Answer:
2.25:)
Step-by-step explanation:
Nathaniel's car used 2/3 of a gallon to travel 11 miles. How many miles can the car go
on one gallon of gas?
Nathaniel’s travel 16.5 miles with one gallon gas
Arithmetic generalization in which letters representing numbers are combined using arithmetic rules. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions.
Given that Nathaniel's car used 2/3 of a gallon to travel 11 miles
We have to find how many miles can the car goon one gallon of gas
2/3 gallons = 11 miles
1 gallon = ?
= (11x 1)/(2/3)
= 33/2
= 16.5 miles
Therefore Nathaniel travel 16.5 miles with one gallon gas
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Question 4(Multiple Choice Worth 6 points)
(03.02 MC)
How does the graph of g(x) = (x + 2)3 - 6 compare to the parent function of f(x) = x³?
Og(x) is shifted 2 units to the right and 6 units down.
Og(x) is shifted 6 units to the right and 2 units up.
g(x) is shifted 2 units to the left and 6 units down.
g(x) is shifted 6 units to the left and 2 units down.
The relationship of the graph g(x) = (x − 2)³ + 6 compare to the parent function of f(x) = x³ is that g(x) is shifted 2 units to the right and 6 units up.
What is translation of coordinates?Translations are a transformation technique that changes the position of an object from one point on the plane to another.
Given is a function, g(x) = (x − 2)³ + 6, we need to compare the graph of g(x) = (x + 2)³ - 6 to the parent function of f(x) = x³
The function compared to f(x) = x³, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up
Hence, the relationship of the graph g(x) = (x − 2)³ + 6 compare to the parent function of f(x) = x³ is that g(x) is shifted 2 units to the right and 6 units up.
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a fair coin is tossed five times, and each time the coin lands tails up. if the coin is then tossed 1990 more times, how many tails are most likely to appear for the 1990 additional tosses?
Probability of getting tails are most likely to appear for the 1990 additional tosses will be 1/32.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
Here,
The coins gets tail always,
=(1/2)^5
=1/32
For the 1990 additional tosses, there is a 1/32 chance that a tail will appear.
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Write an equation in slope-intercept form of the line with the given
characteristics.
slope = 2/5
; passes through (–3, 1)
Answer:
The equation of the line in slope-intercept form is [tex]y=0.4x+2.2[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form can be calculated as follows ?
The first step is to find the slope-intercept form of the given line by the point-slope form formula as follows
[tex]y-y_{1}=m(x-x_{1})[/tex]
Where [tex]m[/tex] is the slope of the line
Write the given value of the slope
[tex]m=\frac{2}{5}[/tex]
Convert the value of the slope into decimal
[tex]m=0.4[/tex]
The second step is to substitute [tex]0.4[/tex] for [tex]m[/tex], [tex]1[/tex] for [tex]y_{1}[/tex], [tex]-3[/tex] for [tex]x_{1}[/tex] in the point-slope form formula
[tex]y-1=0.4(x-(-3))[/tex]
Take out the inner bracket on the right side of the equation
[tex]y-1=0.4(x+3)[/tex]
Expand the right side of the equation
[tex]y-1=0.4x+1.2[/tex]
Add [tex]1[/tex] to both sides of the equation
[tex]y-1+1=0.4x+1.2+1[/tex]
Simplify the equation
[tex]y=0.4x+2.2[/tex]
Hence the equation of the line in slope-intercept form is
[tex]y=0.4x+2.2[/tex]
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PQR is an isosceles triangle in which PQ= PR Mand N are points on PQ and PR such that angle MRQ= angle NQR. Prove that triangles QNR and RMQ are congruent.
We have proved that triangles QNR and RMQ are congruent.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
∠MRQ ≅ ∠NQR . . . . given
QR ≅ RQ . . . . reflexive property
∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR
ΔQNR ≅ Δ RMQ . . . . ASA postulate
Hence, we have proved that triangles QNR and RMQ are congruent.
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Y=4/5x-5
Slope:
Y-intercept:
Charlotte is making 6 pounds of trail mix using raisins and 3 different types of nuts.
The table shows the amounts of different types of nuts that she has.
Type of Nut Amount (in pounds)
almonds
7
8
cashews
1
1
2
peanuts
2
3
8
pecans
1
1
4
walnuts
1
3
4
Charlotte uses all of the almonds, cashews, and peanuts that she has.
Which of the following explains how she can find the exact amount of raisins she needs?
A.
Round
7
8
pound to 1 pound,
1
1
2
pounds to 2 pounds, and
2
3
8
pounds to 2 pounds.
Then add the rounded amounds and subtract that total from 6 pounds.
B.
Add
7
8
pound,
1
1
2
pounds,
2
3
8
pounds,
1
1
4
pounds, and
1
3
4
pounds.
Then subtract 6 pounds from that total.
Answer:
It Should be B because You need to add all of the pounds and subtract it by six
Step-by-step explanation:
Find the value of the specified trig ratio. Be sure to reduce when possible.
The value of cosC is 8/17.
What is the trigonometric ratio?
Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.
Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.
In the figure,
Adjacent=CB=16
hypotenuse=AC=34
The formula for the cos function:
cos[tex]\theta[/tex]=adjacent/hypotenuse
cosC=16/34
divide 16 and 34 by 2 to simplify further
cosC=8/17
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Question 3 of 7
Find the 10th term of the geometric sequence whose common ratio is
1
and whose first term is 7.
A pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%, what is the total amount paid for the jeans?
The total amount that a customer will pay for the jeans is $33.696.
How to calculate the value?From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,
The value of the sales tax will be:
= Sales percentage × Amount
= 5.3% × $32
= $1.696
The total amount paid will be:
= Cost + Tax
= $32 + $1.696
= $33.696
The amount is $33.696.
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A bank machine uses pin numbers of 4 digits. The of odd pin numbers is:
Answer:15
Step-by-step explanation:hope this helps
Alex ha 7 pound of birdeed and 5 bird feeder. Which model how how much birdeed he hould put into each bird feeder?
A. B. C. D
Alex puts (7/5) pounds of food in each bird feeder.
Given that,
Alex has 7 pound of bird food. He puts an equal portion into 5 bird feeders. How much bird food, in pounds, does he put in each bird feeder
Let's assume that he filled each bird feeder with x pounds.
then,
The equation is
(Pound in each feeder) * (Total feeders) = Amount of food.
When all values are present,
→ x * 5 = (7)
→ x = 7 ÷ 5
→ x = (7) * (1/5)
→ x = (7/5) pounds.
Hence, Alex put (7/5) pounds of food in each bird feeder .
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The Grade 8 students had an
end-of-the-year dance.
The disc jockey charged $85 for setting
up the equipment, plus $2 for each
student who attended the dance.
The disc jockey was paid $197.
How many students attended the dance?
a) Write an equation you can use to
solve the problem.
b) Solve the equation.
c) Check your answer and explain
how you know it is correct.
Answer:
1. You can use the equation 2x + 85 = 197
2. 2x+ 85 =197
-85 -85
-------------------------
2x = 112
/2 /2
------------------------
x = 60
x is the number of students that went to the dance
plug in 60 into x in the equation I gave to check
If log 10 to base 8 = X, evaluate log 5 to base 8 in terms of X.
A. 12X
B. X-14
C. X-13
D. X-12
Answer:
Step-by-step explanation:
what is the slope of a line that passes through the points (-1, -3) and (-19,-18)
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
slope of a line :
the measurement of a line's direction in a coordinate plane.It is denoted by m.m = (y₂ - y₁)/(x₂ - x₁)m = tanθA = (x₁, x₂) = (-1, -3)
B = (y₁, y₂) = (-19,-18)
The slope of a line is given as :
slope = (y₂ - y₁)/(x₂ - x₁)
slope = (-19 - (-3))/(-18 - (-1))
slope = (-19 + 3)/(-18 + 1)
slope = ( -16 )/ ( -17)
slope = 16/17.
The slope of the line that passes through the points (-1, -3) and (-19,-18) is 16/17.
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URGENT: If a pack of five compasses sells for $3.95,
How much does one compass cost?
Answer:
0.79 dollars
Step-by-step explanation:
Divide 3.95 by five to find the cost of one compass.
What is the 2s fact?.
The value of 2 factorial would be 2.
What is a factorial of a number?
Factorial is the product of all positive integers less than or equal to a given positive integer, denoted by that integer, and an exclamation point in mathematics. Thus, factorial seven is written 7! which means 1*2*3*4*5*6*7. Factorial zero is defined as one.
As the definition says that the factorial is the product of all the positive integers less than or equal to the given number till one.
We have to find the value of 2 factorial.
2! = 2 * 1
= 2
Hence, the value of 2 factorial would be 2.
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Given that sec(θ) = 8 and tan(θ) < 0, find the following:
cos(θ) =
sin(θ) =
tan(θ) =
csc(θ) =
cot(θ) =
Rationalize denominators and tell which ones are negative.
The value cos(θ), sin(θ), tan(θ), csc(θ) and cot(θ) are 1/8, (-3√7)/8, -3√7, -(8√7)/21 and -√7/21 respectively
How to find the trigonometric ratio of the angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Given that: sec(θ) = 8 and tan(θ) < 0. This implies:
cos (θ) = 1/8 and tan(θ) is negative. This means θ is quadrant 4
(Note: cos (θ) = 1/sec(θ) )
Using the given information, we can sketch the location of the angle θ in the quadrant (See the attached image).
Thus, we can calculate the value of side d using the Pythagoras theorem
d = √(8² - 1²) = √63 = 3√7
The side is -d = -3√7
Note: the side d is negative in the quadrant
Therefore:
cos(θ) = 1/sec(θ) = 1/8
sin(θ) = (-3√7)/8
tan(θ) = (-3√7)/1 = -3√7
csc(θ) = 8/(-3√7) = - (8√7)/21
cot(θ) = -1/(-3√7) = -√7/21
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The legs of an isosceles triangle are 0.3 foot less than twice the base. The perimeter of the triangle is 4.9 feet.
What is the length of one of the triangle’s legs?
A. 1.1 feet
B. 1.4 feet
C. 1.9 feet
D. 2.2 feet
Answer:
it's D of the triangles legs this is the answer
Himesh has blocks like the one shown below. 6 cm -8 cm- -7 cm- He wants to build a 40 cm high tower with such blocks. What is the LEAST number of blocks with which he can do this?
The least number of blocks with which he can do is 168 blocks.
What is the least Common Multiple (LCM)?
The Least Common Multiple (LCM) is a method for determining the smallest common multiple of two or more numbers. A common multiple is a number that is the product of two or more numbers.
Least number of blocks = LCM of 6cm, 7cm, and 8cm.
Multiples of 6 - 6,12,18,24,30,36,42,48,54,60
Multiples of 7 - 7,14,21,28,35,42,49,56,63,70
Multiples of 8 - 8,16,24,32,40,48,56,64,72,80
Common Multiples - 168
Least Common Multiple - 168
So the least number of blocks with which he can do is 168 blocks.
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An equation is shown:
−np − 4 = 2(c − 3)
Which of the following solves for n?
n = the quantity 2 times c plus 2 all over negative p
n = the quantity 2 times c plus 10 all over negative p
n = the quantity 2 times c minus 2 all over p
n = the quantity 2 times c minus 10 all over p
The solution of given equation for n would be n = (2c - 2)/(-p)
In this question, we have been given an equation.
We solve given equation for n.
−np − 4 = 2(c − 3)
−np − 4 + 4 = 2(c − 3) + 4
−np= 2c - 6 + 4
-np = 2c - 2
np = -2c + 2
np * 1/p = (-2c + 2) * (1/p)
n = (-2c + 2)/p
n = (2c - 2)/(-p)
Therefore, the solution of given equation for n would be n = (2c - 2)/(-p)
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Answer:
The answer would be n = (2c - 2)/(-p)
Step-by-step explanation:
Hope this helps! :D
Explain how to find the distance between 1 and -3 on a number line.
Answer: Distance can't be negative, so it must be positive. That's the first thing you need to know. To find the distance, you take the difference between the two points.
1 - (-3) = 4
(second point on the number line) - (first point on the number line)
Mr Pilgrim has a turkey farm. He has one male turkey for evey 17 female turkeys. if he has 289 females, how many male turkeys does he have? can the number of female turkeys be expressed using exponents? if so, how?
There are in total 17 Male Turkey in the farm
What is Division?
Division is one of the four basic operations of arithmetic, which are the methods through which numbers are joined to form new numbers. Addition, subtraction, and multiplication are the other operations.
Solution:
Here we will use the concept of basic division
Since, there is 1 male turkey for every 17 female turkey
Therefore, it can be said that
Total Male Turkeys for 289 Female Turkey = 289 / 17
Total Male Turkey = 17
Yes we can express the number of female turkey in exponent as [tex]17^{2}[/tex]
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You need 2yds of fabric for 3 pillows. And 6yds to cover 9 pillows how much fabric to cover 15 pillows
With respect to the pattern, 10yds of fabric will be required to cover 15 pillows.
Define pattern in mathematics.
A series of identical objects, forms, or numbers is referred to as a pattern in mathematics. Every type of event or thing has a pattern that we can associate with it. An object's membership in a pattern is determined by a rule, which identifies which items do and do not fit the bill.
Solution Explained:
As seen from the question, the patterns are increasing by 4 and 6.
PATTERN 1: 2, 6, 10...
PATTERN 2: 3, 9, 15...
Hence, the next number is 10. So, 10yds of fabric will be required to cover 15 pillows.
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Which best describes the range of the function f x 2 3 x?.
The range of the function f(x) = 2(3)x is best described by y > 0. Particularly the function when the constant is e, a function whose value is a constant raised to the power of the argument.
What is range of function?The difference between the lowest and highest values in a list or set is known as the range. Put all the numbers in order before determining the range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response. The difference between the highest and lowest values for a particular data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the provided data set is 2, 5, 8, 10, and 3. As a result, the range may alternatively be thought of as the distance between the highest and lowest observation.
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A rental car company charges a daily rate of $35 to rent and $0.75 a mile to drive. The bill was $47. Write and solve an equation to find out how many miles were driven on this bill.
Answer:
16 miles
Step-by-step explanation:
Let m be the number of miles.
[tex]35 + .75m = 47[/tex]
[tex].75m = 12[/tex]
[tex]m = 16[/tex]
one of the people involved in the accident says that he was traveling 52 mph when he braked. how long in feet should his car's skid marks be?
Answer:
Step-by-step explanation:
The equation is V = √(20L).
Solve this equation for L and the result is L = V2/20
Since V = 57 mph, putting this value into the equation, L = (57)2/20 = 162.45 ft should be his skid marks
fat content in 10 hotdogs is measured as: 25.2, 21.3, 22.8, 17, 29.8, 21, 25.5, 16, 20.9, 19.5. find a 95% prediction interval that bounds the fat content of the next hot dog.
Statistics with a 95% prediction interval that indicate how much fat the next hot dog will contain 21.83±2.917
Take into account the following sample of n = 10 randomly chosen hot dogs' fat content (in percentage):
A 95% CI for (interval estimate of) the population, given that these were chosen from a normal population distribution
x±[tex]t_{0.025,9} * s/\sqrt{n}[/tex]
= 21.83± 2.262 * 4.079/[tex]\sqrt{10}[/tex]
= 21.83±2.917
But let's say you want to know how much fat will be in a single of this kind of hot dog before you consume it. Just x 21.90 makes a point prediction, which is comparable to a point estimate. Unfortunately, the statistical prediction provides no details regarding accuracy or dependability.
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Planes m and n intersect at line d. line a forms a right angle with line d. line b is diagonal and crosses line d. line c is on plane n and is diagonal. line e is on plane m and is slightly diagonal at the top of the plane. which are skew lines? check all that apply. a and b c and b b and e e and c a and e a and c
the answers are option 2 4 6
Answer:
B,D,F
Step-by-step explanation:
suppose you have 6 pairs of sock in your sock drawer and every pair has a unique color. it is still dark out in the morning when you get dressed, so you just pull socks out of the drawer at random, one at a time, until you have removed two matching socks. what is the probability that you pull out exactly 5 socks from your sock drawer in the morning before you get a matching pair of socks?
The probability there is at least one pair is therefore 1−p.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
It is little known, but socks have individual identities. There are (166) equally likely ways to choose 6 socks from the 16.Now we find the number of ways to choose 6 socks, so that there is no pair among them. There are (86) ways to choose the "types" of sock we will have. For each choice of 6 types, there are 26 ways to choose the actual socks. For at each chosen "type" of sock, we have 2 choices as to which of the two socks of that type to take.hence,The probability there is at least one pair is therefore 1−p.
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