Answer: Oy = 15.5x
Step-by-step explanation: Gas mileage refers to the quantity of miles driven per unit volume of gasoline, typically expressed as "miles per gallon." In the context of the present inquiry, the vehicle in question exhibited a capacity to traverse a distance of 310 miles subsequent to the utilization of 20 gallons of gasoline. Thus, it is possible to calculate the gas mileage through the division of the quantity of gas consumed by the distance elapsed, resulting in:
The fuel efficiency of a vehicle, represented by the metric of gas mileage, is typically calculated by the ratio of distance traveled in miles to the amount of fuel consumed in gallons. In the present case, the gas mileage is equivalent to the quotient of 310 miles by 20 gallons, resulting in an efficiency rating of 15.5 miles per gallon.
How do you express 0.000 000 000 000 1 in exponential form.
Answer:
1 x 10^-12
Step-by-step explanation:
....
Riley wants to put a poster in a frame. The original poster is 11 inches wide and 14 inches tall. The frame will be x inches thick on each side. The
figure shows the poster and its frame.
xin.
xin.
14 in.
xin.
11 in.
xin.
Riley knows he wants the total area of the poster and frame together to be no more than 320 square inches.
Which inequality correctly models this situation?
A 2 + 11x + 14 = 320
B. 2 + 25x + 154 3 320
OC. 4x2 + 11x + 14 < 320
OD
4x2 + 50x + 154 3 320
An inequality that correctly models the situation is:
4x² + 50x + 154 ≤ 320
The correct answer is an option (D)
Let us assume that l represents the length (height) and w represents the width of the poster and frame together.
Here, the original poster is 11 inches wide and 14 inches tall and the frame will be x inches thick on each side.
So, the height l would be,
l = (14 + 2x) inches
and the width w would be,
w = (11 + 2x) inches
We know that the formula for the area of rectangle.
A = l × w
So, the expression for the area of the poster and frame together would be,
A = (14 + 2x) × (11 + 2x)
A = 154 + 22x + 28x + 4x²
A = 4x² + 50x + 154
The total area of the poster and frame together to be no more than 320 square inches.
So, we get an inequality
A ≤ 320 in²
4x² + 50x + 154 ≤ 320 in²
Thus, the correct answer is an option (D)
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Find the complete question below.
[tex]Please help[/tex]
The new cost after the discount and tax are applied is $872.10, which is option (d).
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
First, let's calculate the amount of discount Angel will receive using the coupon code:
Discount = 15% of $950 = 0.15 x $950 = $142.50
Next, let's calculate the new price of the jacket after the discount is applied:
New price = $950 - $142.50 = $807.50
Now, let's calculate the amount of tax that will be applied to the new price:
Tax = 8% of $807.50 = 0.08 x $807.50 = $64.60
Finally, let's add the tax to the new price to get the total cost:
Total cost = $807.50 + $64.60 = $872.10
Therefore, the new cost after the discount and tax are applied is $872.10, which is option (d).
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Find the solution set of the inequality 4 � − 1 < 11. 4x−1<11.
Therefore , the solution of the given problem of inequality comes out to be x< 3, which denotes that x can be any real number below 3.
What is inequality, exactly?The distinction in algebra can be expressed by an amalgamation or set of two numbers since there is no indicator for it. Equity usually comes after equilibrium. The persistent gap in standards is what causes inequality. Disparity and equality are not the same thing. As was the least favourite symbol, despite the fact that its components are typically neither connected nor adjacent to one another.
Here,
We can use the procedures listed below to solve the inequality 4x - 1 11:
To isolate the term with x on one side of the inequality, add 1 to both sides of the inequality in step 1:
=> 4x - 1 + 1 < 11 + 1 4x < 12
Step 2: To find x, multiply both sides of the inequality by 4.
=> 4x/4 < 12/4 x < 3
The answer to the inequality 4x - 1 11 is therefore x< 3, which denotes that x can be any real number below 3.
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the weekly earnings of bus drivers are normally distributed with a mean of $395. if only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?
The value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
To solve this problem, we can use the standard normal distribution table or a calculator that provides the inverse of the standard normal distribution. Let X be the weekly earnings of the bus drivers, then we have:
P(X > $429.35) = 0.011
Using the standard normal distribution table or calculator, we can find the z-score that corresponds to a probability of 0.011, which is approximately -2.33. We can then use the formula for standardizing a normal variable:
z = (X - μ) / σ
where μ is the mean and σ is the standard deviation of the distribution. Substituting the given values, we have:
-2.33 = ($429.35 - $395) / σ
Solving for σ, we get:
σ = ($429.35 - $395) / (-2.33) = $14.57
Therefore, the value of the standard deviation of the weekly earnings of the bus drivers is $14.57.
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question 1 help me asap
Answer:
-1 = (-1/2)(6) + b
-1 = -3 + b, so b = 2
y = -(1/2)x + 2, so m = -1/2 and b = 2
The price of the daily dinner special at Deb’s Dinner increases from $7.00 to $8.75. By what percent does the price of the dinner special increase?
The percent increase for the dinner is 25%
The first step is to calculate the increase
The price rose from $7 to $8.75
Increase= 8.75-7
= 1.75
Therefore the percent increase can be calculated as follows
1.75/7 × 100
= 0.25 × 100
= 25
Hence the percent increase is 25%
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every student who particpated in field day actives received a water bottle. the water bottle. the water bottle cam in 2 different colors. Based on your simulation how many students had to receive a water bottle in order to distribute water bottles in both colors?
Find the line parallel to y=5x+3 that includes the point (-1,6)
Write in y-y1=m(x-x1)
Answer:
y=5x-6
Step-by-step explanation:
Find the volume of the cylinder in terms of π.
A. 154π cm3
B. 406π cm3
C. 539π cm3
D. 1078π cm3
Answer:
Step-by-step explanation:
The correct answer is option D, 1078[tex]\pi[/tex] [tex]cm^{3}[/tex].
The volume of the cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h.
Radius = 7cm Height = 22cm.
Substituting the value in the formula, we get
[tex]\pi[/tex]*[tex]7^{2}[/tex]*22 = 1078[tex]\pi[/tex].
Hence the Answer is 1078[tex]\pi[/tex].
Answer:
3386.64 cm3
Step-by-step explanation:
i use this formula π r² h
for security purposes a jewelry company prints a hidden watermark on the logo of its official documents. the watermark is a chord located 0.7 centimeter from the center of a circular ring that has a radius measuring 2.5 centimeters. what is the length of the chord?
The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.
We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.
0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle.
Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.
sin(θ/2) = 0.7/2.5
[tex]θ/2 = sin⁻¹(0.7/2.5)[/tex]
θ/2 = 0.2793
θ=2×0.2793
θ ≈ 0.5586 radians
Now that we know θ, we can use the formula for the chord length of a circle.
chord length = 2 × radius × sin(θ/2)
Chord Length = 2 × 2.5 × sin(0.2793)
String length ≈ 1.397 cm
Therefore, the chord length is approximately 1.397 centimeters.
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In your notebook, draw a right angle and then draw a bisector of the right angle. Label all parts. What are some properties of the angles formed by the bisector? Use complete sentences for full credit.
The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.
When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties
They have equal measures: The two angles formed by the bisector have the same degree measurement.
They are adjacent: The two angles share a common side and vertex.
They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.
They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.
They are congruent: The two angles formed by the bisector are congruent to each other.
These properties are useful in solving problems involving angle bisectors in geometry.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What are some properties of the angles formed by the bisector?
mrs lopez types at a constant rate the constant of proportionality for the relationship between the number of words she types w, and the number of minutes she types m,is 38 write an equation to show this relationship
The equation that shows the relationship is w = 38m.
Writing an equation to show this relationshipIf Mrs. Lopez types at a constant rate, then the number of words she types is directly proportional to the amount of time she types. We can express this relationship using the formula:
w = km
where w is the number of words typed, m is the number of minutes spent typing, and k is the constant of proportionality.
We are given that k = 38, so we can substitute this value into the formula to get:
w = 38m
Therefore, the equation that shows the relationship between the number of words Mrs. Lopez types and the number of minutes she types is w = 38m.
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You want to conduct a poll to discover the proportion of individuals who believe that global warming is not going to be a problem. If you believe the proportion is about 80%, how many individuals will you need to sample to have a 90% confidence interval with a margin of error no more than 5%?at least 271at least 174at least 246
The number of individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5% is at least 246.
To determine the sample size needed for a 90% confidence interval with a margin of error no more than 5%, we can use the formula:
n = ([tex]z^{2}[/tex] * p * q) / [tex]E^{2}[/tex]
where:
n = sample size
z = z-score for the desired confidence level (in this case, 1.645 for 90%)
p = proportion of individuals who believe global warming is not a problem (0.8)
q = 1 - p (0.2)
E = margin of error (0.05)
Plugging in these values, we get:
n = ([tex]1.645^{2}[/tex]* 0.8 * 0.2) / [tex]0.05^{2}[/tex]
n ≈ 246
Therefore, at least 246 individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5%. The answer is at least 246.
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Destiny sells newspapers at a
newsstand outside of her grocery
store. She normally charges $2.35 for
a newspaper. Today, Destiny has
lowered the price by $0.50. So far, she
has sold 8 newspapers at the new
price. How much money has Destiny
made so far from selling newspapers
at the new price?
Answer:
$14.80
Step-by-step explanation:
First you need to subtract .50 from 2.35, which is 1.85.
Next you need to multiply 1.85 times 8.
1.85 x 8 = 14.80
Therefore, she has made $14.80 since the new price.
Sheryl makes $7 per pair of earrings, e and $13 per necklace, n, she sells what expression represents her total income
Answer:
You just need to create an expression with the variables then add them together to get the total income: 7e + 13n
which graph represents f(x) =3x-2
The graph that represents f(x) =3x-2 is the graph (b)
Which graph represents f(x) =3x-2From the question, we have the following parameters that can be used in our computation:
The equation: f(x) = 3x - 2
From the above equation, we have
f(x) = 3x - 2
The above equation is a linear function with the following features
Slope = 3
y-intercept = -2
This means that the graph intersects with the y axis at y = -2
Using the above as a guide, we have the following:
The graph intersects with the y axis at y = -2 and has a slope of 2 is graph (b)
Hence, the graph that represents f(x) =3x-2 is graph (b)
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If I have this sequence 2, 4, 6, . . . I can describe the rule as add 2
For each sequence below, describe the rule and write the
next two terms.
a)
b)
2, 5, 8,
The rule is
23, 18, 13,
The rule is
I NEED HELP ASAP. ITS DUE TODAY AND IM STUCKKKKKKK
The expression for the area of the triangle is given as follows:
A = 1.5x^4 + x³ - 0.5x².
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, as follows:
A = 0.5bh.
The dimensions for this problem are given as follows:
b = 3x² - x.h = x² + x.Hence the area of the triangle is given as follows:
A = 0.5(3x² - x)(x² + x)
A = 0.5(3x^4 + 3x³ - x³ - x²)
A = 0.5(3x^4 + 2x³ - x²)
A = 1.5x^4 + x³ - 0.5x².
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John is a healthy 20-year-old college student. He weighs 160 lbs and jogs at a moderate pace 3 days per week for 20 minutes. Based on this information, approximately how many grams of protein does he need dail
The protein requirement may be slightly higher, around 1.0 to 1.2 g/kg, this would put his daily protein needs between 72.6 and 87.1 grams.
As a healthy 20-year-old college student who jogs at a moderate pace 3 days per week for 20 minutes, John has an active lifestyle that requires a certain amount of protein to maintain his body.
Protein is an essential nutrient that is needed for the growth and repair of muscles, bones, and other tissues in the body.
According to the Dietary Reference Intake (DRI), the recommended daily allowance of protein for an adult male is 56 grams per day.
However, this amount can vary depending on a person's body weight, activity level, and other factors.
In John's case, he weighs 160 lbs and exercises moderately 3 days per week. Based on this information, he would need approximately 72-80 grams of protein per day.
This is because athletes and people who exercise regularly need more protein to repair and build muscle tissue.
To meet his daily protein requirements, John can include protein-rich foods in his diet such as lean meats, fish, eggs, dairy products, nuts, and beans.
It is also important for him to spread out his protein intake throughout the day rather than consuming all of it in one meal.
John needs approximately 72-80 grams of protein per day to support his active lifestyle and maintain his overall health.
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Consider ▰WXYZ. If WV=18, what is XZ?
WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.
what is trapezium ?A parallelogram with at least two pair of parallel sides is known as a trapezium in geometry (or a parallelogram in American English). The legs of a trapezium are the non-parallel sides, whereas the parallel sides are referred to as the bases. The legs of a zygomatic arch might be equal in length (isosceles) or varied in length (non-isosceles). By averaging the widths of the two bases and multiplying by the height, a trapezium's area can be determined (the perpendicular distance between the two bases). that is Area equals (a + b)*h / 2. where h is the trapezium's height and a and b are the lengths of the base's two parallel sides (the bases).
given
MN can be used in place of XV2 in the equation, and the result is simplified to:
XV² = (1/4) (WX + 18)² + h²
Now, we can add the following expression for XV2 to the equation for WX2:
WX² = 18² + XV²
WX² = 18² + (1/4) (WX + 18)² + h²
Adding and subtracting:
3WX² - 218WX - 18² = 4h²
We can now resolve WX:
WX is equal to (218 sqrt((218)2 - 43(-182))). / (2*3)
WX = 16 or -27
WX must be positive because it measures the width of a trapezoid's side. WX thus equals 16.
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Solve: 11x - 24 = 7x + 76
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 11x - 24 = 7x + 76
Then the value of x will be,
→ 11x - 24 = 7x + 76
→ 11x - 7x = 76 + 24
→ 4x = 100
→ x = 100 ÷ 4
→ [ x = 25 ]
Hence, the value of x is 25.
Hello and greetings Brainly users.
Answer:Therefore, the solution to the equation is x = 25.Step-by-step explanation:It is an exercise of linear equations with one variable is a fundamental topic in the study of algebra. These types of equations are characterized by being first-degree polynomials in one variable, and can be found in various contexts, such as physics, economics, engineering, among others. Therefore, the ability to solve these equations is essential in the training of any mathematics student and in the development of their ability to solve problems in real life situations.
A linear equation with a variable can be solved by means of a series of algebraic operations that allow us to simplify the expression and clear the variable to be solved. These operations include adding, subtracting, multiplying, and dividing, always maintaining equality between both sides of the equation. The ultimate goal is to find the numerical value that satisfies the equation, that is, the value that makes the equality true.
Solving linear equations with one variable is an important skill not only for mathematics students, but also for professionals in various fields. For example, in engineering, linear equations are used to model physical systems and phenomena, and their resolution is necessary to perform calculations and make informed decisions. In the economy, they are used to analyze the behavior of financial variables and make projections for the future.
Now we solve our exercise:
To solve the equation 11x - 24 = 7x + 76 we need to isolate the variable x on one side of the equation.
First, we can simplify both sides of the equation by combining like terms:
11x - 7x = 76 + 24
Which gives us
4x = 100
Next, we can solve for x by dividing both sides of the equation by 4:
4x/4 = 100/4
x = 25
Therefore, the solution to the equation is x = 25.
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PLEASE HELP I have no idea how to do this.. our teacher hasnt been here all week.. and I have no clue what this is..
solve for the value of V (9v+3)° 60°
The value of v is 13 degrees.
What are supplementary angles?Supplementary angles are a set of given measure of angles which add up to 180 degrees. Thus producing a measure of the sum of angles on a straight line.
To determine the value of v in the given diagram, we have;
60 + (9v + 3) = 180 (sum of angles on a straight line)
So that;
9v + 3 = 1890 - 60
9v + 3 = 120
9v = 120 - 3
= 117
v = 117/ 9
= 13
v = 13^o
The value of v in the question is 13 degrees.
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What is the result of the Python expression "3" + "4"?
a) "34"
b) "7"
c) 7
d) "7"
Answer:
a) '34'
Step-by-step explanation:
You want the result of executing the Python expression "3" +"4".
ConcatenationThe tokens "3" and "4" are both strings. In this context, the "+" operator does concatenation of the strings, so the result is the string "34". The Python interpreter outputs this as '34'.
A wedding tent is built in the shape of a right rectangular prism topped with a rectangular pyramid. The dimensions of the prism are 34 ft by 40 ft by 8 ft, and the height of the pyramid is 5 ft. Find the total volume of the tent. Round your answer to the nearest tenth if necessary.
The total volume of the wedding tent is approximately 13146.7 cubic feet.
What is the total volume of the tent?The volume of a rectangular prism is expressed as;
V = w × h × l
The volume of rectangular pyramid is expressed as;
V = (1/3) × l × w × h
Where w is the width, h is height and l is length
To find the total volume of the wedding tent, we need to find the volumes of the rectangular prism and the rectangular pyramid and add them together.
Given that: the dimensions of the rectangular prism are 34 ft by 40 ft by 8 ft.
Therefore, the volume of the rectangular prism is:
V_prism = w × h × l
V_prism = 34ft × 40ft × 8ft
V_prism = 10880 ft³
Next, we find the volume of the rectangular pyramid.
Note that: the dimensions of the base of the rectangular pyramid are the same as the dimensions of the rectangular prism, which are 34 ft by 40 ft.
Hence:
The volume of rectangular pyramid is expressed as;
V_pyramid = (1/3) × l × w × h
V_pyramid = (1/3) × 34ft × 40ft × 5ft
V_pyramid = 2266.7ft³
Now we can find the total volume of the tent by adding the volume of the rectangular prism and the volume of the rectangular pyramid:
V_total = V_prism + V_pyramid
V_total = 10,880 + 2266.7
V_total = 13146.7 ft³
Therefore, the total volume of the tent is 13,146.7 ft³
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Which graph represents the function f(x)=-|x-1|-2
Answer:
its in the picture
Step-by-step explanation:
Graph the absolute value using the vertex and a few selected points.
x y
−1 -4
0 -3
1 -2
2 -3
3 -4
basically, the answer is the graph that looks like this...
hope this helps ;)
find the indicated critical z value. find the critical value that corresponds to a 98% confidence level. group of answer choices
The critical z-value for a 98% confidence level is 2.33.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
Statistics plays a significant role in various fields, including business, economics, social sciences, medicine, engineering, and many others.
To find the critical z value for a 98% confidence level, we need to look up the z-value associated with an area of 0.01 in the upper tail of the standard normal distribution table (since 98% of the area lies within the confidence interval, leaving 2% in the tails).
Using a standard normal distribution table, we can find that the z-value that corresponds to an area of 0.01 in the upper tail is approximately 2.33.
Therefore, the critical z-value for a 98% confidence level is 2.33.
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find the midpoint between -3,5 and 1,6. It is asking to enter a point for the problem.
The midpoint between [tex]-3,5 and 1,6 is (-1,5.5)[/tex]
How can we find the mid point?The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between [tex]-3,5 and 1,6[/tex].
The coordinates of the two points are:
Point 1: ([tex]-3,5[/tex])
Point 2: ([tex]1,6[/tex])
To find the midpoint, we can average the x-coordinates and y-coordinates separately.
Midpoint's x-coordinate = (x-coordinate of Point [tex]1[/tex] + x-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]
Midpoint's y-coordinate = (y-coordinate of Point [tex]1[/tex] + y-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]
According to the problem
Midpoint's x-coordinate = [tex](-3+1)/2= -2/2= -1[/tex]
Midpoint's y-coordinate = [tex](5+6)/2= 11/2 = 5.5[/tex]
So, the midpoint between [tex]-3,5[/tex] and [tex]1,6[/tex] is [tex](-1,5.5)[/tex].
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The elephants at the Hancock Zoo are fed 4 9/10 barrels of corn each day. The buffalo are fed 1/6 as much corn as the elephants. How many barrels of corn are the buffalo fed each day?
Write your answer as a fraction or as a whole or mixed number.
PLEASE PLEASE PLEASE HELP
Answer: 49/60 of corn
Step-by-step explanation:
How I got this answer was I basically paid attention to the wording. 1/6 as much meaning x 1/6. So, I converted 4 9/10 to a fraction and got 49/10. Then, I multiplied 49/10 by 1/6 and got 49/60. The fraction can't be simplified any lower, so it is supposed to be left as is. Hope this helped!
The price of an item has dropped to $77 today. Yesterday It was $140. Find the percentage decrease.
The percentage price of the item has decreased by 45%.
What is the definition of percentage?
A percentage is a quantity or ratio that is stated as a fraction of 100.
"%" is the symbol for percentage.
For example, if 25 of 100 students in a class received a "A," we may represent this as a percentage by dividing the number of "A" students by the total number of students and multiplying by 100:
(25/100) x 100% = 25%
This signifies that 25% of the students in the class received a "A".
Now,
To obtain the % drop, subtract the difference between the original and new prices, divide by the original price, then multiply by 100 to get the percentage decrease.
The difference between the original and updated prices is equal to
140 - 77 = 63
So the percentage decrease is:
(63/140) x 100% = 45%
Therefore, the price of the item has decreased by 45%.
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