Use a graphing calculator to graph y² = x-5 and x² + y² = 49 in the same viewing window. Use the intersect feature to find the coordinates of the intersections of the graphs. Round your answer to the nearest hundredth. Intersections points:
The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The equations are given below.
y² = x - 5 ...1
x² + y² = 49 ...2
From equations 1 and 2, then we have
x² + x - 5 = 49
x² + x - 54 = 0
Use the formula method to calculate the value of 'x'. Then we have
x = [- 1 ± √(1² - 4 · 1 · -54)] / 2
x = [- 1 ± √(1 + 216)] / 2
x = (- 1 ± 14.7309) / 2
x = (- 1 - 14.7309) / 2, (- 1 + 14.7309) / 2
x = -7.865, 6.865
Then the value of the variable 'y' is given as,
y² = x - 5
y² = 6.865 - 5
y² = 1.865
y = ± 1.366
The intersection of the parabola and the circle will be (6.865, 1.366) and (6.865, -1.366). And the graph is given below.
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You are interested in how well people recall visual details based on type of scene;SO you compare recall scores for a group of people who view a humorous scene,a dramatic scene, and scary scene_ between-subjects ANOVA independent samples t test related samples t test within-subjects ANOVA
The statistical techniques of analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are used to test the validity of the hypothesis regarding the comparison of group mean values.
The term "parametric approach" refers to a statistical technique used to compare the means of two normally distributed continuous variables.
In contrast to ANOVA, which is used to compare the means among three or more groups, the Student's t test (also known as the T test) is used to compare the means between two groups.An ANOVA test with a significant P value identifies at least one pair in which the mean difference was statistically significant.
The post-hoc test (multiple comparisons) is utilized to determine whether pair(s) are significant. When at least one covariate (continuous variable) in an ANOVA test is altered to eliminate confounding variables from the outcome, the procedure is known as an ANCOVA. Because inferences about means are made by analyzing variance, the ANOVA test (F test) is referred to as "Analysis of Variance" rather than "Analysis of Means."
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Lin runs 5 laps in 6 minutes
How many minutes per lap is that.
Answer:
0.83 laps per minute
Answer: 0.83 laps per minute.
Step-by-step explanation:
a study of 26 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.87. a. state the decision rule for 0.025 significance level: h0: rho ≤ 0; h1: rho > 0. (round your answer to 3 decimal places.) b. compute the value of the test statistic. (round your answer to 3 decimal places.) c. can we conclude that the correlation in the population is greater than zero? use the 0.025 significance level.
The value of the test statistic using correlation coefficient and sample size is equal to 8.776 ( round up to 3 decimal places.)
As given in the question,
Sample size 'n' = 26
Correlation coefficient 'r' = 0.87
Significance level 'α' = 0.025
a. Decision rule for the system of hypothesis are:
Null hypothesis : H₀ : ρ ≤0
Alternative hypothesis: H₁ : ρ > 0
Value of the test statistic 't'
= r√n-2 / √1 - r²
= (0.87√ 26 - 2) / √1- 0.87²
= 4.3 / √0.2431
= 4.3 / 0.49
= 8.776
Therefore, value of the test statistic using the given values is equal to 8.776.
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Find the slope of table
Answer:
Slope is 4
Step-by-step explanation:
Easy! Just take the first four points on the table. So, (0,6) and (1,10). Then plug those points into y₂ - y₁ over x₂ - x₁ and you'll get your final answer.
when solving a system of linear equations algebraically, how do you know when the system has no solution
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
How do you tell if a system of equations has no solution algebraically?
If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.
What does a system look like if it has no solution?
If a system has no solution, it is said to be inconsistent . The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
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TRUE/FALSE. the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.
It is true that the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.
What is variance?Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.
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Triangles in Real World..
The map shows air travel distances from Minneapolis to four other cities. Use the triangle
inequality to find the range of possible distances between: 1. chicago and houston 2. san francisco and chicago. 3. new york and san francisco. 4. houston and new york
select all valid relational set operators from the list below. select all that apply. group of answer choices plus union unionize except
The Union of South American Nations (UNASUR) is not a regional alliance.
What is the Union of South American Nations?
The Union of South American Nations was formed in 2008 to further the interests of South American nations. It was an intergovernmental union and that was meant to bring more prosperity to the region.
There are also plans to make UNASUR a single-currency union. The Union of South American Nations was never meant to be a regional alliance however.
complete question is
the union of south american nations (unasur) is considered all of the following except (5 points) group of answer choices a supranational organization an intergovernmental union a single-currency union a regional alliance
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A line through (7, 1) and (4, 8) is parallel to the line through (2, x) and (x,-2). What is the value of x?
After solving the equation the value obtained for x will be equal to 5.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information in the question,
The equation of the line passing through the given coordinates will be,
m = (y2 - y1)/(x2 - x1)
The given points are (7, 1) and (4, 8)
Then,
(8 - 1)/(4 - 7) = -7/3
Slope of the line passing through the points (2, x) and (x, -2) then,
(-2 - x)/(x - 2)
Now, we have -7/3 = [tex]-\frac{2+x}{x-2}[/tex]
7x - 14 = 6 + 3x
4x = 20
x = 5
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Use a triple integral to find the volume of the given solid. The solid bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 4.
Using triple integrals we know that the solid in question has a volume of 1024/3³ units.
What is triple integral?Multiple integrals in mathematics is a definite integrals of a function with many real variables, such as for f.
The area of a region enclosed by the function's curve is calculated using the double integral.
It can also be used to figure out how much space is beneath the surface.
The double integral can also be used to calculate the average value of a function with two variables over the rectangular region.
So, the volume of the solid (V) in this problem must be calculated using the triple integral formula in rectangular coordinates:
[tex]V=\iiint d y d x d z[/tex] ...(1)
The following intervals impose restrictions on the solid:
[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]
The triple integral is currently explained as follows:
[tex]$$V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z$$\\[/tex]
Now we integrate three times to get the volume:
[tex]\\\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}$$[/tex]
Therefore, using triple integrals we know that the solid in question has a volume of 1024/3³ units.
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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.
the number of pollinated flowers as a function of time in days can be represented by the function
f(x)=(3) x/2
what is the average increase in the number of flowers pollinated per day between days 4 and 10
The average increase in the number of flowers pollinated per day between days 4 and 10 is 39.
What is average increase?
Average increase refers to the average rate of growth that a variable experiences within a given period.
According to the given question:
The number of pollinated flowers as a function of time in days is represented by the function f(x) = [tex]3^{(x/2)[/tex]
To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula
{f(10) - f(4)}/{10 - 4}
Now f(10) = [tex]3^{(10/2)[/tex]
= 243
Also f(4) = [tex]3^{(4/2)[/tex]
= 9
Therefore average increase = {f(10) - f(4)}/{10 - 4}
= (243 - 10)/10 - 4
= 234/6
= 39
Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39.
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how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other
There are therefore 609638400 different ways to arrange eight men and five women in a line so that no two women are positioned adjacent to one another.
What is fundamental counting principle?The basic counting principle is a method for keeping track of all the potential outcomes in a situation. It states that there are n*m ways to carry out both of these activities if there are n ways to carry out one action and m ways to carry out another action after that.
Here,
Number of ways men can stand,
=8!
=40320 ways
Number of ways women are standing,
=9P5
As shown in the image,
=15120 ways
For arranging both of them,
=40320*15120
=609638400 ways
So there is 609638400 ways of arranging eight men and five women to stand in a line so that no two women stand right next to each other.
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While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
While hiking, Mr. Fury burns 808 calories in 8 hours. At this rate, how many calories does he burn in 60 minutes?
(1): 6,464 calories
(2): 110 calories
(3): 101 calories
(4): 250 calories
808/8 = 101 per hour
60 minutes = 1 hour so:
101 * 1 = 101
2x³ - x² - 6x-1/x-1
This is probably the answer =2x4−x3−6x2−x−1/x
Recycling Do most teens recycle? To find out, an AP Statistics class asked an SRS of 100 students at their school whether they regularly recycle. How many students in the sample would need to say Yes to provide convincing evidence that more than half of the students at the school recycle? The Fathom dotplot below shows the results of taking 200 SRSs of 100 students from a population in which the true proportion who recycle is 0.50. (a) Suppose 55 students in the class’s sample say Yes. Explain why this result does not give convincing evidence that more than half of the school’s students recycle. (b) Suppose 63 students in the class’s sample say Yes. Explain why this result gives strong evidence that a majority of the school’s students recycle.
Suppose if 55 students in the class’s sample say Yes so, there is not sufficient evidence that more than half of the school student recycle.
and Suppose 63 students in the class’s sample say Yes so, there is sufficient evidence that more than half or majority school student recycle.
A.)
According to given data Suppose 55 students in the class’s sample.
n = 100 and x = 55
⇒ p = [tex]\frac{55}{100}[/tex] = 0.55
hence p' = 0.50
so, p > 0.50
Z = [tex]\frac{p-p'}{\sqrt{} \frac{p'(1-p')}{n} }[/tex]
Z = [tex]\frac{0.55-0.50}{\sqrt{} \frac{0.50(1-0.50)}{100} }[/tex]
so, Z = 1
let level of significance α = 0.05
critical Z value at α = 0.05 for one tail test is 1.645
since Z = 1 < z' = 1.645
do not reject at α = 0.05
there is not sufficient evidence that more than half of the school student recycle.
B.)
According to given data Suppose 63 students in the class’s
given data,
X = 63 and n = 100
now P = 63/100 = 0.63
Z = [tex]\frac{0.63-0.50}{\sqrt{} \frac{0.50(1-0.50)}{100} }[/tex] = 2.6
since, Z = 2.6 > Z' = 1.645
⇒ reject at α = 0.05
there is sufficient evidence that more than half or majority school student recycle.
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Find the volume of the olid obtained by rotating the region bounded by y=2x^2, x=0, and y=0 about the x-axi
the volume of the region bounded by y = 2x² is 4π/5unit³
What is volumes of Solids?
We shall encounter several solids and their corresponding volumes when discussing the concept of the volume of a combination of solids. As is common knowledge, the surface areas and volumes of all three-dimensional shapes depend on their dimensions. As we can see in reality, numerous shapes are created by fusing a variety of shapes. For instance, the combination of cone and cylinder shapes creates a tent. Similar to how a cone and a hemisphere combine to form an ice cream cone. As a result, the volume of the solids combined will equal the total of volume of the individual solids.
Given, region y = 2x²
Volume will be V = π/2 ∫(r²) dr
So we have 1/3 π * r² * h
So V = 4π (1/5)
V = 4π/5unit³
Hence, the volume of the solid is 4π/5unit³
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In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 44 inches?
Answer:
22√3 inches
Step-by-step explanation:
You want to know the length of the longer leg of a 30°-60°-90° triangle when the hypotenuse is 44 inches.
Side lengthsThe ratios of side lengths in a 30°-60°-90° triangle are ...
1 : √3 : 2
This means the longer leg is (√3)/2 times the length of the hypotenuse.
ApplicationIn the given triangle, the longer leg is ...
(44 in)(√3)/2 = 22√3 in
sean wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between three store locations: the oak ridge, oak wood, and oak park shopping malls. the most appropriate statistical test/analysis would be the .
The most appropriate statistical test/analysis for Sean who wants to test a hypothesis according to which the mean amount of sales dollars per employee will vary between 3 store locations would be the T-test.
What is the T-test?A T-test is a statistical test which compares the means of two samples. It is used in hypothesis testing, with a null hypothesis which the difference in group means is zero and an alternate hypothesis which the difference in group means is different from zero.
The choice of T-test depends on whether we are studying one group or two groups, and whether we care about the direction of the difference in group means.
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the amount that susan charges per hour for babysitting is directly proportional to the number of children she is watching. she charges $4.50 for 3 kids. how much would she charge to babysit 5 kids? $3.33 $7.50 $6.50 $1.50
Susan would charge $7.50 to babysit 5 kids.
The unitary method is used to calculate the value of a single unit from a given multiple. If the cost of 40 pens is Rs. 400, how do you calculate the value of one pen? The unitary method can be used to accomplish this. Furthermore, once we've determined the value of a single unit, we can multiply that value by the number of units needed.
Given,
Amount charged for 3 kids =$4.50
then,
Amount charged for 1 kid will be [tex]\frac{4.50}{3}=$1.50[/tex]
now, amount charge to babysit 5 kids =1.50*5=$7.50
Thus, Susan would charge $7.50 to babysit five children..
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hello! please help me with this, it’s due tomorrow (picture)
Answer:
[tex]\frac{8}{b^{30} }[/tex]
Step-by-step explanation:
Start within the parentheses
1. Divide coefficients
6/3 = 2
2. Divide variables
When dividing exponents with the same base, in this case b, you subtract.
b^20 - b^30 = b^-10
3. Exponent outside parentheses
When there's an exponent on an exponent, you multiply the exponents.
(2b^-10)^3
8 b^-30
4. Simplify?
This step isn't necessary, but when you have a negative exponent on a variable, the variable can be put in the denominator with a positive exponent.
8b^-30 can become 8/b^30
in a natural deduction problem if your conclusion is a conditional statement that does not appear in any of the premises, then the basic strateguy tells you to do what
In a natural deduction problem, if your conclusion is a conditional statement that does not appear in any of the premises, then it is not a valid argument.
Natural deduction is a process/theory that we use to derive the conclusion of any argument from the premises by using the rules of inference. Now, as the definition itself has established, in natural deduction problems we solve arguments from the premise. But in the argument, we have been told that the conclusion isn't from the premises.
Any argument or conclusion becomes valid if the premise is valid as well. This means that if the conclusion is not in the premise, then it is not valid.
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9. Write y = 4x+8 in standard form.
Answer:
4x - y = -8
Step-by-step explanation:
y = 4x+8
-8 + y = 4x
-8 = 4x - y
4x - y = - 8
An oven is priced at $675.40. there is a 6% sales tax rate. What is the sales tax for the refrigerator in dollars and cents
Answer:
We'll assume that the kitchen appliance (either an oven or a refrigerator) are actually the same, so I'll call it an oven.
The sales tax on an oven priced at 6% is $40.52
Step-by-step explanation:
($675.40)*(0.06) = $40.524, rounded to $40.52
Tom bought a bag full of coal. After one week the bag was 2 3 full. During the next week he used 1 4 of the remaining coal. What fraction was left in the bag?.
We conclude that there is zero (0) fraction of coal left in the bag with Tom.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
The number is represented mathematically as a quotient, where the numerator and denominator are split.
Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
The numerator of a proper fraction is less than the denominator.
So, a fraction of coal left in the bag:
After 1 week the was 2/3 full. So, we have:
1 - 2/3 = 1/3
Next week, he used the remaining 1/3 coal. Now, we have:
1/3 - 1/3 = 0/0
Therefore, we conclude that there is zero (0) fraction of coal left in the bag with Tom.
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Correct question:
Tom bought a bag full of coal. After one week the bag was 2/3 full. During the next week, he used 1/3 of the remaining coal. What fraction was left in the bag?
Expand the given logarithm and simplify. Assume when necessary that all quantities represent positive real numbers. Be sure to factor out any common factors in your final answer.
log5(125/ x^{2}-576)
Answer:
ok you deleted my other answer
Step-by-step explanation:
im just finishing this challenge and you are the last question i need to answer
PLEASE HURRY ITS TIMED
Identify the form the following equation is in
y − 2 = 58(x + 16)
a.point slope form
b.standered form
c.slope intercept form
Pretty sure this is the answer:
C. slope intercept form
a theater has 20 rows with 28 seats in the first row, 33 in the second row, 38 in the third row, and so forth. how many seats are in the theater?
The number of seats in the theater is 1510.
Here we have to find the number of seats in the theater.
Data given:
Total row = 20
number of seats on the first row = 28
number of seats on the second row = 33
number of seats on the third row = 38
Therefore we get the series as 28, 33, 38......., which is in arithmetic sequence.
The common difference (d) = 5
Here we have to find the sum of the series.
The formula for the sum of n term of the arithmetic sequence:
[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)
= 20/2 ( 2× 28 + (20 -1) 5)
= 10 ( 56 + 19×5)
= 10( 56 + 95)
= 10 ×151
= 1510
Therefore the number of seats is 1510.
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F(x) = 6x^3-29x^2+19x+4 and x-4 is a factor of f(x), then find all of the zeros of f(x) algebraically
The zeros of the given function are x= -1/6, x=1 and x= 4
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Divide the polynomial [tex]6x^3-29x^2+19x+4[/tex]by the factor (x-4) using long division method to find other 2 factors:
x-4) [tex]6x^3-29x^2+19x+4[/tex] ( [tex]6x^2-5x-1[/tex]
[tex]6x^3-24x^2[/tex]
______________________
[tex]-5x^2+19x+4[/tex]
[tex]-5x^2+20x[/tex]
__________________________
[tex]-x+4[/tex]
[tex]-x+4[/tex]
__________________________
0
Factors of [tex]6x^2-5x-1[/tex] are (6x+1)(x-1)
Find zeros by equating 3 factors to zero:
(6x+1)(x-1) ( x-4) = 0
=> (6x+1)=0, (x-1) =0 , ( x-4) =0
=> x= -1/6, x=1 and x= 4
Thus, the zeros of the given function are x= -1/6, x=1 and x= 4
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define two variables and translate the sentence into an inequality. the number of grams of saturated fat is more than seven times the number of grams of unsaturated fat
After translating sentence in to inequality we get x > 7*y.
Let us suppose two variables are x and y.
First let's understand what inequality means?
Inequalities specify the relationship between two values that are not equal. Equal does not imply inequality. Typically, we use the "not equal symbol ≠" to indicate that two values are not equal. But various inequalities are used to compare the values and determine whether they are less than or greater than.
Assume x as grams of saturated fat.
Assume y as grams of unsaturated fat.
Given as grams of saturated fat is more than seven times
grams of unsaturated fat.
[tex]x > 7*y[/tex].
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