The rewritten form of the given expression using the fewest possible terms as required is; 7/30t - 21.
What is the rewritten form of the given expression?It follows from the task content that the given expression is to be rewritten using the fewest terms.
Since the given expression is;
( 2/5t - 7 + 2/3t ) - (5/6t + 14)
By getting rid of the parentheses; we have;
2/5t - 7 + 2/3t - 5/6t - 14.
By collecting like terms; we have;
2/5t + 2/3t - 5/6t - 7 - 14
7/30t - 21.
Therefore, the required rewritten form of the given expression is; 7/30t - 21.
Read more on rewritten form of expressions;
https://brainly.com/question/28757930
#SPJ1
At a football stadium, 5% of the fans in attendance were teenagers. If there were 340 teenagers at the football stadium, what was the total number of people at the stadium?.
The total number of people at the stadium was 6800 people .
A Percent in mathematics is defined as a number or ratio that is expressed as a fraction of 100 , it is denoted by sign "%" .
For Example : 2% is = 2/100 .
In the question ,
it is given that ,
percent of teenagers fans in the stadium is = 5%
number of teenagers present at the football stadium is = 340
which means 5% represents 340 people ,
So , 1% will be 340/5 = 68 people .
the total percent of people present in the stadium is = 100% ,
multiplying both sides by 100 ,
we get ,
So , 100% = 68 × 100 = 6800 people
Therefore , The total attendance at the football stadium was 6800 people .
Learn more about Percent here
https://brainly.com/question/19261078
#SPJ4
What are the maximum dimensions of a rectangle with a perimeter of 12.
Answer:
3x3 should be the maximum dimensions of a rectangle with a perimeter of 12.
What is the sum of the infinite geometric series?
first of all, let's find the common ratio in this geometric sequence, by simply dividing a any of the terms by the term right behind it, hmmm say -12 and 16
[tex]16~~,~~-12~~,~~9~~,~~-\cfrac{27}{4}~\hfill \stackrel{\textit{\LARGE common ratio}}{\cfrac{-12}{16}\implies -\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ \qquad \qquad \textit{sum of an infinite geometric sequence} \\\\ \displaystyle S=\sum\limits_{i=0}^{\infty}\ a_1\cdot r^i\implies S=\cfrac{a_1}{1-r}\quad \begin{cases} a_1=\textit{first term}\\ r=\textit{common ratio}\\ \qquad -1 < r < 1\\[-0.5em] \hrulefill\\ a_1=16\\[1em] r=-\frac{3}{4} \end{cases}[/tex]
[tex]S=\cfrac{16}{ ~~ 1-\left( -\frac{3}{4} \right) ~~ }\implies S=\cfrac{16}{ ~~ 1 + \frac{3}{4} ~~ }\implies S=\cfrac{16}{~~ \frac{ 7}{ 4} ~~}\implies S=\cfrac{64}{7}[/tex]
A store is having a 12-hour sale. The total number of shoppers who have entered the store thours after it begins is modeled by the function S defined by [tex]S(t)=0.5 t^4-16 t^3+144 t^2[/tex] for [tex]0 \leq t \leq 12[/tex]. At time [tex]t=0[/tex], when the sale begins, there are no shoppers in the store. The rate at which shopper's leave the store, measured in shoppers per hour, is modeled by the function [tex]L[/tex] defined by [tex]L(t)=-80+\frac{4400}{t^2-14 t+55}[/tex] for [tex]0 \leq t \leq 12[/tex]. According to the model, how many shoppers are in the store at the end of the sale (time [tex]t=12[/tex] )? Give your answer to the nearest whole number.
At the end of the sale, there were a total of 196 customers in the store for the given function.
What is a function?The earliest known attempt to the notion of function may be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity.
The total number of shoppers in the store is the number of shoppers present at the start of the sale Plus the number of shoppers who entered the store minus the number of shoppers who left.
Given that there were no shoppers in the store before the sale began, the number of shoppers in the store at the start of the sale is 0.
It is assumed that the number of customers who have entered the store is represented by S(t)=0.5t⁴-16t³+144t².
So, at t=12, the number of shoppers in the store is S(12)=
0.5(12)⁴-16(12)³+144(12)²
S(12)=3456 shoppers.
L(t)= -80+(4400/t²-14t+55)
At t=12,
[tex]\int\limits^{12}_0 {L(t)} \, dt[/tex]=[tex]\int\limits^{12}_0[/tex]( -80+(4400/t²-14t+55))dt
At the end of the sale, there were a total of 196 customers in the store.
To know more about function, visit:
https://brainly.com/question/28193995
#SPJ1
In the figure below, k Il and m || n. Find the values of x and z.
A
Answer:
z = 36
x = 120
Step-by-step explanation:
What is the answer?? please and thank you
Answer:
the answer is no
Step-by-step explanation:
If the length of an rectangle is '' x-4 '' and the width is '' 3x-3 '' What would be the expression to represent the perimeter.
The expression that represents the perimeter of the rectangle is 8x - 14
What is a rectangle?A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
Length of rectangle(L) = x - 4
Width of rectangle(W) = 3x - 3
Perimeter of rectangle = 2(L + W)
L = x - 4, W = 3x - 3
Perimeter of rectangle = 2( x - 4 + 3x - 3)
Perimeter of rectangle = 2( 4x - 7) which is 8x - 14
In conclusion 8x - 14 is the expression for the perimeter of the rectangle
Learn more about perimeter of rectangles: https://brainly.com/question/24571594
#SPJ1
The ale tax on a car that old for $13,500 i $910. At thi rate, how much higher i the tax on a car that ell for $16,500
The tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
We have,
First car price is = $13,500
and tax of the first car is = $910
Second car price is = $16,500
and tax of the second car is = ?
so,
$13,500 ----- 100,
$910 ----- x
x = 910 * 100 / 13500
x = 6.7
therefore, the rate of tax is 6.7%
so, we will calculate the tax for the second car,
$16,500 ----- 100,
y ----- 6.7
y = 6.7 * 16,500 / 100
y = $1105.5
difference of tax price between two cars = $1105.5 - $910 = $195.5
Hence, the tax on a car that sells for $16,500 at the rate of 6.7% is $195.5 higher.
To learn more about the percentage visit,
https://brainly.com/question/24877689
#SPJ4
On a number line, point d is at -6, and point e is at 8. point f lies between points d and e. if is , where does point f lie on the number line? point f is at on the number line.
The point F lies on 4.5 in the number line.
What is the number line?
The number line is a One dimensional representation of point referring by a number only.
We know that if a point divides a line joining the points at x, y in the number line respectively in m:n ratio then that point lies on
= (my+nx)/(m+n) in the number line.
Here in the given problem that,
Point D lies on -6 in the number lin
Point E lies on 8 in the number line
And F lies between D and E points and DE:EF = 3:1
So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.
So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5
Hence, the point F lies on 4.5 in the number line.
To learn more about the Number Line visit,
brainly.com/question/4727909
#SPJ4
Which function matches the graph?
A. f(x)=(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)
Answer:
Choice B
Step-by-step explanation:
The graph crosses the xy-plane at the following places for x:
x = -5
x = -2
x = 3
x = 7
Look at choice B.
Setting (x - 3)^2, (x + 5)^2, (x - 7) and (x + 2) to zero and solving for x leads to the crossing locations on the xy-plane as shown on the graph.
a 36 year old woman on chronic cyclosporine treatment for bilateral lung transplantation visits the emergency department complaining of extreme headache, nausea and vomiting. her exam is notable for bp 239/165, normal cardiac exam, bibasilar pulmonary rales, and 1 lower extremity edema. ekg showed asymmetric inverted t-waves in i, avl, and v4-6. in an effort to acutely control her blood pressure, which of the following is true?
The best treatment for this patient's acute blood pressure control is to administer an intravenous (IV) antihypertensive medication such as labetalol or nitroprusside. Additionally, it is important to assess for underlying causes of her elevated blood pressure such as infection, kidney disease, or heart failure.
What is blood pressure?
Blood pressure (BP) is indeed the force exerted by moving blood against blood vessel walls. The heart's action of trying to pump blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) just above atmospheric pressure in the immediate vicinity. Along with respiratory rate, pulse rate, oxygen levels, and body temperature, blood pressure is among the vital signs that medical professionals consider when assessing a patient's health.
To learn more about blood pressure
https://brainly.com/question/10828142
#SPJ4
show that if f is a function from s to t, where s and t are finite sets with |s| > |t|, then there are elements s1 and s2 in s such that f(s1)
T|=|S|⟹ there is bijection F:S→T.
What are bijection function?A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.
In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.
No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.
One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.
According to our question-
The function f:ST |S||T| has an injective and not a surjective nature.
Assume an injective function exists: g:TS|T||S|. |T|=|S|
(this follow from the Cantor-Bernstein theorem).
|T|=|S|⟹ F:S:T has a bijection.
learn more about bijective functions click here:
https://brainly.com/question/13837935
#SPJ4
The F distribution's curve is positively skewed.
T/F
Answer: True
Step-by-step explanation:
-The f-distribution curve is positively skewed towards the right with a range of 0 and ∞
The value of F is always positive or zero. It never has negative values.
PLEASE HELP ME
What is the y-intercept of this line?
I keep getting confused someone please help me and explain it better to me
Answer:
2
Step-by-step explanation:
The y-intercept is the point at which the graph crosses the y-axis.
(I have marked it in blue on the attached graph).
From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.
A. Ue Pythagora’ Theorem to find the altitude of the triangle hown. B. Write the trigonometric ratio for a 60° angle. C. Write the trigonometric ratio for a 30° angle
The Trigonometric ratios are:
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
H/P = Cosecθ
H/B = Secθ
B/P = Cotθ
Where,
'P' represents the perpendicular
'B' represents the base
'H' = represents the hypotenuse
P/H = Sinθ
B/H = Cosθ
P/B = Tanθ
A. As the values of p, b or h are not given.
Pythagoras Theorem states that:
h² = p² + b² or h = [tex]\sqrt{p^2 + b^2}[/tex]
Altitude of a triangle is usually given by the perpendicular,
So,
h² = p² + b²
h² - b² = p²
p² = h² - b²
p = [tex]\sqrt{h^2 - b^2}[/tex]
B. The trigonometric ratios for θ = 60°
Sin 60 = √3/2
Cos 60 = 1/2
Tan 60 = √3
C. The trigonometric ratios for θ = 30°
Sin 30 = 1/2
Cos 30 = √3/2
Tan 30 = 1/√3
Learn more about Trigonometry at:
brainly.com/question/26719838
#SPJ4
Can someone please help me
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]n^{4}[/tex]
This is already simplified.
[tex]\frac{1}{n^{-5}}[/tex]
This is already simplified.
[tex]n^6 . n^{-8}[/tex]
= [tex]n^{6 - 8}[/tex]
= [tex]n^{-2}[/tex]
[tex]n^7 . p^8[/tex]
= [tex]n^{7 + 8}[/tex]
= [tex]n^{15}[/tex]
[tex]\frac{1}{n^3}[/tex]
This is already in simplified form.
Thus,
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
-7(8x + 5) = 5x+10
Solve for x simplify
(No solution, Infinitely many solutions, One solution)
The equation -7(8x + 5) = 5x+10 has one solution of x which satisfies the equation. The solution is x = -45/61.
What is solution of system of equation?
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitutes solutions of the system.
According to the given question:
Given equations is -7(8x + 5) = 5x+10
Simplifying both sides to get value of x
-7(8x + 5) = 5x+10
-56x - 35 = 5x + 10
-61x = 45
x = -45/61
Therefore x has one solution which is -45/61
To know more about solution of system of equations visit
https://brainly.com/question/28022879
#SPJ1
Line d passes through points (6, 9) and (2, 4). Line e passes through points (5, 3) and
(10, 7). Are line d and line e parallel or perpendicular?
PLEASE HELP ASAP, WILL GIVE 10 POINTS, BRAINELST, 5 STAR, AND RATING!
Answer:
Neither
Step-by-step explanation:
Line d:
m = 4-9/2-6 = -5/-4 = 5/4
Line e:
m = 7-3/10-5 = 4/5
It would be neither because if it was perpendicular, one of the slopes' would have to be negative.
A box of cereal states that there are 99 calories in a
3/4 cup serving. What is the unit rate for calories per cup? How many calories are there in 4 cups of the cereal?
The number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a box of cereal states that there are 99 calories in a 3/4 cup serving.
The number of calories per cup is calculated as,
3 / 4 cup = 99 calories'
1 cup = 99 x (4 / 3 )
1 cup = 132 calories
The number of calories for 4 cups of cereal,
1 cup = 132 calories
4 cup = 132 x 4 calories
4 cup = 528 calories
Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
Therefore, the number of calories in one cup is 132 calories and the number of calories in 4 cups is 528 calories.
To know more about an expression follow
https://brainly.com/question/18762453
#SPJ1
almost every american adult has this thing
Answer: omm
but I need this so
Step-by-step explanation:
Consider the scatter plot, its line of best fit, and the corresponding residual plot of each data set. State whether a linear model is appropriate for the data and justify your answer.
Linear regression equation: y = 14.08x - 163.13, r = 0.9746
No, a linear model is not appropriate for the data because; the residual plot indicates that the residuals are far off the horizontal.
Is a linear model appropriate for the data given?It follows from the task content that it is required to determine if a linear model is appropriate for the given data.
By observation of the scatter plot and the line of best fit; it is evident that the residuals are large (meaning that actually values are far off the predicted values).
Conclusively, the residual plot is a confirmation of the inappropriateness of a linear model for the given data. This follows from the fact that the residuals are large as evident in the how far the residual plot points are to the horizontal.
Read more on residual plot;
https://brainly.com/question/3297603
#SPJ1
A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also
a sphere with a radius of 0.78 inches. Select all the true statements.
The volume of the tennis ball is exactly 2 times the volume of the squash
ball.
The volume of the tennis ball is approximately 3 times the volume of the
squash ball.
The volume of both the tennis ball and squash ball is proportionate to the
scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
The volume of the tennis ball is 5.067 cubic inches and the volume of the
squash ball is about 0.63 cubic inches.
The two true statements about these are,
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
Given, A tennis ball is a sphere with a radius of 1.56 inches. A squash ball is also a sphere with a radius of 0.78 inches.
So, The volume of the tennis ball is (4/3)π(1.56)³ = 16 cubic inches.
The volume of the squash ball is (4/3)π(0.78)³ = 2 cubic inches.
The volume of both the tennis ball and squash ball is proportionate to the
the scale factor of the radii.
The scale factor of the volume of the tennis ball to the volume of the
squash ball is approximately 8.
learn more about sphere here :
https://brainly.com/question/12063484
#SPJ1
Select the values that make the inequality h<3h<3 true. (Numbers written in order from least to greatest going across.) -5 -2 0 2 2.9 2.99 2.999 3 3.001 3.01 3.1 4 6 8 11
The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.
What is an inequality in mathematics?An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠, <, or ≤ symbols.
The specified inequality is; h < 3·h < 3
When h < 3·h, we get;
h is a positive number larger than 0, such that we get;
When h < 0, 3·h < h
Therefore; h > 0
The inequality, 3·h < 3, indicates;
3·h < 3
h < 3/3 = 1
h < 1
Which indicates that we get;
0 < h < 1
Therefore, non of the values make the inequality, h < 3·h < 3
Learn more about inequalities here:
https://brainly.com/question/27030238
#SPJ1
¿What is the answer the EG ?
Ques) What is the symbol (∑)?
This symbol is used to denote the sum of multiple numbers.
This symbol is generally put by an index that varies to encompass all terms that must be considered in the sum of all the numbers.
In order to calculate the arithmetic mean of a set of data, the first step is to add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean
Mean = ∑ x/n
To know more about ∑ check here:
https://brainly.com/question/28163163
An electronic manufacturer determine that the profit P (in dollar) obtained by producing x unit of a DVD player and y unit of a DVD recorder i approximated by the model P(x, y) = 8x 10y − (0. 001)(x2 xy y2) − 10, 000. Find the production level that a maximum profit. What i the maximum profit?
The production level that a maximum profit is 186000 and the maximum profit will at the points of (200, -4000) , under the concept of absolute maximum value.
The P(x, y) = 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000, the first partial differentiate of the given equation with respect to x and y,
Px= ( 8x+ 10y − (0. 001)(x²+ xy+ y²) − 10, 000) = 8-0.001(2x-y) ....2
Py= 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000) = 10-0.001(x-2y) ... 3
Considering the above equation to be equal to zero :
=>8-0.001(2x-y) =0 =>0.001(2x-y) =8 .....4
=>10-0.001(x-2y) =0 =>0.001(x-2y) = 10 ...5
Solving the equations 4 and 5 we get the lues of x and y we get are :
x= 2000, and y = -4000 , Now the partial differentiate for the equations 2 ad 3 are with respect to x and y :
pxx(x,y)=-0.002
pyy(x,y)= 0.002
pxy(x,y) =-1
The discriminant of the function wil be at (2000,-4000):
D = 0.002*-0.002 -(-1)^2 =-1.0004 ,here D <0, so the critical values (200, -4000) reaches the maximum value .So the production level will be :
P(2000, -4000) = 8x+ 10y − (0. 001)(x2+ xy+ y2) − 10, 000 = 186000
To know more about maximum value refer to the link https://brainly.com/question/14316282?referrer=searchResults.
#SPJ4
7. A tour guide charges $28 to take four people on a tour. How much does the tour guide charge per person?
Answer: $7
Step-by-step explanation:
We know that $28 for four people.
So we take 28 divided by 4 and we get $7 per people
30 plus 50 written as 2 factors
The expression 30 _ 50 can be written as 2 factors as: 5(6 + 10).
What is a Factor?A factor, in mathematics, can be described as an integer that is a divisor of another integer that will produce a value it can be multiplied with to can that same integer it divides.
For example, if m/n = a, and (m)(a) = n, then m and n are factors.
Given the expression, 30 + 50, we can write this expression as product of factors as shown below:
5 into 30 is 6
5 into 50 is 10.
Therefore:
5(6 + 10)
Therefore, the two factors of the expression, 30 + 50 are written as: 5(6 + 10).
Learn more about factors on:
https://brainly.com/question/25829061
#SPJ1
Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven.
Sample Mean car 1: 250.3 mi/ 10 gal
Sample mean car 2: 246.1 mi/10 gal
Question: Find the medians for Car 2 and Car 2
Answers in bold
Median of car 1: 249
Median of car 2: 251
====================================================
Explanation:
This is the data set for car 1
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5}202 & 247 & 241 & 223 & 246\\\cline{1-5}253 & 271 & 241 & 291 & 249\\\cline{1-5}259 & 257 & 261 & 246 & 268\\\cline{1-5}\end{array}[/tex]
Which when written out as a single long line, we have this:
202, 247, 241, 223, 246, 253, 271, 241, 291, 249, 259, 257, 261, 246, 268
Sort those values from smallest to largest to get this set
202, 223, 241, 241, 246, 246, 247, 249, 253, 257, 259, 261, 268, 271, 291
There are n = 15 items in that set.
n/2 = 15/2 = 7.5 which rounds to 8
The middle-most item, aka median, is in slot 8.
There are 7 items below the median, and 7 items above it. Giving us 7+1+7 = 15 items total.
Start at "202" and count 8 slots to the right until you arrive at 249 which is the median of the car 1 data set. Make sure you are looking at the sorted data set.
Follow similar steps for the car 2 data set. You should get 251 as the median of the car 2 data set.
Please Help me With this ASAP (20 Points)
Answer:
200*1-0.95-0.95+0.9025
200*1-1.9+0.9025
200*0.0025
0.5
Solve the inequality. 2x + 13 < 35
Answer:
x < 11
Step-by-step explanation:
there you go :)
