Given:
Truck average=20 miles per gallon.
Required:
Cost in dollars
Explanation:
First of all we are going to divide 320 miles with 20 miles to calculate the average per gallon.
\(\begin{gathered} \frac{320}{20} \\ \\ =16\text{ miles} \end{gathered}\)Logan's truck average =16 miles.
Now to calculate the price of gasoline in dollars
we have to multiply our calculates miles with the price of gasoline in dollars
which is equal to=
\(16\times2.00=32dollars.\)Required answer:
16 miles , 32 dollars
A normal distribution has a mean of 85.8 and a standard deviation of 4.83. Find the data value corresponding to the value of z given. (Enter your answer to four decimal places.)
Answer:
The data value corresponding to z = 1.96 in a normal distribution with mean 85.8 and standard deviation 4.83 is approximately 94.2238 (rounded to four decimal places).
Step-by-step explanation:
To find the data value corresponding to a given value of z, we use the formula:
z = (x - μ) / σ
where z is the standardized value (in standard deviation units), x is the data value we want to find, μ is the mean, and σ is the standard deviation.
Rearranging this formula to solve for x, we get:
x = z * σ + μ
Substituting the given values, we have:
x = z * 4.83 + 85.8
Let's say we want to find the data value corresponding to z = 1.96 (which corresponds to the 97.5th percentile in a standard normal distribution). Then we can plug this value into the formula:
x = 1.96 * 4.83 + 85.8
Simplifying the right-hand side, we get:
x = 94.2238
Therefore, the data value corresponding to z = 1.96 in a normal distribution with mean 85.8 and standard deviation 4.83 is approximately 94.2238 (rounded to four decimal places).
Write down the corresponding side and angles from given congruent triangles.
Answer:
Hope the pictures will help you...........
10m + n2/4 when m= 5 and n=4
Answer:
52
Step-by-step explanation:
10(5) + (4×2)/4
50+ 8/4
50+ 2
52
Does exercises improve reaction time? Francie & Sebastian used an online game to measure the reaction time of 15 randomly selected students from their school before and after each student had run two laps on a track.What is the response variable?
To analyse the influence of exercise on reaction time, the researchers equation might have utilised the average change in reaction time for the group as a whole or looked at individual changes in reaction time.
What does exercise do?In several trials, regular exercise has been proven to enhance reaction time. It is feasible that running two laps around a track will improve reaction time for the students in this study.
In this study, the response variable is the reaction time of 15 randomly selected students before and after running two laps on a track. The researchers measured reaction time using an online game, which was most likely a timed task that required participants to respond fast to a stimuli. To analyse the influence of exercise on reaction time, the researchers might have utilised the average change in reaction time for the group as a whole or looked at individual changes in reaction time.
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Find all solutions
for cotx=-1
Answer:
\(\cot(x) = -1\) whenever \(\displaystyle x = k\, \pi-\frac{\pi}{4}\) radians, where \(k\) could be any integer (\(k \in \mathbb{Z}\), which includes positive whole numbers, negative whole numbers, and zero.)
Step-by-step explanation:
\(x = 45^\circ\) (as in isoscele right triangles) would ensure that \(\displaystyle \cot(x) = 1\). Since cotangent is an odd function, \(\cot(-45^\circ) = -1\).
Equivalently, when the angles are expressed in radians, \(\cot(-\pi / 4) = -1\).
The cycle of cotangent is \(\pi\) (or equivalently, \(180^\circ\).) Therefore, if \(k\) represents an integer, adding \(k\, \pi\) to the input to cotangent would not change the output. In other words:
\(\displaystyle \cot\left(k\, \pi - \frac{\pi}{4}\right) = \cot(-\pi / 4) = -1\).
Hence, \(\displaystyle x = k\, \pi-\frac{\pi}{4}\) would be a solution to \(\cot(x) = -1\) whenever \(k\) is an integer.
Since \((-\pi / 4)\) is the only solution to this equation in the period \((0,\, \pi)\), all real solutions to this equation would be in the form \(\displaystyle x = k\, \pi-\frac{\pi}{4}\) (where \(k\) is an integer.)
PLEASE HURRY AND ANSWER!!!!
The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.
How to calculate the probability of the chosen event?To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:
Probability = possible outcome/ sample space
Where possible outcome = 2
sample space = A,B,B,B,C,C,D,D,D,E = 10
Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.
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helpppp...........................
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
a hexagon has 6 sides , then
sum = 180° × (6 - 2) = 180° × 4 = 720°
12
the polygon has 5 sides , so
sum = 180° × (5 - 2) = 180° × 3 = 540°
sum the interior angles and equate to 540
y + 90 + 120 + 90 + 110 = 540
y + 410 = 540 ( subtract 410 from both sides )
y = 130
13
the polygon has 7 sides , so
sum = 180° × (7 - 2) = 180° × 5 = 900°
sum the interior angles and equate to 900
p + 90 + 141 + 130 + 136 + 123 + 140 = 900
p + 760 = 900 ( subtract 760 from both sides )
p = 140
Rowan bought a large bag of jellybeans. She divided the jellybeans into 9 smaller bags that each contained 6 ounces. Write a division EQUATION (not answer) that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought.
The division equation that could be used to find the amount of jellybeans, b, in ounces, that were in the original bag that Rowan bought is given as follows:
6 = b/9.
How to obtain the division equation?The division equation is obtained applying the proportions in the context of this problem.
The number of ounces per bean is given by the division of the total amount of jellybeans and the number of bags.
The parameters for this problem are given as follows:
6 ounces per bag.9 bags.Hence the division equation is given as follows:
6 = b/9.
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Determine the value of f(4) given the function shown. *
f(x) = x² + 3
A. 19
B. -1
C. -5
D. -13
The value of function f (4) is,
⇒ f (4) = 19
We have to given that;
The function is,
⇒ f (x) = x² + 3
Now, WE can find the value of f (4) by substitute x = 4 in above function as,
⇒ f (x) = x² + 3
Plug x = 4;
⇒ f (4) = 4² + 3
⇒ f (4) = 16 + 3
⇒ f (4) = 19
Thus, The value of function f (4) is,
⇒ f (4) = 19
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Compare -4 ____ -12 9 ___ -35
Answer:
-4>-12
9>-35
Step-by-step explanation:
Answer: -4 >-12 9>-35
Step-by-step explanation:
if you run at an average speed of 10 mi/h, how long will it take you to run 2.5 miles?
Answer:
10 minutes
Step-by-step explanation:
10 divided by 2.5
help with these questions immediately
Problem 1
Answer: Choice C) 1/2--------------------
Explanation:
Let's plug 8 into f(x)
\(f(x) = \frac{x+3}{x^2-4x-21}\\\\f(8) = \frac{8+3}{8^2-4(8)-21}\\\\f(8) = \frac{8+3}{64-32-21}\\\\f(8) = \frac{11}{11}\\\\f(8) = 1\\\\\)
Repeat for g(x)
\(g(x) = \log_{4}(x)\\\\g(8) = \log_{4}(8)\\\\g(8) = \frac{\log(8)}{\log(4)}\\\\g(8) = \frac{\log(2^3)}{\log(2^2)}\\\\g(8) = \frac{3*\log(2)}{2*\log(2)}\\\\g(8) = \frac{3}{2}\\\\\)
I used the change of base formula in the third step.
Lastly, we subtract the results like so
\((g-f)(x) = g(x) - f(x)\\\\(g-f)(8) = g(8) - f(8)\\\\(g-f)(8) = \frac{3}{2} - 1\\\\(g-f)(8) = \frac{3}{2} - \frac{2}{2}\\\\(g-f)(8) = \frac{3-2}{2}\\\\(g-f)(8) = \frac{1}{2}\\\\\)
========================================================
Problem 2
Answer: Choice A) 8--------------------
Explanation:
Through trial and error (I recommend the rational root theorem), you should find that the roots of R(x) are: -1, 3, and 8
We'll only focus on positive x values. So we focus on the roots 3 and 8.
It turns out that the R(x) curve dips below the x axis when x is between 3 and 8. When x > 8 is when R(x) is positive and goes upward forever. This represents when the company is making money.
The company does make money when x is between 0 and 3; however, this is a short timespan compared to the other interval. So it's much more effective and realistic to say that the company makes money after 8 days.
In other words, yes the company makes money between day 0 and day 3, but from day 3 to day 8 is when the company loses money. Ultimately the company is profitable again when it's beyond day 8.
you invest $2000 in an account that pays simple interest of 2% for twenty years. what amount of money will you have in 20 years
Answer:
$2971.9
Step-by-step explanation:
2000*(1+2%)^20 = 2971.895
Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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The owner of the Texans football team wants to paint their red, white, and blue logo on the side of a building at their training facility. However, the existing paint, which would comprise the background for the logo, is beginning to deteriorate. The owner is considering re-painting the building with a special weatherproof paint prior to adding the logo. If the special background paint costs $1.25 per square foot, how much money will the owner have to spend on the paint for the background
Answer:
$393.75
Step-by-step explanation:
cost of special background paint = $1.25 per square foot
Area of background = area of triangle + area of rectangle
= 1/2 ( b*h) + L * B
= 1/2 ( 5 * 6 ) + 5 * 4 = 15 + 20 = 35 yd^2
Given that 1 yd^2 = 9 ft^2
35 yd^2 = ( 9 * 35 ) ft^2
Hence area of background = 315 ft^2
Cost = 315 * 1.25 = $393.75
For older browsers that do not support media queries, Cascading Style Sheets (CSS) provides the _____ keyword to hide style sheets from those browsers.
Answer:
24
Step-by-step explanation:
1 2 3 4
5. SOLVE THIS EQUATION BELOW
Answer:
4( p+r) = q
Step-by-step explanation:
p = q/4 - r
Add r to each side
p + r = q/4 -r+r
p+r = q/4
Multiply each side by 4
4( p+r) = q/4*4
4( p+r) = q
Explain how to determine if a number is a solution of the equation. n + 6 = 33 for n = 27
Answer:
n= 27 is the only solution to the equation
Step-by-step explanation:
n + 6 = 33
Subtract 6 from each side
n+6-6 = 33-6
n = 27
Neveah invested $80,000 in an account paying an interest rate of 5 1/8% compounded continuously. Aaliyah invested $80,000 in an account paying an interest rate of 5 3/8% compounded monthly. After 13 years, how much more money would Aaliyah have in her account than Nevaeh, to the nearest dollar ? PLEASE HELP
Answer:
$4894
Step-by-step explanation:
Answer:
4894
Step-by-step explanation:
The monthly rents (in dollars) paid by 9 people are given below.
(Note that these are already ordered from least to greatest.)
mean,median.
780,910,980,1000,1025,1045,1070,1095,1185
Suppose that one of the people moves. His rent changes from 1185 to 100
Answer:
increases by 30
Step-by-step explanation: its right
Please help me solve this, it’s the last question.
The value of the double integration is 7776 after solving and integration. the answer is 7776.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
Double integration (x + y) dA
y = x²
y² = 216x
y = √216 √x
∫∫(√216 √x + x²)
After solving:
\(\rm \int _0^{36}\int _0^6\:\left(\sqrt{216}\:\sqrt{x}\:+\:\:x²\right)dxdy\)
=7776
Thus, the value of the double integration is 7776 after solving and integration. the answer is 7776.
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A pizzeria has two different types of crust, 3 types of cheese and 4 toppings. A personal pizza can only have one type of cheese and one topping. What is the probability of choosing a thin crust with parmesan cheese and pepperoni?
Answer:
1/24
Step-by-step explanation:
So let's first find the total number of ways the pizza can be made.
2 types of crust
3 types of cheese
4 toppings
So if we choose crust 1, we have 3 options for cheese. For each of these options, we have 4 options for toppings. 4 x 3 will give us the number of topping-cheese combinations available, and likewise, we can apply this to the two crusts, getting 4 x 3 x 2, or 24.
Next, we will find the probability of choosing a thin crust with parmesan cheese and pepperoni. That's 1 crust, 1 cheese, and 1 topping, giving us 1/24 as this is a single combination.
(Probability of event)/(All possible events)
1/24
Which of the following is a value of r for which (r + 2)(r − 3) = 0?
Answer:
r = -2 or r = 3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
r2−r−6=0
Step 2: Factor left side of the equation.
(r+2)(r−3)=0
Step 3: Set factors equal to 0.
r + 2 = 0 or r − 3 =0
r = −2 or r = 3
Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples? Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples?Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples?Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples? Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples? Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her friend then divided the cost of the purchase evenly. Which expression can be used to determine how much Nicole and her friend each paid for the apples?
140,100,71.4, ,36.44 what is the missing number
The required missing number is 51.02
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar2, ar3, ar4, ar5, .....
Given here the numbers 140,100,71.4, ,36.44
clearly 140/100=100/71.4=1.4
Thus the given set of numbers form a geometric progression with common ratio 1.4
Therefore the complete set of numbers are 140,100,71.4,51.02,36.44
Hence, the required numbers is 51.02
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My dad is X years old and i am Y years old. How old shall we be in 10 years time.
I'm assuming X and Y are current present day ages.
Simply add 10 to each variable to find the future ages ten years from now.
Your dad's future age = X+10
Your future age = Y+10
Since we don't know what X or Y is, we cannot combine those terms. We leave them as is.
Answer:
\(\bold{x+10,y+10}\)
Step-by-step explanation:
Hi there!
Right now, your dad's age is X years.
In 10 years, it will be x+10.
If your age is y years, in 10 years, it will be y+10.
No matter what x is, no matter what y is, it will be x+10 and y+10.
Thus, x+10 and y+10 is our final answer.
Hope it helps! Enjoy your day!
\(\bold{GazingAtTheStars}\)
An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sink hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point A on one side of the sink hole and B on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the other ends of the two ropes meet at point C. Then you recreate the same triangle by using the distance from AC and BC and creating new segments CE and CD. The distance DE is 52.2 ft.
a. What type of triangles have you created?
b. How do you know the triangles are congruent?
c. How far across is the sink hole?
d. What is the perimeter of the triangle ABC?
A) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
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Answer:
Step-by-step expA) The type of triangles are congruent triangles
B) By the use of SAS Congruency Postulate
C) The distance across for the sink hole is: 52.2 ft
D) The perimeter of triangle ABC is: 172.2 feet.
How to solve congruent triangles?
A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.
B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.
C) We know that:
AB = ED = 52.2
AB is the distance across the sink hole. Thus, it is 52.2 feet
D) AB = 52.2
BC = 70
AC = 50
Thus:
Perimeter of triangle ABC = AB + BC + AC
Perimeter of triangle ABC = 52.2 + 70 + 50
Perimeter of triangle ABC = 122.2 + 50
Perimeter of triangle ABC = 172.2
The perimeter of triangle ABC is 172.2 feet.
lanation:
I need help pleaseeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation: [-2.19] = -3
[3.67] = 3
[-0.83] = -1
The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.
This can be generalized as given below:
[x] = -2, -2 ≤ x < -1
[x] = -1, -1 ≤ x < 0
[x] = 0, 0 ≤ x < 1
[x] = 1, 1 ≤ x < 2
Answer:
y = - \(\frac{3}{2}\) x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line
m = \(\frac{0-3}{0-(-2)}\) = \(\frac{-3}{0+2}\) = - \(\frac{3}{2}\) , then
y = - \(\frac{3}{2}\) x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (0, 0 )
0 = - \(\frac{3}{2}\) (0) + c = 0 + c , so
c = 0
y = - \(\frac{3}{2}\) x + 0 , that is
y = - \(\frac{3}{2}\) x
Solve each equation.
2(−3)=14
-5(−1)=40
12(+10)=24
16(+6)=11
57(−9)=25
Answer:
jkudrhytiu4wry bui634y uiyb4uiyttui4ytui4yuityu34w ytiuyy4ty4oi8t4otiu4ioyt
Step-by-step explanation:
ryeropiutopier5uoiyturloiuy6otieruoiyluriluyrtuur6
4. Sketch the graph of F(x) = 1 +x/x²-1
The graph of the function is attached below.
What is the graph of a function?The graph of a function shows the correlation between its inputs (represented by x-values) and matching outputs (represented by y-values). It is a means of illustrating the actions and traits of a function.
Plotting points that conform to the function's rule in a cartesian coordinate system results in the graph of the function. An input-output pair for the function is represented by each point on the graph. The point's x-coordinate represents the input value, while its y-coordinate represents the output value.
We can further use the graph to determine the range, domain, y-intercept, x-intercept and so many others from a graph.
In the given problem;
The graph of the function f(x) = 1 + x / x² - 1 is attached below;
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