a mirror line, reflection is a type of transformation that reverses the shape so that each point is at the same distance from the mirror line as its reflected point.
Figure H
Mapped onto figure I
The required transformation:
reflection along y=x.
To learn more about transformations visit:
https://brainly.com/question/11709244
#SPJ1
a population of adult wildebeests in a certain region of africa have weights that are normally distributed with a standard deviation of 579 lbs. how large of a sample is needed to estimate the mean weight to within 135 lbs with a 99% confidence level?
Sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
What is confidence interval?
In statistics, the probability that a population parameter will fall between a set of values for a predetermined percentage of the time is referred to as the confidence interval. Analysts frequently employ confidence ranges that include 95% or 99% of anticipated observations.
Z(α/2) at 99% confidence level = 2.576
λ = 579
margin of error = ( Z(α/2) * λ ) / √n = 135
(2.576 * 579) / √n = 135
On simplifying, n ≈ 123
So, sample size 123 is needed to estimate the mean weight to within 135 lbs with a 99% confidence level
To Learn more about the confidence interval form the link:
https://brainly.com/question/15712887
#SPJ1
Graph the line that has a slope of -4/3 and includes the point ( -6,2)
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Slope intercept form:The slope-intercept form a line is given by
y = mx + c,where m is the slope of a line and c is the y-intercept.
Here we use the Slope intercept form to find the line of the equation by using the equation we will draw the graph of the line
Here we have
Slope of line = -4/3
The point of the line
As we know y = mx + c is the line Here m is the slope of the line
From the given data, m = -4/3
=> y = (-4/3)x + c
=> 3y = -4x + 3c
Given that the point on the line is (-6, 2)
=> 3(2) = -4(-6) + 3c
=> 6 = 24 + 3c
=> 3c = 18
=> c = 6
Therefore,
The equation of the line is 3y = -4x + 18 and the Graph can draw as given in the picture.
Learn more about the Slope intercept form at
https://brainly.com/question/29146348
#SPJ1
Hello this is the question
Answer:
A. 36/5
Step-by-step explanation:
cross multiply
6/5 = x/6
5x = 36
x = 36/5
Answer:
A) [tex]\frac{36}{5}[/tex]
Step-by-step explanation:
[tex]\frac{6}{5}[/tex] = [tex]\frac{x}{6}[/tex] Cross multiply and solve for x
36 = 5x Divide both sides by 5
[tex]\frac{36}5}[/tex] = [tex]\frac{5x}{5}[/tex]
[tex]\frac{36}{5}[/tex] = x
Help please i can’t do the math right I’m not getting any of those 4 options right
Answer:
B
Step-by-step explanation:
970 + 2436 = 3406
The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
[tex]\frac{7t}{7}[/tex] = [tex]\frac{21}{7}[/tex]
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
Pamela is 9 years younger than jiri. The sim of their ages is 49. What is jiri’s age ?
Answer: 40
Step-by-step explanation:
all you have to to is subtract
9 from 49 = 40
Answer:40
Step-by-step explanation:49-9=40
A right triangle is shown, where the horizontal leg has a measure of 48 centimeters (cm), and the hypotenuse has a measure of 73 cm.
Answer:
55
Step-by-step explanation:
Using the Pythagorean theorm:
a^2+b^2=c^2
48^2+b^2=73^2
b^2=73^2-48^2
b^2=3025
b=55
Find the inverse of f(x) = 2(x-2) ^2 +1
Find the inverse of y = ^3√x-3
Answer:
f^-1(x) = 2(x-2)^2 + 1
f^-1(x) = (x+3)^3
Step-by-step explanation:
The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.
3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.
The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.
Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.
To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace y with x in the original function to obtain x = ^3√y-3.
3. Solve for y in terms of x to obtain y = (x+3)^3.
The inverse function can then be written as f^-1(x) = (x+3)^3.
Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.
The side of a cube has a length of 4x³y6 cm. The volume of the cube can be found using
the formula V = S³. What is the volume of the cube in cubic centimeters?
PLEASE HELP
Answer:
find my dad
Step-by-step explanation:
on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
Learn more about number line
brainly.com/question/13425491
#SPJ4
Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness,
extrema, asymptotes, and end behavior.
f(x)=3•e^2x
A graph is a collection of points and the connections between some subset of those points that may or may not be empty in mathematical terms.
What are the values of the terminologies of the graph ?The given function is f (x ) = [tex]3e^{2x}[/tex]
1. Domain :
The function has no undefined points or domain constraints . Therefore the domain is -∞ < x < ∞ .2.Range :
The range of the exponential function is of the form f(x) > kSince k = 0, f(x) > 03.Continuity:
The graph is a single, continuous curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We can observe that the function is basically continuous.4.Behaviour that is either increasing or decreasing:
For any x in the domain, as x grows, f(x) shrinks. This indicates that the function behaves in a diminishing manner.5.Symmetry:
It is clear to see the graph of f(x) has no symmetry.6.Boundedness:
When we choose negative values, the graph of f(x) expands upward exponentially, showing that it is unbounded above.7.Extrema:
There are no extreme points for the function.8.Asymptotes:
This curve does not have any vertical asymptotes, despite the way it seems. Simply put, the curve's negative-x region is expanding so swiftly that it resembles an asymptote. For any x < 0, there is a value for f(x). However, a horizontal asymptote exists , y = 0.9.End behaviour :
As [tex]\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty[/tex] As,[tex]\:x\to \:-\infty \:,\:f\left(x\right)\to \:0[/tex]Refer image for graph.To learn more about Asymptotes , refer:
https://brainly.com/question/4138300
#SPJ1
Reduce to the standard form
1) -18/45
2) -3/-15
3)28/56
4)45/99
The fractions reduced to standard form are -2/5, 1/5, 1/2 and 5/11 for 1), 2), 3), and 4) respectively
How to reduce fractions to standard form?
To reduce a fraction to standard form, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). The GCD is the largest number that can be evenly divided into both the numerator and the denominator.
Given:
1) -18/45
The GCD of 18 and 45 is 9. Thus:
-18/45 = -2/5
2) -3/-15
The GCD of 3 and 15 is 3. Thus:
-3/-15 = 1/5
3) 28/56
The GCD of 28 and 56 is 28. Thus:
28/56 = 1/2
4) 45/99
The GCD of 45 and 99 is 9. Thus:
45/99 = 5/11
Learn more about reduction of fraction to standard form on:
https://brainly.com/question/11562149
#SPJ1
1)-6/15
2)1/5
3)1/2
4)5/11
1) -18/45
⇒-6/15
2)-3/-15
⇒-1/-5
⇒1/5
3)28/56
⇒4/8
⇒1/2
4)45/99
⇒15/33
⇒5/11
For more information regarding division of fractions
https://brainly.com/question/1622425
Write an equation that passes through the point (4,-3) and is perpendicular to the line 4x+y=3
Answer:
y = 1/4x - 4
Step-by-step explanation:
4x + y = 3
y = -4x + 3
Perpendicular slope = 1/4
y = 1/4x + b
-3 = 1/4(4) + b
-3 = 1 + b
b = -4
y = 1/4x - 4
What are the slope and Y intercepted of the relationship?
The slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
What is the slope-intercept form of the line?
The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y-intercept (0, b). In the formula, b represents the y value of the y-intercept point.
To find the slope of the equation, we need to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, we can first divide both sides of the equation by 5 to get:
2x + y - 3 = 0
Then, we can add 3 to both sides to get:
y = -2x + 3
Now comparing the equation with y = mx + c, we can say that
the slope is -2 and the y-intercept is 3.
Hence, the slope of the equation 10x+5y-15=0 is -2 and the y-intercept is 3.
To learn more about the slope-intercept form of the line, visit:
https://brainly.com/question/25722412
#SPJ1
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
The expressions in the table represent the number of canned goods collected by two homerooms during a charity food drive.
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
Write an expression that shows the total number of cans collected by both homerooms.
Part B
The students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom. Write an expression that represents how many more cans were collected.
The expression that shows the total number of cans collected by both homerooms is 14n - 4
The expression for more cans collected is 8n - 7 > 6n + 3
The total number of cans collectedFrom the question, we have the following parameters that can be used in our computation:
Homeroom Cans Collected
Mr. Juarez 8n−7
Ms. Wade 6n+3
The total number of cans collected is calculated as
Cans collected = Mr. Juarez + Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
Cans collected = 8n - 7 + 6n + 3
Evaluate the like terms
Cans collected = 14n - 4
How many more cans were collectedHere, we have
Mr. Juarez's homeroom collected more cans
This means that
Mr. Juarez > Ms. Wade
Substitute the known values in the above equation, so, we have the following representation
8n - 7 > 6n + 3
Hence, the expression is 8n - 7 > 6n + 3
Read more about expressions at
https://brainly.com/question/4344214
#SPJ1
Mikaela purchased a paddleboard originally priced at $699. If all merchandise was on sale for 40% off and the state tax rate is 7. 25%, what is the total amount that mikaela spent on the paddleboard?.
The total amount that Mikaela spent on the paddleboard will be $449.80.
What is the percentage?The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths.
As per the given,
Original price = $699
The selling price = $699 - 40% of $699
⇒ $699 - 0.40 x $699 = $419.4
The state tax (assuming it applied to the selling price) will be as,
7.25% of $419.4 = (7.25/100) x 419.4 = $30.4065
Final amount = $419.4 + $30.4065 = $449.80
Hence "Mikaela will have spent $449.80 in total on the paddleboard".
For more about the percentage,
brainly.com/question/13450942
#SPJ1
What is the value of p in the equation 8p 2 = 4p - 10?
Answer:
Step-by-step explanation:
A bakery used `25\%` less butter this month than last month.
The bakery used `240` kilograms of butter this month.
How much did it use last month?
In linear equation, The amount of butter used is an illustration of equivalent ratio.
The amount of butter used last month is 300kg.
What is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Because the bakery used 25% more last month, the amount they used is then calculated using
Amount = ( 1 + 25%) * last month
Substitute 240kg for Last Month
Amount = ( 1 + 0.25) * 240
Remove brackets
Amount = 1.25 * 240kg
= 300 kg
Hence, the amount of butter used last month is 300kg.
Learn more about linear equation
brainly.com/question/11897796
#SPJ1
Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
[tex]51.4^{\circ}[/tex]
Step-by-step explanation:
Since this is a right triangle, the cosine formula says
[tex]\cos(x) = \dfrac{5.3}{8.5}[/tex]
[tex]\longrightarrow cos(x) = 0.6235[/tex]
[tex]So\\\\x = \cos^{-1}(0.6235) = 51.4256^{\circ}[/tex]
Rounded to the nearest tenth this would be
[tex]51.4^{\circ}[/tex]
please help with 4 and 6 its my 4th time asking with no response
The solution is
a) The compound interest for the second period is $ 2.01 and the amount after the second period is $ 404.01
b) The compound interest for the first period is $ 114.125 and the amount is $ 18,374.125
The compound interest for the second period is $ 114.83828125 and the amount after second period is $ 18,488.96
What is Compound Interest?
Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
a)
Let the principal be P = amount after first period = $ 402
Now , the rate of interest r = 6 %
The compound interest is calculated by compounding monthly
Now , the interest for the second period = ( PRT / 100 x 12 )
Substituting the values in the equation , we get
The interest for the second period = ( 402 x 6 x 1 ) / 1200
The interest for the second period = $ 2.01
The amount after the second period = amount after first period + interest for the second period
The amount after the second period = 402 + 2.01
The amount after the second period = $ 404.01
b)
Let the principal be P = $ 18260
The rate of interest r = 2.5 %
The compound interest is calculated by compounding quarterly
Now , the interest for the first period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the first period = ( 18260 x 2.5 ) / 400
The interest for the first period = 45650 / 400
The interest for the first period = $ 114.125
The amount for the first period = 18260 + 114.125
The amount for the first period = $ 18,374.125
Now , the principal for the second period = interest + amount of first period
The principal for the second period = $ 18,374.125
The rate of interest = 2.5 %
The interest for the second period = ( PRT / 4 x 100 )
Substituting the values in the equation , we get
The interest for the second period = ( 18374.125 x 2.5 ) / 400
The interest for the second period = 45935.3125 / 400
The interest for the second period = $ 114.83828125
The amount for the second period = 18,374.125+ 114.84
The amount for the second period = $ 18,488.96
Hence , the amount and interest is calculated
To learn more about compound interest click :
https://brainly.com/question/21270833
#SPJ1
Mrs. Boggs asked her students to create a cylinder to hold
chocolate candies using a standard piece of paper (8.5 inches by 11 inches.)
Some of the students made cylinders that were 11 inches tall, and others created cylinders that were 8.5 inches tall.
The students began discussing the amount of chocolate candies
that each person could store. Oliver said that each cylinder
would hold the same amount of chocolate candies because they used the same size paper. Anna disagreed.
Who is correct? Try it out with a piece of paper and then use the calculations on the next page to compare.
The cylinder made with a paper size of 8.5 inches by 11 inches is having more volume and thus contains more chocolate, so, the statement by Oliver is wrong.
What is cylinder?
A cylinder is a three-dimensional solid that maintains two parallel bases spaced at a set distance from one another. These bases often have a circular form (like a circle).
Given:
The size of the first paper = 8.5 inches by 11 inches,
The size of the second paper = 11 inches by 8 inches,
The width of the paper when folded becomes the circumference of the cylinder circle, so,
Circumference of the cylinder for the first case = 2 × π × r
11 = 2 × π × r,
r = 1.75 inches,
The volume of the cylinder for the first case = π × r² × h
The volume of the cylinder for the first case = π × (1.75)² × 8.5
The volume of the cylinder for the first case = 81.78 inches³
Calculate the volume for the second case,
Circumference of the cylinder for the second case = 2 × π × r,
8.5 = 2 × π × r
r = 1.35 inches
The volume of the cylinder for the second case = π × (1.35)² × 11
The volume of the cylinder for the first case = 63.24 inches³
As we know, the cylinder with a higher volume contains more chocolate.
To know more about cylinders:
https://brainly.com/question/15891031
#SPJ1
"the time since dinosaurs became extinct is roughly equal to _____ average human lifespans"
average human lifespan: 2.4 x 10^4
time since dinosaurs became extinct: 2.4 x 10^10
The time since dinosaurs became extinct is roughly equal to 10⁶ average human lifespans
How to complete the blanks in the statementFrom the question, we have the following parameters that can be used in our computation:
Average human lifespan = 2.4 x 10^4Time since dinosaurs became extinct = 2.4 x 10^10Rewrite the exponents properly
So, we have the following representation
Average human lifespan = 2.4 x 10⁴Time since dinosaurs became extinct = 2.4 x 10¹⁰This means that
Number of times = Time since dinosaurs became extinct/Average human lifespan
Substitute the known values in the above equation, so, we have the following representation
Number of times = 2.4 x 10¹⁰/2.4 x 10⁴
Evaluate the quotient
Number of times = 10⁶
Hence, the number of times is 10⁶
Read more about scientific notations at
https://brainly.com/question/27862246
#SPJ1
The ratio of a to b is 4/7. If a is 16, find the value of b.
Answer:
B=28
Step-by-step explanation:
need help! can't figure it out :/
Answer:
please tell me if you get the answer. I need it too!
In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
At the left tail(negative infinity) it goes to negative infinity.At the right tail(positive infinity) it goes to positive infinity.More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
