To write the word name of a number, we start from left to right. in the thousands place, we have 51, so this is "fifty-one thousand". The rest is 104, we is "one hundred four". All together, we have:
"Fifty-one thousand one hundred four"
3. Brust is riding his bicycle north away from an intersection at a rate of 15 miles per hour. Sully is driving his car towards the intersection from the west at a rate of 30 miles per hour. If Brust is 0.4 miles from the intersection, and Sully is 1 mile from the intersection, at what rate is the distance between the two of them increasing or decreasing?
The graph shows the situation of Brust and Sully. The distance between them is d
If x is the distance from Sully to the intersection and y is the distance from Brust to the intersection, the distance d is
[tex]d=\sqrt[]{x^2+y^2}[/tex]The rate of change of d in time is computed by taking the derivative:
[tex]d^{\prime}=\frac{xx^{\prime}+yy^{\prime}\text{ }}{\sqrt[]{x^2+y^2}}[/tex]We have the following parameters:
x=1, y=0.4, x'=-30, y'=15
Substituting:
[tex]d^{\prime}=\frac{(1)(-30)+(0.4)(15)\text{ }}{\sqrt[]{1^2+0.4^2}}[/tex]d' = -22.3 miles per hour
Since d' is negative, the distance is decreasing
The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
Your employer promises after 6 months to give you a 15% pay raise in addition to your new pay. How much will your monthly income be after the 15% pay increase?
Lets assume that the actual pay is the 100%, if after 6 months you get a rais of 15% in addition of your new pay, then the monthly income after the raise will be the 115% of the actual pay
A Little League baseball diamond has four bases forming a square whose sides measure 60 feet each. The pitcher's mound is 46 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher's mound to third base. Round to the nearest tenth of a foot.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Square
side = 60 feet
pitcher's mound from home plate = 46 feet
distance from the pitcher's mound to third base = ?
Step 02:
Diagram:
Step 03:
distance from the pitcher's mound to third base
side 1 = 60
side 2 = 46
angle 1 = 90 / 2 = 45
a ² = b ² + c ² - 2 * b * c* Cos A
a ² = 60² + 46² - 2(60)(46) Cos 45
a² = 1812.771
a = √1812.771
a = 42.576
The answer is:
The distance from the pitcher's mound to third base is 42.6 feet.
a cube has a volume of seven units. what is the edge length of a cube?
Given:
The volume of the cube = seven units.
Let a be the edge length of the cube.
Consider the formula for the volume of the cube.
[tex]V=a^3[/tex]Substitute V=7 in the formula, we get
[tex]7=a^3[/tex]Taking cubic root on both sides, we get
[tex]\sqrt[3]{7}=a[/tex][tex]T\text{he edge length of the given cube is }\sqrt[3]{7}\text{ units.}[/tex]or
[tex]T\text{he edge length of the given cube is }1.91\text{ units.}[/tex]If the measures of two pair of complementary angles are added together then the sum is equal to the measures of two right anglestrue or false
ANSWER : FALSE
EXPLANATION : The sum of two complementary angles is 90°. Adding the measure of two right angles (right angles is a 90° angle) is equal to 180°.
Therefore, adding the two pairs of complementary angles is not equal to the sum of two right angles.
felicia owns 80 shares of electrify us power cooperative that pay dividends of $129. at this rate, what dividend would felicia recive after buying 600 shares.
The dividend that Felicia will receive after buying 600 shares is $967.50.
How to calculate the value?Dividends are regular profit-sharing payments made by a company to its shareholders. The board of directors of a company decides on the price per share as well as when and how often dividend payments are made. Dividend stocks can provide a steady stream of income, which is especially valuable during times of inflation.
From the information, Felicia owns 80 shares of electrifying us power cooperative that pay dividends of $129. It should be noted that the dividend rate will be:
= $129 / 80
= $1.6125
Therefore, the amount for 600 shares will be:
= 600 × $1.6125
= $967.50
The dividend is $967.50.
Learn more about dividend on:
brainly.com/question/25845157
#SPJ1
So basically I have to reflect triangle STU across line ST and I need to find a valid reason of why the image of U will coincide with J. I need guidance please
Solution
- The reflection of an object across a line implies that the distance between the object and the reflection line is the same as the distance between the image and the reflection line.
- This implies that if the distance between the point U and the reflection line ST is x, then, the distance between the reflection line and the image of U must be a distance of x as well.
- This is illustrated below:
- From the above, we can see that distance x is a perpendicular distance from point U to reflection line ST.
- However, we must not just assume that distance x lands at point J.
- We can however show that this is the case because of the SSS congruency. That is,
[tex]\begin{gathered} SU\cong SJ\text{ \lparen Given in the question\rparen} \\ UT\cong TJ\text{ \lparen Given in the question\rparen} \\ ST\text{ is a common side for both triangles SUT and SJT} \end{gathered}[/tex]- Since both triangles are congruent, we can proceed to conclude that from line ST to point J is also a distance of x.
- Therefore, the image of U will coincide with J given that ST is the reflection line
part A Jasmine ran 5 miles in 42 minutes at what rate did Jasmine run Jasmine ran at a rate of ? minutes per mile
We will find the rate as follows:
[tex]r=\frac{5}{42}[/tex]So the rate is the distance divided by the time it took to traverse.
A Labrador retriever weighs 50kg. After a diet and exercise program the dog weighs 41kg. What is the percentage loss in weight.
inital weight = 50 kg
Final weight = 41 kg
loss = 50 - 41 = 9 kg
[tex]\begin{gathered} \text{percentage loss=}\frac{9}{50}\times100 \\ \text{percentage loss=}\frac{900}{50} \\ \text{percentage loss = }18\text{\%} \end{gathered}[/tex]Based on the density graph below, what is the probability of a valuein the sample space being anywhere from 0 to 20?
Answer
Option A is correct.
Probability of a value in the sample space being anywhere from 0 to 20 = 80%
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of boxes from 0 to 20 = 20
Total number of boxes in the density graph = 25
Probability of a value in the sample space being anywhere from 0 to 20 = (20/25) = 0.8 = 80%
Hope this Helps!!!
y=-2x + 4 3y + 6x = 12 O One Solution O No Solutions o Infinitely Many Solutions
To find the number of solutions of a system of linear equations you need to identify the slope (m) of each equation
[tex]y=mx+b[/tex]If the slope is the same in both lines the system has no solution.
If the slope is different in the lines the system has one solution.
If the equation are the same (incluided the value of b) the system has infinitely many solutions.
In the given equations the slope is:
First equation:
[tex]y=-2x+4[/tex]Slope: m=-2Second equation:
[tex]3y+6x=12[/tex]Write the equation in slope-intercept form by solving for y:
[tex]\begin{gathered} 3y+6x-6x=-6x+12 \\ 3y=-6x+12 \\ \\ y=-\frac{6}{3}x+\frac{12}{3} \\ \\ y=-2x+4 \end{gathered}[/tex]Slope: m= -2In this case as the equatinos are the same the system has infinitely many solutionsAnswer below due to inability to type out the following question.
ANSWER
[tex]11.04\text{ or }\frac{-2+\sqrt{580}}{2}[/tex]EXPLANATION
Given that:
In the figure provided, the triangle EFG is similar to the triangle is ECD
FE = 12
CD = 12
FG = CF + 2
To find the length CF, apply the similarity triangle theorem
[tex]\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}[/tex]Substitute the given data into the above equation
[tex]\begin{gathered} \text{ }\frac{12}{CF}=\frac{CF+2}{12} \\ \text{ cross multiply} \\ \text{ 12}\times12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm\sqrt{2^2-4\times1\times(-144)}}{2} \\ \text{ x}=\text{ }\frac{-2\pm\sqrt{4+576}}{2} \\ \text{ x }=\text{ }\frac{-2\pm\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+24.083}{2} \\ \text{ x }=\frac{22.083}{2} \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }\frac{-2+\sqrt{580}}{2} \end{gathered}[/tex]I need help with number 5. Here is the problem:Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.
To have a pictorial representation of this problem (the track), we will have the figure below:
To find the length of the track, we will sum up the length of two sides of the square and the circumference of the two half semicircles.
We will find the length of the square thus:
[tex]\begin{gathered} A=l^2 \\ 128=l^2 \\ \sqrt[]{128}=l \\ 11.314ft=l \\ \text{Each side of the square is 11.314ft} \end{gathered}[/tex]Now we will find the circumference of a half-circle:
[tex]=\frac{\pi D}{2}[/tex]Since the length of the square is also the diameter of the half circle:
[tex]\begin{gathered} D=l=11.314 \\ \text{Circumference of half-circle:} \\ =\frac{\pi(11.314)}{2} \\ =17.772ft \end{gathered}[/tex]The length of the track will be calculated with this expression:
[tex]=\text{length of two sides of the square + circumference of two half-circles}[/tex][tex]\begin{gathered} =2(11.312ft)+2(17.772ft) \\ =22.624ft+35.544ft \\ =58.168ft \\ \text{The length of the track is 58.168ft} \end{gathered}[/tex]what is 13 divided by 113.1
A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement? Round to the nearest hundredth percent
Answer
Percent Error = 0.195%
Explanation
Percent error is given as
[tex]\text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent}[/tex]Error = | (Incorrect value) - (True value) |
Incorrect value = 103 miles per hour
True value = 102.8 miles per hour
Error = | (Incorrect value) - (True value) |
Error = | 103 - 102.8 |
Error = 0.2 miles per hour
[tex]\begin{gathered} \text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent} \\ \text{Percent Error = }\frac{0.2}{102.8}\times100\text{ percent} \\ \text{Percent Error = 0.195 percent} \end{gathered}[/tex]
Hope this Helps!!!
Which one of the following equations defines the line that contains the point (1,2) and is parallel to the line 4x+3y=7?
Please help ASAP *image imported*
The coach is building shelves to store and organize the team’s collection of 175 game videos how many shelves will be needed if one shelf holds 28 videos?
7 shelves will need to store and organize the team's collection of 175 game videos.
Given:
The team’s collection of 175 game videos.
one shelf holds 28 videos.
Number of shelves = total videos/one shelf hold capacity.
= 175/28
= 6.25
since we cannot have 0.25 shelf we take it as 1.
So number of selves = 7 shelves.
Therefore 7 shelves will need to store and organize the team's collection of 175 game videos.
Learn more about the shelves and game videos here:
https://brainly.com/question/1080819
#SPJ1
100 divided by 72,144
Answer:0.00138611665
Step-by-step explanation:
If Lydia invests $3000 in a certificate of deposit and d dollars in a stock, write an expression for the total amount she invested.
ANSWER:
[tex]\text{ total amount }=3000+d[/tex]STEP-BY-STEP EXPLANATION:
The total invested is equal to 3000 investment and the previous money in stock, therefore, the expression would be:
[tex]\text{ total amount }=3000+d[/tex]Simplify the following expression by distributing and combining like terms.-5(k+6) + 7(k-4)
The given expression is
[tex]-5(k+6)+7(k-4)[/tex]To solve this, first, we use the distributive property.
[tex]-5(k+6)+7(k-4)=-5k-30+7k-28[/tex]Then, we reduce like terms.
[tex]2k-58[/tex]Therefore, the simplest form of the given expression is 2k - 58.What is the value of sin C? a) 15/17b) 15/8c) 8/15d) 8/17
Answer:
d) 8/17
Explanation:
From trigonometry, we know that in a right triangle:
[tex]\sin \theta=\frac{Opposite}{\text{Hypotenuse}}[/tex]From the diagram:
• The side, opposite C, is 8.
,• The ,hypotenuse, is 17.
Therefore:
[tex]\sin C=\frac{8}{17}[/tex]HELPPP I also have to round it yo the nearest tenth if possible
In a circle v, UTw =50 solve for X . If mUW= (9x-34)
Answer:
X=14.9
Step-by-step explanation:
mUW=2 . m <utw
so (9x - 34) = 2.50
9x - 34 = 100
x = 14.9
Give the name of the parent function and describe the transformation represented.
5 units to the left and 2 units downwards
Explanation:[tex]f(x)\text{ = |x + 5| - 2}[/tex]The parent function:
f(x) = |x|
Name of parent function is absolute value function
The transformtion from parent function to the new function:
[tex]\begin{gathered} \text{from f(x) = |x| to f(x) = |x + 5| - 2} \\ \text{For translation:} \\ f(x)\text{ = |x + a| (translation to the left)} \\ f(x)\text{ = |x - a| (translation to the right)} \\ \\ So\text{ f(x) = |x + 5| is a translation of 5 units to the left} \end{gathered}[/tex][tex]\begin{gathered} For\text{ translation: } \\ f(x)\text{ = |x| + a (translation upwards)} \\ f(x)\text{ = |x| }-\text{ a (translation downwards)} \\ \\ So\text{ f(x) = |x| - 2 is a translation downwards} \end{gathered}[/tex]Combining both transformation:
f(x) = |x + 5| - 2 is a translation of 5 units to the left and 2 units downwards
10 Find x. 30° 5V3 10 5 73 1073
Do you have a pcture of this problem?
thanks
5
Hello please help I don’t know what I’m doing wrong
Explanation:
The domain of a function is the input value of any function for which the function exists.
For the function;
(f+g)(x) = 2x² + x
From the given function, we can see that the function will exist for all values of x i.e. the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (f-g)(x) = x
Similarly for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function (fg)(x) =x^4 + x^3
Also for this function, the input variable exists on all real values.
The domain of the function in interval notation will be expressed as
(-∞, ∞)
For the function given as (f/g)(x) = 1 + 1/x
The function will not exist when x = 0. The function will be undefined at this point. The required domain of this function in interval notation will be:
[tex]D=(-\infty,0)U(0,\infty)[/tex]
what is the volume of the can in cubic inches in terms of
Given data:
The height of the cylinder is h=9 in.
Th diameter of the cylinder is d=6 in.
The expression for the volume of the cylinder is,
V=(πd^2h)/4
Substitute the given values in the above expression.
[tex]\begin{gathered} V=\pi(6in)^2(9\text{ in)}\frac{1}{4} \\ =81\pi in^3 \end{gathered}[/tex]Thus, the volume of the given figure is 81 in^3. so C) option is correct.
Jennifer. Leigh Anne, and Karyn went out to eat. Jennifer bought an entrée for $12.95 and split a $4.95 dessert with Karyn, who bought a sandwich for $7.95. Leigh Anne bought soup for $3.95, a salad for $6.95, and coffee for $1.70. Determine the total amount each should pay if tax is 6% and each one tips 15% of her individual bill rounded up to the next quarter.
The total amount Leigh Anne spent is $3.95 plus $6.95 plus $1.7, that is $12.6. Since they pay a tax of 6% and a tip of 15%, she pays a total of 21% extra; this 21% can be obtained by the tule of three:
[tex]\begin{gathered} 12.6\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot12.6}{100}=2.65[/tex]Therefore, Leigh Anne spent a total of $15.25.
Assuming the dessert was split in half, then Jennifer spent a total of $15.43. To this amount we have to add the tax and tip. By the same logic as before we have:
[tex]\begin{gathered} 15.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot15.43}{100}=3.24[/tex]Therefore, Jennifer spent $18.75
Finally Karyn spent $10.43, obtaining the extra amount we have:
[tex]\begin{gathered} 10.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]Then:
[tex]x=\frac{21\cdot10.43}{100}=2.19[/tex]Therefore, Karyn spent $12.75.