[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\begin{cases} h=1\\ k=3 \end{cases}\implies y=a(x-1)^2 + 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=5 \end{cases} \\\\\\ 5=a(2-1)^2 + 3\implies 2=a(1)^2\implies \cfrac{2}{(1)^2}\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 +3 \end{array}} ~\hfill[/tex]
A hose fills a hot tub at a rate of 3.49 gallons per minute. How many hours will it take to fill a 343-gallon hot tub? Question content area bottom Part 1 It will take enter your response here hours to fill the hot tub. How many hours does it take to fill the hot tube?
If hose fills a hot tub at a rate of 3.49 gallons per minute. Then 1.64 hours will it take to fill a 343-gallon hot tub
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given,
A hose fills a hot tub at a rate of 3.49 gallons per minute.
We need to find how many hours will it take to fill a 343-gallon hot tub
3.49/1=343/x
Apply cross multiplication
x=343/3.49
x=98.28 minutes
1 hr=60 minutes
So divide 98.28/60
1.64
Hence, it takes 1.64 hours to fill the hot tub.
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What operation do you use when you distribute the number that is outside the
parenthesis to all of the numbers that are
inside the parenthesis?
Answer:
multiplication
Step-by-step explanation:
you multiply. I know this because I am in pre algebra right now and we learned about this again. If you are doing division then it’s the opposite same for subtraction as well as addition.
Which of the following is an equivalent form of the compound inequality -33> -3x - 6 ≥
-36?
The equivalent form of the compound inequality is -9>-x≥-10.
What is a compound inequality?A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true. It consists of the union or combination of the solution sets for the various statements. A conjunction is a compound inequality that contains the word "and." Even though "and" and "or" are considered to be conjunctions of speech, their meanings in mathematics are distinct from their grammatical counterparts. The conjunction (part of speech) "or"—when used to demonstrate this point—is whenever used in a compound inequality, it creates a disjunction, as the name suggests. Simply keep in mind that "con" stands for "with another" and "dis" for "one OR the other."
Calculation:Given -33>-3x-6≥-36.
Dividing everything by 3 we get -11>-x-2≥-12.
Now adding to every side we get compound inequality as -9>-x≥-10.
The equivalent form of the compound inequality is -9>-x≥-10.
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a dining hall had a total of 20 tables— some long rectangular tables and some round ones. Long tables can seat 10 people. Round tables can seat 8 people. on a busy evening, all 182 seats at the tables are occupied. a write a system of equations to represent this scenario
The solution of linear equations in two variables gives the following results.
The number of long tables = 11The number of round tables = 9 What are linear equations in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Given:
Total number of tables in dining hall = 20 people
The number of people who can seat at long table = 10 people
The number of people who can seat at the round table = 10 people
According to the question, let’s assume a linear equation in two variables
number of long tables = x
number of round tables = y
⇒ x +y=20 ………… (1)
⇒10 x + 8 y=182 ………...(2)
Multiply equation (1) by 8 and subtract it from equation 2.
⇒ 10x+8y=182 ………… (2)
⇒ 8x+8 y=160 ………....(1)
⇒2x=22
⇒x=11
now put the value of x in equation (1) we get,
⇒11+y=20
⇒y=20-11
⇒y=9
Therefore, the number of long tables = 11
The number of round tables = 9
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What is the inverse of 12/(x-1)
100 points please I really want to figure this out
The inverse of the expression represented as 12/(x-1) is (12/x) + 1
How to determine the inverse of the expression?From the question, we have the following parameters that can be used in our computation:
12/(x - 1)
The given parameter is an expression
Also, we can see that the above expression is a quotient expression
So, we start by expressing it as an equation
This is represented as
y = 12/(x - 1)
Swap/Switch the positions of the variables x and y
So, we have the following representation
x = 12(y - 1)
This gives
y - 1 = 12/x
Make y the subject
y = (12/x) + 1
Hence, the inverse is (12/x) + 1
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six pounds of potatoes cost 12.90 how much would 3.5 pounds cost
HELP
Answer:x=$7.31
Step-by-step explanation:6lbs
$12.90 x
6lbs x=($12.90 )(3.4 lbs)
6lbs x=43.86$lbs
6lbs x/6lbs=43.86$lbs/6lbs
What is the probability of getting a ten or a jack from a deck of pocker cards
The probability of getting a 10 or a jack from a deck of poker cards (52 cards) is 15.38%.
What is probability?Probability is concerning about numerical description
Is how likely is an event is occur or how likely it is true.
As per the given sequence -
there are four 10 cards and four jack cards respectively
4+4=8
If you want to get one from the 52 cards, so it's 8 out of 52. 8/52
To calculate the percentage, you must multiply 8 by 100, then divide by 52.
Thus,
8*100/52=15.38
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5) A woman wants to borrow $12,000 to buy a car. She wants to repay the loan by monthly installments
for 4 years. If the interest in the loan is 10.5% per year, compounded monthly, what is the amount of
each payment?
Answer:
to much money to buy a car I try to work it down to 10k
Decide where the first digit of the quotient should be placed. Do not complete the
division.
The first digit in the quotient of 1, 592 64 is in the
Choose...
place.
The first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.
How to find the quotient with Long division?
When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.
In this question, when we perform long division, we compare;
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.
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Which box-and-whisker plot represents this data: ?
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from 18 to between 24 and 26 with no median value.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 8 and 10 to 28 with a median between 20 and 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 to between 26 and 28 with a median between 20 and 22.
A box-and-whisker plot which represents the given data is: B. A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
What is a box-and-whisker plot?In Mathematics, a boxplot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
By using an online box-and-whisker plot calculator, the five-number summary for the given data set include the following:
Minimum = 6.First quartile = 13.Median = 22.Third quartile = 27.5.Maximum = 30.By critically observing the box-and-whisker plots (see attachment), we can logically deduce that boxplot A correctly represents the given data set.
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Complete Question:
Which box-and-whisker plot represents this data: 6,9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?
a. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6)
b. What is the equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2)
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0,-6) is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2,-2) is y = -1/m * x - 2
what is intercepts?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
a. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (0, -6) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-6).
Therefore, the equation of the line is y = -1/m * x - 6
b. The equation of the line that is perpendicular to the graph and intercepts the y-axis at (2, -2) can be written as:
y = mx + b
where m is the slope and b is the y-intercept.
Since the line is perpendicular to the graph, the slope of the line is the negative reciprocal of the slope of the graph. The y-intercept is (-2).
Therefore, the equation of the line is y = -1/m * x - 2
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35/17 as rounded decimal tenths place
A decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller. What is the average class size currently?
Answer: 21 students
Step-by-step explanation:
A number being 30% smaller means that it has reduced to 70% of its original size.
This means we can multiply the original value by its new percentage, 30x0.7=21 students.
Δ PQR, P=(4 x+11)°, m∠Q=(2 x+1)°, and m∠R=(7 x-14)°. Find m∠P.
Answer:
67°
Step-by-step explanation:
Th sum of the interior angles of a triangle is 180. Set the measurements of the three sides to 180 and solve for x. Then substitute in the value for x in 4x +11
4x + 11 + 2x + 1 + 7x -14 = 180 Combine like terms
13x - 2 = 180 Add 2 to both sides
13x = 182 Divide both sides by 13
x = 14
Plug this in for x
4x + 11
4(14) + 11
56 + 11
67
PLEASE SOLVE FOR X I REALLY NEED HELP
Answer:
Below
Step-by-step explanation:
The bisector divides the base into lengths proportionate to the two sides (Angle Bisector theorem)
x+ 2 = 15/(15+20) * 14
x = 4 units
Please help me with this problem
a) The null hypothesis is: [tex]H_0: p \leq 0[/tex]
b) The alternative hypothesis is: [tex]H_1: p > 0[/tex]
c) The test statistic is: z = 9.71.
d) The correct option is of: A. Yes.
e) The confidence interval is of: 0.0819 < p < 0.1336.
What are the hypothesis tested?
At the null hypothesis, it is tested if there is not enough evidence that the proportion for men is greater, that is, the subtraction is not greater than 0:
[tex]H_0: p \leq 0[/tex]
At the alternative hypothesis, it is tested if there is evidence that the proportion for men is greater, that is, if the subtraction is greater than 0, hence:
[tex]H_1: p > 0[/tex]
We have a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01, hence the critical value is of:
z = 2.327.
Thus the decision rule regarding the test statistic is given as follows:
z < 2.327 -> not enough evidence of difference -> do not reject the null hypothesis.z > 2.327 -> enough evidence of difference -> reject the null hypothesis.What are the mean and the standard error of the distribution of differences?For each sample, the mean and the standard error are given as follows:
Men: [tex]p_m = \frac{88}{800} = 0.11, s_m = \sqrt{\frac{0.11(0.89)}{800}} = 0.0111[/tex]Women: [tex]p_w = \frac{6}{2750} = 0.0022, s_w = \sqrt{\frac{0.0022(0.9978)}{2750}} = 0.0009[/tex]Hence, for the distribution of differences, the mean and the standard error are given as follows:
Mean: p = 0.11 - 0.0022 = 0.1078.Standard error: s = sqrt(0.0111² + 0.0009²) = 0.0111.What are the test statistic and the conclusion:The test statistic is given by the division of the mean by the standard error of the sampling distribution of the difference of sample proportions, hence:
z = 0.1078/0.0111 = 9.71.
z > 2.327 -> enough evidence that the proportion is greater.
What is the confidence interval?The confidence interval is obtained as the mean plus/minus the multiplication of the standard error and of the critical value.
Then the bounds of the interval are:
Lower bound: 0.1078 - 2.327 x 0.0111 = 0.0819.Upper bound: 0.1078 + 2.327 x 0.0111 = 0.1336.More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
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A train travels for 3.75 hours at 80 miles an hour. Use the formula d = r. t, where
d = distance, r = rate, and t = time, to find the distance the train traveled.
The distance traveled is
miles.
The solution is
The distance traveled by train would be 300 miles.
What is the relation between speed, distance, and time?
You can use the equivalent formula d = rt which means distance equals rate times time. To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time. To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.
A train travels for 3.75 hours at 80 miles per hour.
The distance traveled = speed * time
= 3.75 * 80
= 300 miles.
Hence, the distance traveled by train would be 300 miles.
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I need help with this question.
Dude I am so sorry that I do not know this answer
which equation is in slope-intercept form?
Answer: y = 3/2x +-9
Step-by-step explanation:
The equation in slope-intercept form, y = mx + b, is the equation y = 3/2x +-9.
See attached for more information on slope-intercept form.
Learning geometry is tricky but test your knowledge for sure. Please help me. Thank you!!!
The area of the paper that remains is 375.04cm².
What is an area?
The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Here,
We take it that the semicircles cover the full width of the paper.
So the radius is 16/2 = 8 cm
Since there are two of them, the area is full circle.
First, we find the area of the rectangle before the cuts were made.
Area = L * W
L = 36
W = 16
Area = 36×16 = 576 cm²
Now, we find the area of the circle cutouts.
r = 8
Area = pi * r²
Area = 3.14 * 8²
Area = 3.14 * 64
Area = 200.96cm²
Now, we find the total area left
Total Area Left = rectangle - circle
Total Area Left = 576 - 200.96
Total Area left = 375.04cm².
Hence, the area of the paper that remains is 375.04cm².
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Find the mean and standard deviation of the sample data in the table. (Round your answers to two decimal places.) x = [1, 2, 3, 4, 5]
f(x) = [2, 13, 15, 11, 13]
The mean and standard deviation of the sample data in the table is 182 and 508 respectively.
To calculate the mean and standard deviation,
mean= E(x)
= ∑x*f(x)
= 1(2) + 2(13) + 3(15)+4(11) + 5(13)
=2+26+45+44+65
=182
Standard deviation = E(x²)
= ∑x²*f(x)) - E(x)
=1(2) + 4(13) + 9(15)+16(11) +25(13) - E(x)
= 2 +52+135+176+325 - E(x)
=690 - 182 - E(x)
=508
The mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The three most frequently employed measures of central tendency are the mean, median, and mode.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
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Assume that a sample is used to estimate a population mean
μ
. Find the 90% confidence interval for a sample of size 52 with a mean of 85.5 and a standard deviation of 12.3. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.
Confidence interval for given data is (82.156,88.843)
What is confidence interval?The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.
The alpha value determines the confidence level, which is the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.
general form of a confidence interval is:
point estimate + Z SE (point estimate)
Formula for confidence interval is given by
[tex]X[/tex] ± [tex]Z\frac{s}{\sqrt{n} }[/tex]
Where:
X is the mean
Z is the chosen Z-value from the table above
s is the standard deviation
n is the number of observations
In given ques
X = 85.5, Z=1.960, s =+ 12.3, n= 52
confidence interval = 85.5± (1.960×12.3/√52)
(82.156,88.843)
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Graph the linear equation by solving for y first.
4x+5y=-2
Solving for y, the linear equation is: y = -4/5x - 2/5.
The table showing the corresponding y-value for each x-value is:
x | -8 -3 2 7
y | 6 2 -2 -6
The graph is in the attachment.
How to Graph a Linear Equation?To graph the linear equation of 4x + 5y = -2, rewrite in slope-intercept form by solving for y.
4x + 5y = -2
5y = -4x - 2
y = -4/5x - 2/5
Complete the table given by plugging each value of x into the linear equation, y = -4/5x - 2/5.
For x = -8:
y = -4/5(-8) - 2/5
y = 6
For x = -3:
y = -4/5(-3) - 2/5
y = 2
For x = 2:
y = -4/5(2) - 2/5
y = -2
For x = 7:
y = -4/5(7) - 2/5
y = -6
The complete table is:
x | -8 -3 2 7
y | 6 2 -2 -6
See the graph below.
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the chart shows the number of points different players scored during a game. what is the ratio of marcus's points to scott's points? responses
The ratio of Marcus's point to Scott's point will be = 1 : 2
According to the table given attached below,
We can find the ratio of the squares,
First, let us know about the definition of Ratio and Proportion.
The ratio is defined as the comparison between the two similar quantities
The fraction can also be represented as a ratio using the ' : ' sign
For example, let us consider two numbers a and b
In fraction, we could write it as = [tex]\frac{a}{b}[/tex]
Writing it as a ratio = a : b
According to the table given below,
Marcus's points = 7
Scott's points = 14
The ratio of Marcus's points to Scott's points = [tex]\frac{Marcus}{Scott}[/tex]
14 / 7
2 / 1
2 : 1
Therefore, The ratio of Marcus's point to Scott's point will be = 1 : 2
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What is equivalent to 2
Answer:
4 6 8 10
Are the ans
Step-by-step explanation:
Plus 2 each time
which of the following is the best approximation of the volume of this cylinder
Radius=8
Height=3
Answer:
..........................
The plane is perpendicular to the axis but does not go through the vertex.
The plane intersects the double cone at only the vertex.
The plane is not intersecting the vertex, not parallel to the axis, not perpendicular to the axis, not parallel to the side of the cone, and it intersects only one cone.
The plane is tangent to both of the cones.
answers:
line
point
circle
elipse
match these
The plane is perpendicular to the axis but does not go through the vertex. The plane intersects the double cone at only the vertex is ellipse.
How to identify the properties of an ellipse?A planar curve that has two focal points is normally called an ellipse on the condition that at every point on the curve, it will be seen that the sum of the two distances from the focal points is constant. This generalizes the shape of a circle, which is a unique variety of an ellipse whereby the two focus points coincide.
The plane is said to not be intersecting with the vertex, not parallel to the axis nor perpendicular to the axis, then not parallel to the side of the cone, but it intersects only one cone is called a circle.
A circle is defined as a closed, two-dimensional object whereby every point in the plane is seen to be equally spaced from a central point. The line of reflection symmetry is seen to be formed by all lines that transverse the circle. Additionally, every angle has rotational symmetry around the center.
Thus, the conclusion is that the first two options are properties of an ellipse.
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an employer agrees to pay $5,000 for medical insurance and contribute an additional 5% of the employees'
Answer: $5,250
Step-by-step explanation:
1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.
It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.
Help i dont know how to do this problems.
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
10 and 2x - 8 are parallel lines.
10 = 2x - 8
10 + 8 = 2x
18 = 2x
x = 9 (black)
7 and -17 + 2x are the two parts of a line separated by a midpoint.
7 = -17 + 2x
7 + 17 = 2x
2x = 24
x = 12 (orange)
7 and x + 15 are two parts of a line separated by a midpoint.
7 = x + 15
7 - 15 = x
x = 8 (purple)
m∠2 = 4x + 8
one angle = 45°
Other angle = 180 - 104 = 76°
The sum of the triangles is 180.
45 + 4x + 8 + 76 = 180
4x = 180 - 129
4x = 52
x = 12.75 (green)
Thus,
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
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One year, the population of a city was 102,000. Several years later it was 110,160. Find the percent increase.
Answer:
8% increase
Step-by-step explanation:
Difference between the two populations: 110160 - 102000 = 8160
Difference ÷ Initial population: 8160 ÷ 102000 = 0.08