The required form of a parabola in vertex form is y = a(x - h)² + k.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The standard form of a parabola in vertex form is:
y = a(x - h)² + k
where (h, k) is the vertex of the parabola and a determines the direction of opening (a > 0 for an upward-facing parabola and a < 0 for a downward-facing parabola). The coefficient also determines the shape and steepness of the parabola.
Thus, the required form of a parabola in vertex form is y = a(x - h)² + k.
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Round to 2 decimal places *
1 point
An architect is designing a building topped with a hemispherical dome. She
creates a scale model of the building using a scale of 0. 25 inch : 1 foot. In
the scale model, the diameter of the dome is 23. 75 inches.
What will be the circumference, in feet, of the actual dome?
The circumference of the dome will be 149.15 feet or 47.5π feet
A scale is defined as the ratio of the dimensions of an object that is represented as a draft to the real or true dimensions of the object being drafted.
The figure on the left of the ratio sign can represent the size and dimensions of the model with respect to the actual size or dimensions of the object.
On the other way, the figure on the right-hand side represents the actual dimensions and size of the real object.
So, if an object is being drawn with the ratio, of 1cm: 5cm it means that the size of the object is being reduced because every 5cm of the actual object will always represent 1cm in the drawing.
If the object is being drawn by a scale of 5cm: 1cm then the actual size of the object will be increased. After that for every 1cm in the actual dimensions of the object, it can be a 5cm representation in the drawing.
Now, draws a scale of 0.25 inches: 1 foot. If the diameter of the dome is 23.75 inches, then the actual diameter of the dome is:
0.25 inches ------- 1 foot
23.75 inches -------? feet
= 23.75/0.25 × 1
d= 95 feet
so, the real diameter of the dome is 95 feet.
The dome is a hemisphere that is half of a sphere. So, the formula for finding the circumference of a sphere is πd, then the hemisphere will be πd/2. As we know the diameter is 95 feet, and the circumference of the hemisphere =
(π × 95)/2
=47.5π feet
Or
if the value of π = 3.14, then the circumference is calculated as (3.14 × 95)/2 = 149.15 feet
Therefore, the circumference of the dome is 149.15 feet or 47.5π feet.
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The length of the yarn is less than 7.5 inches.
Answer:
that means it's a short yam
The length of the yarn is n < 7.5 inches.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
The length of the yarn is less than 7.5 inches.
Let the length of the yarn is n inches.
To show the length of the yarn:
We will establish an inequality.
So,
n < 7.5 inches.
Therefore, n < 7.5 is the inequality.
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Solve the system of equations for a and b:
The solution to the system of equations in this problem is given as follows:
a = 327.9.b = 0.71.How to solve the system of equations?The system of equations for this problem is defined as follows:
42 = ab^6.15 = ab^9.From the first equation, we have that:
ab^6 = 42
a = 42/(b^6)
a = 42b^(-6).
Replacing on the second equation, we have that the value of b is obtained as follows:
15 = 42b^(-6) x b^9
15 = 42b³
b = (15/42)^(1/3)
b = 0.71.
Then the value of a is obtained as follows:
a = 42 x (0.71)^(-6)
a = 327.9.
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The diameter, D, of a sphere is 8.6 cm . Calculate the sphere's volume, V .
Use the value 3.14 for π , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is ______.
Answer: Observational
Step-by-step explanation:
If it is a experiment then you can conclude that a variable caused a response
In statistics, correlation refers to the degree to which two variables are related or associated with each other. When the correlation between two variables is close to 1.0, it indicates a strong positive relationship between them. However, it is important to note that this strong correlation does not necessarily imply a cause-and-effect relationship between the two variables, especially in a study where certain conditions may not be met.
A study is a systematic investigation aimed at acquiring knowledge and understanding of a particular phenomenon or subject matter. In order to establish a causal relationship between two variables, certain conditions need to be met, such as the establishment of a temporal sequence, a clear association between the variables, and the elimination of any confounding variables that may influence the outcome. These conditions are essential for any study seeking to establish a cause-and-effect relationship between variables.
In the absence of these conditions, even if the correlation between two variables is close to 1.0, it cannot be concluded that the explanatory variable causes changes in the response variable. This is because correlation does not imply causation. Correlation simply indicates the strength of the association between two variables, but it does not provide information about the direction or the underlying mechanisms of the relationship.
For instance, consider a study examining the relationship between smoking and lung cancer. The study finds a strong positive correlation between smoking and lung cancer, indicating that smokers are more likely to develop lung cancer than non-smokers. However, this correlation alone does not necessarily prove that smoking causes lung cancer. There may be other factors such as air pollution, family history, or genetics that could influence the development of lung cancer.
In summary, the correlation between two variables is a measure of the strength of the association between them. A high correlation does not necessarily imply a cause-and-effect relationship between the variables, especially in a study where certain conditions may not be met. It is important to consider these conditions and rule out other factors that could influence the outcome before drawing any conclusions about the causal relationship between two variables.
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14) Determine the base and height of the given parallelogram, and then find the area
The base of the given parallelogram is 11. 8 cm and the height is 6. 5 cm.
The area of the parallelogram is 76. 7 cm ²
How to find the area of a parallelogram ?The base is the dimension of the parallelogram that is shown either at the top or bottom of the shape. In this case, it is 11. 8 cm. The height is the distance from the top to the bottom which is 6. 5 cm in this case.
The area of a parallelogram is:
= Base x Height
= 11. 8 x 6 . 5
= 76. 7 cm ²
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Find the sum of the squares of the solutions of $x^2-13x+4=0$.
The sum of the squares of the solutions of the mentioned equation is 161.38.
The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.
x² - 13x + 4 = 0
Based on Dharacharya formula, stated as -
x = - b ± ✓b² - 4ac/ 2a, we get the roots -
x = 12.7 and 0.3
Now, the next formula to solve will be -
x = 12.7² + 0.3²
Taking the square of each number
x = 161.29 + 0.09
Performing addition on Right Hand Side of the equation
x = 161.38
Thus, the required answer is161.38.
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WHICH OF THE FOLLOWING ARE POLYNOMIAL FUNCTION
8Y=10X3-4
One example of a polynomial function is given as follows:
p(x) = x^3+4x^2-3x+2
What are the conditions for a polynomial function?There are two conditions for a polynomial function, and they are listed as follows:
Variable x is present only in the numerator of the function.The definition of the function contains only numeric non-negative exponents.For the example, we have that the exponents are 3, 2, 1 and 0, while it contains only a numerator.
Missing InformationThe problem is incomplete, hence the general procedure to identify a polynomial function was given.
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please solve. will give brainliest.
Julie bought g gallons of gasoline for $2.75 per gallon and c cans of oil for $3.35 per can. If she bought 8.4 gallons of gasoline and 7 cans of oil, how much did she spend in all?What expression can be used to determine the total amount julie spent on gasoline and oil?
Answer: The amount Julie spent on gasoline can be calculated as g * $2.75 = 8.4 * $2.75 = $23.10.
The amount Julie spent on oil can be calculated as c * $3.35 = 7 * $3.35 = $23.45.
So, the total amount Julie spent on gasoline and oil can be calculated as $23.10 + $23.45 = $46.55.
The expression to determine the total amount Julie spent on gasoline and oil can be written as g * $2.75 + c * $3.35.
Step-by-step explanation:
Neha is developing multiple neighborhoods. The following data points represent the number of new homes that
will be built in each neighborhood.
Sort the data from least to greatest.
5
12
13
20
26
29
30
31
Find the median number of houses.
From the given data points representing the number of new homes that built in each neighborhood. The median number of houses is 26.
The median is the middle value of a set of numerical data when the data is arranged in ascending or descending order. In a set of odd number of data points, the median is the middle value. In a set of even number of data points, the median is the average of the two middle values.
To find the median, you arrange the numbers in order from least to greatest and then pick the middle number(s).
5, 12, 13, 20, 26, 29, 30, 31
In this case, there are 8 numbers, so the median is the middle number, which is 26.
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The Sum of radius and hieght of cylinder is 21 cm and
total surface area of cylinder is 660 cm². find
hieght and
volume of cylinder.
Answer:
5 cm^2
Step-by-step explanation:
I just had this same question and I got it right.
hope this helps
August electro billThe local utility company released a report showing the August electric bills of their customers. This box-and-whisker plot shows the results
The maximum value of the August electric bills of used by customers using the box and whisker plot is equal to $320 .
In box and whisker plot , Data is plotted in as it is divided into :
Five number summary set of data ,
Minimum value ,Maximum value, First Quartile, Third Quartile , Median.
Data of August electric bills ($) as per given data is:
200 240 160 280 320
Minimum value = $160
Maximum value = $320
First quartile = $200
Third Quartile = $280
Median = $240
Therefore, the maximum value of the August electric bills shown as box and whisker plot is $320.
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_____The above question is incomplete ,the complete question is:
The local utility company released a report showing the August electric bills of their customers. This box-and-whisker plot shows the results.
200 240 160 280 320
August electric bills ($) What is the maximum value?
What conversion factor fraction is used to convert feet to inches?
OA. 10 inches/1 foot
OB. 1 foot/12 inches.
OC. 1 inch/10 feet
OD. 12 inches/1 foot
SUBMIT
Lamar drinks 8 fluid ounces of water with breakfast, 6 fluid ounces of water with his vitamins, 16 fluid ounces of water with his lunch, 16 fluid ounces of water with his dinner, and 32 fluid ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in fluid ounces that he drinks in a week.
Lamar drinks 8 fluid ounces of water with breakfast, 6 fluid ounces of water with his vitamins, 16 fluid ounces of water with his lunch, 16 fluid ounces of water with his dinner, and 32 fluid ounces of water from a bottle he carries throughout the day. Write and evaluate a numerical expression for the amount of water in fluid ounces that he drinks in a week.
The required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.
Lamar drinks water with,
Breakfast = 8 ounces
Vitamins = 6 ounces
Lunch = 16 ounces
Dinner = 16 ounces
Bottle = 32 ounces
To find A numerical expression for the amount of water in ounces that he drinks in a week.
One day consumption of water by Lamar is
We know that,
1 week = 7 days
One day consumption of water = 78 ounces
1 week (7 days) consumption of water = 7× One day consumption of water
= 7× (8+6+16+16+32) ounces
= 7×78 ounces
= 546 ounces
Therefore, the required numerical expression for the amount of water in ounces that he drinks in a week is 7× (8+6+16+16+32) ounces and the value is 546 ounces.
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g/16 = 16 step by step
Answer:
Below
Step-by-step explanation:
There is only ONE step
g/16 = 16 multiply both sides of the equation by 16
g = 256 Done.
Evaluate 64 divided [4 multiply (27 — 5 exponand 2)]
Before solving this expressions, you must understand the PEMDAS rule.
Parentheses.Exponents.Divide.Multiply.Addition.Subtraction.This rule must be used to solve this problem.
Answer Step by StepQuestion: 64 ÷[4 ×(27 - 5²)]
According to PEMDAS rule, we start with parentheses.
Step 1: 27-5². 5² = 5x5 = 25. 27 - 25 = 2.The equation is now 64 ÷[4×(2)]
2. Step 2: [4×2] = 4×2 = 8.
The equation is now 64 ÷ 8.
3. Step 3: 64 ÷ 8 = 8.
The answer to 64 ÷[4 ×(27 - 5²)] = 8.
ConclusionThis concludes solving 64 ÷[4 ×(27 - 5²)]. If this helps you, please leave a heart and stars to rate this answer. Leave a comment if you have questions or concerns.
how many times is the letter f (any case) in the following? if fred is from a part of france, then of course fred's french is good.
The count of letter f (any case) in ' if fred is from a part of france, then of course fred's french is good', is 8.
A word, phrase, or sentence in which no letter of the alphabet appears more than once is known as a heterogram (from the prefix hetero-, meaning "different," and the suffix -gram, meaning "written"). The same idea has also been denoted by the phrases isogram and nonpattern word.
Language on Vacation: An Olio of Orthographical Oddities, written by Dmitri Borgmann in 1965, mentions the idea, however he refers to it as an isogram. Borgmann asserts that he "introduced" the term "isogram" in a 1985 essay. Although he uses the term "isogram" in the paper itself, he also offers the name "asogram" to prevent confusion with lines of constant value like contour lines.
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2 of the walls are 11 and 11, there's 3 more walls to find. Break the room into rectangles and then do Base × height then add both rectangles together and get the sum:
What's the area and the perimeter in sqaure feet?
The area and the perimeter of the room having rectangular shaped base are respectively, 121 feet² & 44 feet
What is the area & perimeter?An area is total space occupied by two-dimensional or flat surfaces. In other words we can say that it is a number of unit squares present in a closed figure. We use various units for measurement of area like, cm², m², ft², mm².
Perimeter is a mathematical term, which means total outer boundary of a figure, we define it only for two dimensional figures.
Perimeter = Sum of length of the all the sides
Given that,
2 of the walls are 11 and 11,
The room is into rectangle shape,
Base area of room = length x width
= 11 x 11
= 121 feet²
Perimeter of base of the room = Sum of lengths and widths
= 11 + 11 + 11 + 11
= 44 feet
Hence, the area and perimeter are respectively 121 feet² & 44 feet
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A wheel of cheese has a radius of 7 inches and a height of 3 inches. What is the approximate surface area of this wheel of cheese? Use 3.14 for pi.
The approximate surface area of this wheel of cheese is 437.6 square inches.
As per the given data, a wheel of cheese has a radius of 7 inches.
Radius r = 7 inches.
Also, a wheel of cheese has a height of 3 inches.
Height h = 3 inches
Also, given to consider the value of pi as 3.14.
π = 3.14
Here we have to determine the total surface area (TSA)of the wheel of cheese.
Since the cheese is a cylinder shaped thing.
The formula for the total surface area (TSA) of the wheel:
TSA = 2πr (r + h)
Substituting the values of the variables into the formula, we have
= 2 (3.14)(7)(7 + 3)
= 2 (21.88)(10)
= 2 (218.8)
= 437.6 square inches.
Therefore the total surface area is 437.6 square inches.
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ABC Bank is offering to double your money! They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account, how long will it take to double your money.
The number of years that it takes to double your money will be 12 years.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
They say that if you invest with them at 6% interest compounded annually they will double your money. If you invest $500 in the account. Then the equation is given as,
$1,000 = $500 x (1 + 0.06)ⁿ
2 = (1.06)ⁿ
ln 2 = n ln 1.06
n = ln 2 / ln 1.06
n = 11.90
n ≈ 12 years
The number of years that it takes to double your money will be 12 years.
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40 POINTS
A linear relationship is given in the table.
x y
6 7
4 5
0 1
−2 −1
What is the slope of the relationship?
3
2
1
−1
Answer:
1
Step-by-step explanation:
To find slope, m, we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]
The top Y on the table is 7 and the bottom one is -1, so we'll plug those into the top.
The top X on the table is 6 and the bottom one is -2, so we'll plug those into the bottom
[tex]m = \frac{7 - ( - 1)}{6 - ( - 2)} [/tex]
[tex]m = \frac{8}{8} = 1[/tex]
there are 7 train stations. one way ticket indicates a departing station and an arriving station. how many tickets are needed?
There are 7 train stations. One way ticket indicates a departing station and an arriving station. Total 42 tickets are needed.
There are 7 train stations.
One way ticket indicates a departing station and an arriving station.
We have to determine how many tickets are needed.
A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here.
In permutation, the elements must be arranged in a specific order, whereas in combination, the order of the elements is irrelevant.
Generally A permutation is the configuration of objects in a specific manner or order. When dealing with permutation, one should consider both selection and arrangement.
From the question;
n = 7
r = 2
[tex]^{n}P_{r}=\frac{n!}{(n-r)!}[/tex]
[tex]^{7}P_{2}=\frac{7!}{(7-2)!}[/tex]
[tex]^{7}P_{2}[/tex] = 7!/5!
[tex]^{7}P_{2}[/tex] = (7 × 6 × 5!)/5!
[tex]^{7}P_{2}[/tex] = 7 × 6
[tex]^{7}P_{2}[/tex] = 42
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Please help me with this Question, EXPLAIN and answer.
p.s I know that the answer is 0.99 but I still need the explanation. :)
AnswerStep-by-step explanation:
.99 is right, you already know.
So first,
8 Down arrow 2
means sqrt8
The 8 goes inside the sqrt and the 2 goes outside (its called an index) but we like never write that 2. Its just a normal square root. If you are using a calculator (I think practically, you must use a calculator) you can find sqrt8. Then
take
sqrt8 UpArrow 6
means (sqrt8)^6
this is 8^3 or on the calculator 512.
Next,
512 SideArrow 500
means 500/512
this is .9765625
Lastly,
.9765625 DownArrow 4
means
4throot(.9765625)
Your calculator might have a 4throot button, but you can use 1/4 power instead because all roots can be written like fraction powers.
When .9765625 is in your calculator screen you can just use the ^ button or x^y button to raise it to the 1/4 power. (Use .25 for 1/4 or use parenthesis on the (1/4) )
(.9765625)^.25
~= 0.99
see image.
can someone please help me(15 points will give brainliest!!!)
Answer:
a ) $11.5
b.) 10 million gallons
Step-by-step explanation:
a.) Since it's asking for p if x = 20, we can plug 20 into the original equation
[tex]0.2(20) + 4p = 50[/tex]
0.2 times 20 is 4
4 + 4p = 50. Next we would subtract 4 from each side giving us
4p = 46. Lastly, divide each side by 4
p = 11.5
b.) If the p, also known as p increases by 50 cents, that means it goes from 11.5 to 12.
Now we plug in 12 to p and look for x, the opposite
[tex]0.2x + 4(12) = 50[/tex]
4 times 12 is 48, making it
0.2x + 48 = 50. This is where we subtract 48
0.2x = 2. and lastly, divide by 0.2, making...
x = 10
So demand decreased by 10 million because 20-10=10
WILL GIVE BRAINILEST
Answer:
1b
Step-by-step explanation:
Five students came for after-school tutoring. Lin’s teacher assigned each of them the same number of problems to complete. Then he assigned each student 2 more problems to one of the students. 27 problems were assigned in all. write an equationfor the story the find the number of problems originally assigned by the teacher.
Step-by-step explanation:
you add all the numbers then you can get the answer
The giant kangaroo rat is an endangered species native to California. Each decade, researchers at a nearby university estimate the giant kangaroo rat population in the San Joaquin Desert. The most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1 3 each decade. Write an exponential equation in the form y=a(b)x that can model the estimated population of giant kangaroo rats in the San Joaquin Desert, y, in x decades.
The exponential equation for the decay of the Kangaroo is written as [tex]y = 73000(\dfrac{1}{3})^x[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the most recent estimate, conducted this year, concluded that there are about 73,000 giant kangaroo rats in the desert. The population is expected to decrease by a factor of 1/3 each decade.
The exponential expression can be written as:-
[tex]y = 73000(\dfrac{1}{3})^x[/tex]
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How do you find the intervals on which the function is continuous given y=2(x+4)2+8?
The interval of continuity of the function is continuous given y = 2 (x + 4 ) 2 + 8 is (-∞, ∞).
Function Continuity IntervalsA function is continuous at a point if the function value exists and is finite at that point, and the limit of the function as the input approaches that point from the left and right side is equal to the function value at that point. In other words, the function has no sudden jumps or discontinuities at that point.
In the case of the function y = 2(x + 4)² + 8, the function is defined and continuous for all real numbers x. There are no values of x for which the function is undefined or has a discontinuity, so the function is continuous for all values of x, meaning that the interval of continuity is (-∞, ∞).
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