Answer:
$1471.49
Step-by-step explanation:
1571.13-80=1491.13
1491.13+456.82=1947.95
179.48+74.73+82.70+139.55=476.46
1947.95-476.46=1471.49
help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.
What is an expression?An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.
Calculation:It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as
f(x) = 0.48 ln(x+2) + 27
Here x is the distance in miles from the eye of the hurricane.
f(x) is the pressure of the mercury in a barometer in inches
So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is
(Here f(x) = 28)
f(x) = 0.48 ln(x+2) + 27
⇒ 28 = 0.48 ln(x+2) + 27
⇒ 0.48 ln(x+2) = 28 - 27
⇒ ln (x+2) = 1/0.48
⇒ ln(x+2) = 2.0833
Applying exponential base "e" on both sides, we get
(x+2) = [tex]e^{2.0833}[/tex]
⇒ x + 2 = 8.0309
⇒ x = 8.0309 - 2 = 6.0309
When the result is rounded to the nearest whole number, we get x = 6 miles.
Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.
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MODELING REAL LIFE Oak Street intersects Walnut
Street and Maple Street at their midpoints. A parade float
starts at point S, travels up Walnut Street to Oak Street, up
Oak Street to Maple Street, over Maple Street to Spruce
Street, and then down Spruce Street to the starting point.
About how far does the float travel? Round your answer to
the nearest hundredth place.
Answer:4.05
Step-by-step explanation: Walnut divided by 2 is 0.9 and Oak is 0.9. Maple is 0.45 and Spruce. All that is added up to 4.05
A rectangular dog pen is constructed using a barn wall as one side and 80 meters of fencing for the other three sides. Find the dimensions of the pen that give the greatest area.(example to write an answer: 20m×15m).
Let the dimensions of the pen be L for the length and W for the width. The area of the pen is L*W.
We are given that the width of the pen is 80 meters and that the length of the pen is greater than the width. Therefore, the length of the pen must be greater than 80 meters.
Since the area of the pen is L*W, the area will be greatest when L is as large as possible and W is as large as possible. Therefore, we can set L equal to 80 and W equal to 80 to find the dimensions of the pen that give the greatest area:
L = 80
W = 80
The dimensions of the pen that give the greatest area are 80 meters by 80 meters. Therefore, the answer is 80m x 80m.
The dimensions of the pen are 20 m × 40 m and the area will be 600 m².
What is the area?An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure. The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.
As per the given data in the question,
Let the length of the rectangle is x and,
Let the width of the rectangle is y.
So, the equation will be,
2x + y = 80 (1)
y = 80 - 2x (2)
Use the formula of the area of a rectangle,
A = x × y
Substitute y = 80 - 2x in the above formula,
A = x × (80 - 2x)
= 80x - 2(x)²
= -2x² + 80x
dA/dx = -2x² + 80x
A' = -4x + 80
-4x = -80
x = 80/4
x = 20 m
Substitute x = 20 in equation (2)
y = 80 - 2(20)
y = 40 m
So, the area should be,
A = 20 × 40
A = 600 m².
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Triangle DEF is similar to a triangle ABC. What is the slope of the line that passes through the hypotenuse of the Two similar triangles?
Answer:
D. Slope is 1
Step-by-step explanation:
Start at any point on the line. Go up 1 (rise of 1). Go right 1 (run of 1). You're on the line again.
slope = rise/run = 1/1 = 1
please show work on this, I need help
A horizontal asymptote of a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
How do you type a horizontal line symbol?The fastest way to add a horizontal line or rule is to use the AutoFormat feature. When you type certain characters three times in their own paragraph and then press Enter, those characters instantly become a full-width horizontal line.How to insert a horizontal line in Word using the keyboardPolynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials.The polynomials can be identified by noting which expressions contain only the operations of addition, subtraction, multiplication, and non-negative integer exponents. The non-polynomial expressions will be the expressions which contain other operations.Place your cursor on a blank line where you want to insert a horizontal line. ...To insert a basic line, type three or more hyphens (---) in a row.Hit "Enter" on your keyboard. ...Move this line by pressing "Enter" on your keyboard on a line of text above the line.
6. x = 28 degrees
7. z = 1.6 cm
6. Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:
50 + 69 + (2 x +5) = 180
combine like terms:
119 + 2 x + 5 = 180
124 + 2 x = 180
subtract 124 from both sides:
2 x = 56
divide by 2 both sides:
x = 56 / 2
x = 28 degrees
Problem 7.
If the two triangles are congruent, then the side MN must equal side RS.
Since MN measure 1,8 cm, then RS must also measure 1.8 cm
and we can write the equation:
1.8 = 3 z - 3
adding 3 to both sides:
1.8 + 3 = 3 z
4.8 = 3 z
dividing both sides by 3:
z = 4.8 / 3
z = 1.6 cm
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Find the point of intersection for the pair of linear equations.
x+y= -8.5
y = 2x + 4.4
A. (-4.3, -4.2)
B. (-4.1, 4.4)
C. (1.9, -3.7)
D. (-3.1, 2.4)
If n = 19,
¯
x
= 36, and s = 2, construct a confidence interval at a 99% confidence level. Assume the data came from a normally distributed population. Give your answers to three decimal places.
<
μ
The three decimal places are :28.288< μ < 43.712
What is meant by normally distributed population?A normal distribution is one in which the values are evenly distributed above and below the mean. A population has a perfectly normal distribution if the mean, mode, and median are all equal. The mean, mode, and median for a population of 3,4,5,5,5,6,7 are all 5. The normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, indicating that data near the mean occur more frequently than data far from the mean.degree of freedom = 17-1 = 16
critical t value = 2.1199
lower limit = 36-2.1199*15/sqrt(17) = 28.288
Upper limit = 36+2.1199*15/sqrt(17) = 43.712
Answer:28.288< μ < 43.712
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Kira wants to attend a college that will cost her $14,800 for the first year. To pay for it, her aunt gave her a special gift of $10,000 . Kira is also going to start saving $100 per month. How many years will it take Kira to save enough for the first-year cost?
The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by the following.
S = 10(1-ekx)
When $675 is spent on advertising 2900 units are sold.
(a) Complete the model by solving for k. (Round your answer to 4 decimal places.)
k =
(b) Estimate the number of units that will be sold if advertising expenditures are raised to $925.
units
Answer:
as a result you get approximately 2.8949 which in thousands of units is 2894 (rounded down since you can't have a fraction of a unit).
Write the equivalent fraction with a denominator of 100100 .
\frac{9}{10}=
10
9
=
The equivalent fraction with a denominator of 100 will be;
⇒ 90 / 100
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The fraction is,
⇒ 9 / 10
Now,
Since, The fraction is,
⇒ 9 / 10
Hence, The fraction with denominator 100 is;
⇒ 9 / 10 = 9×10 / 10×10
= 90/100
Thus, The equivalent fraction with a denominator of 100 will be;
⇒ 90 / 100
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An independent variable that studied using related samples in all conditions is called a
An independent variable studied by using related samples in all conditions is called a within subjects factor.
An independent variable is defines as the variable that is modified or controlled in a scientific experiment. It reflects the rationale or cause for an outcome.
The variables that the experimenter adjusts to test their dependent variable are known as independent variables. A change in the independent variable has a direct effect on the dependent variable. The impact on the dependent variable is assessed and documented.
Examples of Independent Variables
A scientist is experimenting with the effect of light and dark on the behaviour of moths by turning on and off a light. The amount of light is the independent variable, while the moth's reaction is the dependent variable.
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Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent.
Answer:
HL
Step-by-step explanation:
to solve this we first must see what is congruent
we see that both triangles are right triangles
that means that we can use HL (hypotenuse length) to solve
we must first see if HL works though
we see that the hypotenuses are both equal
that means that we can use HL
that is your answer
In a class of 30 students, 16 have a cat and 15 have a dog. There are 11 students who have a cat and a dog. what is the probability that a student has a dog given that they do not have a cat?
Write equations for the horizontal and vertical lines passing through the point (4,-3)
The equation of vertical line passing through the point (4,-3) will be x = 4
And, The equation of horizontal line passing through the point (4,-3) will be y = - 3.
What is mathematical expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The horizontal and vertical lines passing through the point (4,-3).
Now,
Since, The horizontal and vertical lines passing through the point (4,-3).
Hence, The equation of vertical line passing through the point (4,-3) is the value of x.
So, We get;
The equation of vertical line is,
⇒ x = 4
And, The equation of horizontal line passing through the point (4,-3) is the value of y coordinate.
So, We get;
The equation of horizontal line is,
⇒ y = - 3
Thus, The equation of horizontal line is , y = - 3
And, The equation of vertical line is, x = 4
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The formula below models the number of calories consumed daily by a person owning x acres of land in a developing country. Estimate the number of a 2200 calories per day.
C(x)=270 ln (x+1)+1900
For an average intake of 2200 calories per day, the number of acres of land owned is approximately (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)
For an average intake of 2200 calories per day, the number of acres of land owned will be 2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, The function that models the number of calories consumed daily by a person owning x acres of land in a developing country is,
C(x)=270 ln (x+1)+1900
If an average intake of 2200 calories per day,
C(x)= 2200
2200=270 ln (x+1)+1900
2200-1900=270 ln (x+1)
270 ln (x+1)=2200-1900
270 ln (x+1)=300
ln (x+1)=300/270
ln (x+1)=1.11
(x+1)=ln⁻¹(1.11)
x+1=e¹¹¹
x=e¹¹¹-1
x=3.034-1
x=2.034≈2
Thus, for an average intake of 2200 calories per day, the number of acres of land owned will be 2.
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12
A culture of bacteria triples every hour. If there are 5 bacteria after the first hour,
how many bacteria will there be after one day?(One day= 24 hours)
5 x 3²⁴ bacteria will there be after one day.
What is exponents?
Exponentiation could be a calculation, written as bⁿ, involving 2 numbers, the bottom b and also the exponent or power n, and pronounced as "b to the n".
Consider what is actually happening in the question.
You begin with 5 bacteria, and after 1 hour it has tripled so you now have
5x 3=15.
Next hour, it triples again so you now have 5 x 3 x 3=45
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 3⁴ means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
n x 324 where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is 5 x 3²⁴.
Hence 5 x 3²⁴ bacteria will there be after one day.
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The strongest recorded earthquake was in Chile in 1960 and had an intensity of 316227.77 cm. What was its magnitude? (Round your answer to one decimal place.)
Answer:
5.5
Step-by-step explanation:
earthquake is measured with the Ritcher Scale:
R (Magnitude) = ㏒base 10 (I)
where I = Intensity
thus,
R = ㏒ base 10 (316227.77)
R ≅ 5.5
Adam has 18 counters. He gives 10 of the counters to Lesley. what fraction of the 18 counters does Adam have now
Adam have 4 / 9 fraction of the 18 counters. A fraction is a number that is stated as a quotient by dividing the numerator and the denominator.
What is a fraction ?Fraction a number that is stated as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. A fractional equation is one that contains one or more terms that are fractions. The first step in solving a fractional equation is to eliminate the fractions by multiplying both sides of the equation by the LCD of each term.
Adam has 18 counters
Lesley get 10 counters
Adam have 18 - 10 = 8
8 / 18 = 4 /9
Adam have 4 /9 fraction of the counters.
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Y varies directly as x and inversely as the square of z.y=8 when x=25 and z=5. Find y when x=2 and z=6
The value of y when x = 2 is 16/25 and when z = 6 is 200/36
What is proportionality constant?The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship.
Given that, Y varies directly as x and inversely as the square of z and y=8 when x=25
That means, y ∝ x and y ∝ 1/z²
Let constant of proportionality be k, then,
y = kx and y = k/z²
Now, finding k, when x = 25
8 = k25
k = 8/25
For x = 2,
y = 8/25X2
y = 16/25
Finding k when y = 5
8 = y/25
y = 200
Now, when z = 6
y = 200/36
Hence, The value of y when x = 2 is 16/25 and when z = 6 is 200/36
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James and Elizabeth buy some clothes.
James buys 5 shirts and 4 jumpers. He pays £163.
Elizabeth buys 3 shirts and 2 jumpers. She pays £89.
Assume that each shirt has the same cost and that each jumper has the same
cost.
Work out the cost of one shirt and the cost of one jumper.
Cost of one shirt £
Cost of one jumper £
Answer:
£15 and £22
Step-by-step explanation:
let,the cost of one shirt be X and one jumper be y.Then according to question,
5x+4y=163-----(1)
also,
3x+2y=89------(2)
Now, multiplying eqn (2) by 2 and then subtracting from (1),we get
5x+4y=163
6x+4y=178
- - -
_________
-x=-15
:.x=15
Putting value of X in eqn (1),
5×15+4y=163
or,4y=163-75
or,y=88/4
:.y=22
Hence cost of one shirt is £15 and one jumper is £22.
Select all of the verbal phrases which can be represented by the expression 25.75x + 10.
25.75 plus 10
25.75 times a number x, plus 10
25.75 times a number x, plus 10 times a number x
the product of 25.75 and x, plus 10
the product of 25.75 and 10
The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
What is mathematical verbal expression?An algebraic expression that may contain various operations, quantities, and variables is translated into words as a mathematical verbal expression.This can be demonstrated by verbally expressing the mathematical statement "90 - 4(a + 8)" as "90 reduced by 4 times the sum of a number "a" plus 8."Students may also need to convert verbal expressions into algebraic expressions or equations when studying math. In word problems, where students must search for precise terms that identify the procedure required to answer the problem, this is frequently utilized. Decreased by, increased by, less than, more than, sum of a number and "x," and the total of two numbers are a few examples of these expressions.Hence, The verbal phrases which represented by the expression are 25.75 times a number x, plus 10 and the product of 25.75 and x, plus 10.
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John and his friends are dining at a restaurant. The bill comes to $334.43. John tips the waiter 16.5% of the total bill amount. He estimates that the total amount they need to pay is about $390. Is this a reasonable estimate?
Answer:
Yes
Step-by-step explanation:
What is the answer to this?
Ashley used the method shown below to add 3/5 and 1/4
Step 1 3/5 + 1/4 = 0.6 + 0.25
Step 2 0.85 = 85/100
Step 3 17/20
Is Ashley's work correct? If not, which is the first incorrect step?
All steps are correct.
The first incorrect step is Step 1.
The first incorrect step is Step 2.
The first incorrect step is Step 3.
the answer will be "all steps are correct"
To the nearest hundredth, 11.6÷0.95
is about
on dividing the given term we get
12.2105.
2. For each of the following functions, determine the average rate of change over the specified interval.
From x=4 to x=10
Average rate of change for given function from x=4 to x=10 is -0.66
What is average rate of change?Average rate of change can be defined as slope of function between two fixed values of x. It can also be defined as change in function per unit or we can say as an average.
At x = 4 we have y = 8
At x = 10 we have y = 4
As y is nothing but value of function f(x) at x.
So, we can write them as f(4) = 8 and f(10) = 4
Average rate of change (from x = a to x=b) = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Using above formula of average rate of change and substituting for x=4 to x=10, we get
Average rate of change = [tex]\frac{4-8}{10-4} = \frac{-2}{3}[/tex]
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Need help pelase 7th grade math help
The constant of proportionality of the image of actual height and height on set of the items is 20 / 11
Table
= 15.4 inchesStool
= 9.9 incheswindow
= 4 inchesBucket
= 2 inchesHow to get the constant of proportionalityConstant of proportionality are used to increase or decrease image. The situation of increment is usually called magnifying.
solving for the constant of proportionality, assuming the factor is k
height on set * k = actual height
44 * k = 80
k = 80 / 44
k = 20/11
Height on set for other items
Table
= 28 ÷ 20/11
= 15.4 inches
Stool
= 18 ÷ 20/11
= 9.9 inches
window
= 80/11 ÷ 20/11
= 4 inches
Bucket
= 40/11 ÷ 20/11
= 2 inches
The Constant of proportionality is calculated to be 20/11
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A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer: 1058000 tickets
Step-by-step explanation:
23000 x 46 = 1058000
1058000 tickets
[5-TI] 4. The layout of Joe's yard is shown below. Joe must spread out topsoil to a depth
of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and
contains 10 cubic yards of topsoil. How much will the topsoil cost to complete
this job?
75 feet
64 feet
36 feet
53 feet
19 feet
22 feet
The total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB).
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that Joe must spread out topsoil to a depth of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and contains 10 cubic yards of topsoil.
In 10 yards³ = 466,560.1 in³
Assume the length and breadth to be [L] inches and [B] inches. The height is 15 inches.
Volume of the layout will be -
V = (15 x L x B) in³
466,560.1 in³ of the topsoil costs $67.89.
1 in³ of the topsoil will cost $(67.89/466560.1)
(15 x L x B) in³ of the topsoil will cost -
$(67.89/466560.1) x (15LB)
(1.46 x 10⁻⁴)(15LB)
Therefore, the total cost of the topsoil needed to cover the layout will be
$(1.46 x 10⁻⁴)(15LB)
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Need an answer help please
Answer:
see explanation
Step-by-step explanation:
the mistake is that a zero should be inserted to indicate the x - term
the standard form of a polynomial of degree 3 is
ax³ + bx² + cx + d
given
[tex]\frac{3m^3-2m^2-150}{m-4}[/tex]
there is no m- term in the numerator so a zero has to be inserted in its place, that is
4 | 3 - 2 0 - 150
↓ 12 40 160
---------------------------
3 10 40 10