The acceleration of the particle is 1 foot per second square
How to determine the acceleration of the particle?From the question, we have the following parameters that can be used in our computation:
Velocity function v(t) = −t2 + 5t − 3
Express properly
So, we have
v(t) = -t² + 5t − 3
At time t = 3 seconds, we have
v(3) = -(3)² + 5(3) − 3
Evaluate
v(3) = 3
So, we have
Acceleration = v(3)/3
This gives
Acceleration = 3/3
Evaluate
Acceleration = 1 foot per second square
Hence, the acceleration is 1 foot per second square
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What is the range of the function with the graph given below ?
The graph in the question is a parabola that opens downwards.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions like print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This means that the range of the function is all real numbers less than or equal to the y-intercept of the parabola, which is 0 in this case. Therefore, the range of the function is all real numbers less than or equal to 0.
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A group of friends went to lunch. The bill before sales tax and tip was $37.50. A sales tax of 8% was added. The group then tipped 18% on the amount after the sales tax was added. What was the amount, in dollars, of the sales tax?
What was the total amount the group paid, including tax and tip?
Sales Tax = $3.00
The total amount paid by the group was $48.15
The amount of the sales tax can be calculated by multiplying the pre-tax bill of $37.50 by the sales tax rate of 8%:
Sales tax = $37.50 * 8% = $3.00
The total amount paid including tax and tip can be calculated by adding the amount of the sales tax to the pre-tax bill and then calculating the tip on the new total:
Total = $37.50 + $3.00 + ($37.50 + $3.00) * 18% = $37.50 + $3.00 + $7.65 = $48.15
So the total amount paid by the group was $48.15.
an altitude is drawn from the vertex of an isosceles triangle forming a right angle and two congruent triangles. as a result, the altitude cuts the base into two equal segments. the length of the altitude is 30 inches, and the length of the base is 10 inches. find the triangles perimeter. round to the nearest tenth of an inch.
The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches
How to find the perimeter of the isosceles trianglePerimeter of a triangle refers to the surface dimensions, this is calculated by the formula
Perimeter, P = a + b + c
where
a, b, c are sides of the triangle
The third side of the triangle will be calculated using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches
plugging the values as in the problem
let x be the required distance
x² = 30² + 5²
x² = 900 + 25
x² = 925
x = √925
x = 30.41 inches
Perimeter of the isosceles triangle
= 30.41 + 30.41 + 10
= 70.82 inches
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PLEASE FAST WILL GIVE BRANILY
A 12-foot tall tent pole is secured to the ground using a piece of rope 15 feet long from the top of the tent pole to the ground. If the tent pole makes a 90-degree angle with the ground, determine the number of feet along the ground from the tent pole to the rope.
3 feet
9 feet
19 feet
81 feet
Answer:
3 feet
Step-by-step explanation:
To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:
x^2 + 12^2 = 15^2
Solving for x, we get:
x = sqrt(15^2 - 12^2)
x = sqrt(9)
x = 3
Therefore, the distance from the tent pole to the rope is 3 feet.
i am number between 47 and 53 no two of my factors are the same number what number am i
A number between 47 and 53 such that the prime factors are not repeated is:
3*17 = 51
How to find the number?Remember that any number can be written as a product of prime factors.
If we want to find a number between 47 and 53, such that there are no repeated factors, we just need to take different primes and multiply them.
For example:
2*3*5*7 = 210
There are no repeated factors, but the number is not in the desired range.
2*5*7 = 70
Still not in the range.
You can try some times until you get for example:
3*17 = 51
This a number in the desired range, such that their prime factors are not repeated.
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Can any1 help with this pls
Rewrite 12x4y3 − 48x3y4 using a common factor.
Answer: 12x^3 y^3 (x − 4y)
(GCF is: 12x^3 y^3)
Step-by-step explanation:
This is the best I can do, sorry that I don't have an explanation.
6y2 + 3y - 1 4 for y = 1
The value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]
Why use the vertex form?In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.
In the equation we are given the value of y as: 1
[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]
Therefore, we can say that the value of the given polynomial is: 8
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Complete question is: Find 6y2 + 3y - 1 4 for y = 1
Two sides
Of the x that are multiplied together to get the top number of the x but added together to get the bottom number of the x like 24 too 25 on bottom
As a result, we take the square root of the both sides since if two expressions are equal, then so are their square roots.
What is the definition of the square root?By multiplying the square root of a positive integer by oneself, the number is obtained. As an illustration, 5 is the square root of 25, since 5 × 5 equals 25. Since (5) (5) = 25, 5 is also the square root of 25 as you can see. The symbol, which is, is always used to indicate the square root of a number of a variable x.
Here,
In this case, we're using the square to solve a quadratic equation.
Never forget to use both the negative and positive roots of the equation and to square the values of both sides.
We can accomplish this because to the rule that states that if two expressions are comparable, then their square roots are also equivalent.
As a result, we take the square root of both sides since if two expressions are equal, then so are their square roots.
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According to historical data, it is believed that 12% of American adults work more than one job. To investigate if this claim is still accurate, a random sample of 100 American adults is selected. It is discovered that 18 of them work more than one job. A researcher would like to know if the data provide convincing evidence that the true proportion of American adults who work more than one job differs from 12%. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the Large Counts Condition is not met. No, the randomness condition is not met.
Answer: The conditions for inference are met in this scenario.
In order to use inference to determine if the true proportion of American adults who work more than one job differs from 12%, the following conditions must be met:
The sample must be randomly selected from the population.
The sample size must be large enough (usually at least 30).
The sample must be representative of the population.
In this case, it is stated that a random sample of 100 American adults was selected, which meets the first condition.
The sample size of 100 is also large enough, which meets the second condition.
There is no information given about whether the sample is representative of the population, but this is not necessary for the conditions for inference to be met.
Therefore, the conditions for inference are met in this scenario.
Step-by-step explanation:
parallel abcd is similar to parallelogrem efgh. what is the lenght of gh?
The value of side GH as shown in the parallelogram is 2 units
What is an parallelogram?Parallelogram is a polygon that has four sides (quadrilateral) and opposite sides are always equal and parallel to each other
Two shapes are said to be similar if they have the same shape and the ratio of their corresponding sides are proportional. Also, their corresponding angles are equal to each other.
Parallelogram abcd is similar to parallelogram efgh, hence:
FG/BC = GH / CD
substituting:
7/21 = GH / 6
GH = 6 * 7/21 = 2
GH is 2 in
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17. Among 2.6, 2.006, 2.66 and 2.08, the largest number is (a) 2.006 (b) 2.08 (c) 2.6
Answer:
2.66
Step-by-step explanation:
Answer:
2.66
Step-by-step explanation:
look at first at tenths for the biggest no .if there is a tie proceed to hundredths for biggest no and so on
a parallelogram has sides that are in the ratio of 7:5 the premeter of the parallelogram is 48 how long does the longer side
Hello there!
Answer:
14
Step-by-step explanation:
Let the smaller side is x. Then the largest side is x * 7/5.
Perimeter is equal to 2 * (x + 7/5 * x) or 48.
2 * (x + 7/5 * x) = 48
5/5 * x + 7/5 * x = 24
12/5 * x = 24
12/5 * 5/12 * x = 24 * 5/12
x = 10.
Tha larger side is 10 * 7/5 = 14.
Step-by-step explanation:
Given ,
Ratio of the sides of a parallelogram are 7:5Perimeter of a parallelogram is 48To Find : Which side is longer
We know the formula to find the perimeter of a parallelogram is,
[tex]P = 2(a+b)[/tex]
We take 'x' to find out which side is longer
[tex]48 = 2(7x+5x)\\48 = 2(12x)\\48 = 24x\\\frac{48}{24} = x[/tex]
[tex]2 = x[/tex]
Side a = 7x = 7 x 2 = 14
Side b = 5x = 5 x 2 = 10
Side a [tex]\geq[/tex] Side b
Hence, side a is longer
A train traveled 250 mi in 2 hours. If it traveled at the same rate of speed how long would it take the train to travel 600 mi
4.8
Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.
Please help! Ubehebe crater in death Valley has a diameter of a little more than 1/2 a mile. If Latisha walks around its rim at a rate of 2 mph, about how long will it take her to walk all the way around the crater? Round your answer to the nearest tenth. Use 3.14 for pi.
The time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
What is speed?Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.
here,
Ubehebe crater in Death Valley has a diameter of a little more than 1/2 a mile.
Circumference of the rim,
= πD
= 3.14 × 1/2
= 1.57 mile
Time = Distance/speed
Time = 1.57 / 2
Time = 0.785 hours
Thus, the time required for Latisha to walk around the rim at a rate of 2 mph is 0.235 hours.
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The value of a second-hand car is £8,000.
Each year it loses 20% of its value.
Work out the value of the car after 5 years.
The value of the car will be £2,621 after 5 years.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.
Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.
This is a situation of exponential decay.
Hence, using the exponential decay formula =
A = P(1-r)ⁿ
Where A is final value, P is principal value, r is rate of decrease and n is the number of years.
Here, we will find A, and we have,
P = £8,000.
r = 20% = 0.20
t = 5
Therefore,
A = 8000(1-0.20)⁵
A = 8000(0.80)⁵
A = 8000(0.32768)
A ≈ 2,621
Hence, the value of the car will be £2,621 after 5 years.
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-15 POINTS- Find the length of the indicated side of the similar figure X=[?]
how long would it tak to go 75 miles if you can go 45 mph
What is the value of y in the equation y = 1/4 x divided by 2 when x =32
The value of y is 16 when x = 32 for equation y = (1/4)x divided by 2.
What is an equation?Mathematical expressions with two algebraic expressions on either side of the equals (=) sign are called equations. It displays how the expressions on the left and right sides are equally related. We have LHS = RHS in any mathematical equation. Equations can be solved to get the value of an unknown variable that represents an unknown quantity. If there is no "equal to" symbol, a statement is not an equation.
The given equation is
y = 1/4 x divided by 2
So,
y = ((1/4)x)/ 2
y = (2/4) × x
Put x = 32
y = 2/4 ×32
y = 2 × 8
y = 16
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Keshia goes to the post office to mail a package and a few letters. Stamps cost 49 cents each. It will cost $7.65 to mail the package. Keshila has 10.00. a. Write an inequality to represent this situation, where x is the number of stamps.
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
Define Inequality.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."
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Y’all helppppp questions on the photo
The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?
expression can be defined as with the minimum of two variables or numbers and at least one math operation.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
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The division expression is equivalent to the given expression is (13/ 3)/ (-5/6)
What is expression ?expression can be defined as with the minimum of two variables or numbers and at least one math operation.
What is division?Division is one of the four basic mathematical operations of arithmetic, along with addition, subtraction, and multiplication. The division operation is represented by the symbol ÷ or /, and it is the inverse operation of multiplication.
Given expression,
= 4 1/3 / (-5/6 )
= (13/3 )/ (-5/6)
= 13*6 / -15
= -26/5
By evaluating the other expressions to find its equivalent,
(13 / 3) / (-5/6)
= 13 * 6 / -15
= -26/5
Hence , the expression 4 1/3 / (-5/6 ) is equivalent to (13 / 3) / (-5/6) .
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One root of the equation 4x² + 12x + k = 0, k = Z and x = R, is five times the other root.
Find the value of k.
We found the value of K is 5 and the root of equation is x = -1/2 and x = -5/2
What is quadratic equation?An equation of second order polynomial having one variable is called quadratic equation. Second order means the highest power used with variable is 2.
How to determine the value of k in the question?We are given, 4x²+ 12x +k =0, k =Z and x = R
the quadratic equation is 4x²+12x+k =0
we know the roots of a quadratic equation is x = - b ± √ (b² - 4ac) / 2a
when the quadratic equation is ax²+bx+ c= 0
Hence, roots of the equation given in question will be,
x = - 12 ±√ (12² - 4×4×k) / 2×4
x = - 12 ± √(144-16k) / 8
as per the condition given in question, one root of this equation is 5 times the other root.
hence, - 12 -12 √(144-16k) / 8 = [- 12 + √(144-16k) / 8] × 5
multiplying both sides by 8
- 12 - √(144-16k) = [-12 + √(144-16k)] ×5
- 12 - √(144-16k) = - 60 + 5√(144-16k)
- 12 + 60 = 6√(144-16k)
48 = 6√(144-16k)
8 = √(144-16k)
64 = 144 -16k
16k = 80
k = 5
the value of k =5
by putting the value of k =5
x = -12 ± √ (144 - 80) / 8 = (-12 ± 8) /8
x = -1/2 and x = -5/2
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Find the slope of the line that has an equation of 4x-2y=6
4x - 2y = 6
2y = 4x - 6
y = (4x - 6)/2
y = 2x - 3
When the angle of elevation to the sun is 49°, Naomi's shadow is 5 feet long. The
shadow of a nearby tree is 8 times as long as her shadow. How tall is the tree to the
nearest foot?
Answer:
46 feet-------------------------------
The height h of the tree is opposite to 49° angle of a right triangle with the other leg:
5*8 = 40 feet longUse tangent to find the value of h:
tangent = opposite/adjacenttan 49° = h/40h = 40*tan 49°h = 46 feet (rounded)The height of the tree is 40 feet to the nearest foot.
How can the height of the tree be found?
It can be found using similar triangles.
Let's call the height of the tree "x".
Since the angle of elevation to the sun is 49°, we have two similar triangles:
Triangle 1: Sun - Naomi - Ground (illustration attached)
Triangle 2: Sun - Tree - Ground
The height of Naomi, 5 feet, is one of the corresponding sides in the two triangles, and the height of the tree, x feet, is the other. We know the ratio of their heights is 8:1, so:
x ÷ 5 = 8
Solving for x, we find that:
x = 40
So the height of the tree is 40 feet to the nearest foot.
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find the truth value Of 3+4= 12, then 3+2=6
The truth value of "If 3 + 4 = 12, then 3 + 2 = 6", is true.
What is Truth Values?Truth value is defined as whether the given proposition is either true or false, not both.
Here the proposition is of the form if p, then q.
Here p is the statement 3 + 4 = 12 and q is the statement 3 + 2 = 6.
Here, both of the propositions are false.
The truth value of 'if p, then q' is false only when p is true and q is false. In all other cases the truth value is true.
Here, since both of the statements are false, the truth value is true.
Hence the truth value of the given proposition is true.
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Drag each question to the correct location on the table.
Classify the questions as statistical or not statistical.
Each of the questions should be correctly classified as statistical or not statistical as follows:
Not statistical question: "How many hours did I jog yesterday?"Not statistical question: "How many students in my class can swim?"Not statistical question: "How many students in my class watch television?"Statistical question: "How many hours a day do the students in my class watch television?"Statistical question: "How many TV shows did each student in my class watch yesterday?"Statistical question: "How many days a week did each student in my class go swimming in the last month?"What is a statistical question?In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"
What is a non-statistical question?A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"
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Which fraction is equivalent to -3/5
Answer: 3/-2
Step-by-step explanation:
3/-2 and -3/2 mean the same thing and give same result if we divide the numerator by denominator.
hope that helps...
please help me answer this question.
The distance between points E(-8, 7) and L(-1, 4) on the coordinate plane is √58 units
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The distance between two points in the coordinate plane is given as:
[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The distance between points E(-8, 7) and L(-1, 4) is:
[tex]EL = \sqrt{(4-7)^2+(-1-(-8))^2}=\sqrt{58}[/tex]
The distance is √58 units
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SOMEONE PLEASE HELPPP
The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;
[tex]\bar {x}[/tex] ≈ 13.05
Median = 13.60
What is the mean and median of a dataset?The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.
The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.
The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;
The number of data points = 28
The sum of the data is; (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5
The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05
The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;
2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2
The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;
Median = (12.6 + 14.6)/2 = 13.60
The median is 13.60
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Solve for x. 6x−24=x−2
OPTIONS:
Enter answer in the box!
X = [?]
Answer:
point A
Step-by-step explanation: