[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~-8 - 1~~)^2 + (~~-4 - (-6)~~)^2} \implies d=\sqrt{(-8 -1)^2 + (-4 +6)^2} \\\\\\ d=\sqrt{( -9 )^2 + ( 2 )^2} \implies d=\sqrt{ 81 + 4 } \implies d=\sqrt{ 85 }\implies d\approx 9.2[/tex]
Given the speeds of each runner below, determine who runs the fastest.
\text{Adam runs 13 feet per second.}
Adam runs 13 feet per second.
\text{Stephanie runs 199 feet in 17 seconds.}
Stephanie runs 199 feet in 17 seconds.
\text{Noah runs 1 mile in 592 seconds.}
Noah runs 1 mile in 592 seconds.
\text{Katie runs 878 feet in 1 minute.}
Katie runs 878 feet in 1 minute.
Katie runs fastest among all .
What is the units of conversion ?
Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.
Given:
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
Speed of Noah = 1 mile in 592 seconds
Speed of Katie = 878 feet in 1 minute
Now on converting all the units to one single unit,we get
1 mile = 5280 feet
1 minute = 60 seconds
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
= [tex]\frac{199}{17}[/tex] feet per second
= 11.705 feet per second
Speed of Noah = 1 mile in 592 seconds
= 5280 feet in 592 seconds
= [tex]\frac{5280}{592}[/tex] feet per second
= 8.919 feet per second
Speed of Katie = 878 feet in 1 minute
= 878 feet in 60 seconds
= [tex]\frac{878}{60}[/tex] feet per second
= 14.6333 feet per second
Hence ,Katie runs fastest among all sice its speed is the highest .
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Find the slope of the line that passes through (5, 9) and (3, -5). Write your answer in simplest form.
Therefore the slope of the line passes through (5, 9) and (3, -5) comes out to be 7.
What is slope?By computing the ratio of the vertical to horizontal distance (rise over run) between two points, the slope—a numerical value that defines how steep a line is—is often calculated.
Here,
The slope of line that passes through (5, 9) and (3, -5)
Slope= gradient between the two points
Slope= (y2-y1)/(x2-x1)
Where y2= -5
Y1= 9
X2= 3
X1= 5
=> (-5-9)/(3-5)
=> -14/-2
=> 7
Therefore the slope of the line passes through (5, 9) and (3, -5) comes out to be 7.
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Use synthetic division to completely factor this polynomial.
3x4 - 14x³ 3x²+54x -40
Which expressions are factors of the polynomial?
-
(3x - 5)
(x + 4)
(x - 4)
(x 2)
(x + 2)
0 (x + 1)
(x - 1)
(3x + 5)
The expressions are factors of the polynomial 3x4 - 14x³ 3x²+54x -40 are
(x + 4)(x + 2)(x + 1)(x - 1)What are polynomials?Generally, To factor a polynomial using synthetic division, we need to find a factor of the polynomial that can be divided into the leading coefficient and the constant term of the polynomial.
In this case, the leading coefficient is 3 and the constant term is -40. One factor of 3 and -40 is (-4)(10).
The complete factorization of the polynomial is 3x⁴ - 14x³ + 3x² + 54x - 40 gives The remainder is 0, so the other factor is (x - 4)(x + 2)(x - 1)(x + 1).
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A young boy is growing at a rate of 3.5 cm per month. He is currently 90 cm
Answer:
it's 25.7
Step-by-step explanation:
you just divide the 90 by 3.5
what is a proportional relationship between x and y; proportional relationship calculator; proportional relationship formula; what is a proportional relationship example; proportional relationships 7th grade; is y=x/2 a proportional relationship; proportional relationship example problems
The proportional equation has a general form. The proportional relation is:
y = k/x
The letters y and x are variables that can vary, and the letter k is the constant of proportionality. A constant of proportionality is a constant ratio between the y and x variables. The constant of proportionality can be found by calculating y/x.
A proportional relationship is a relationship between two variables in which as one variable changes, increases, or decreases, the other variable changes at a constant rate. A constant ratio is considered a constant ratio between two variables. Proportional relationships can be identified by proportional equations, graphs, or tables. The proportionality equations discussed in this lesson have the general form: The graph is displayed as a straight line. The table is pairs of numbers with a constant ratio between the pairs.
A linear relationship is written as: y = mx + b, where m is the slope and b is the y-intercept.A direct proportional relation is written as y = k/x. where k is the constant of proportionality. A direct proportional relationship is a linear relationship where k is the slope and the y-intercept is zero.Therefore, only linear relationships with zero y-intercept are directly proportional.
For example:
If 1 hat is $20, 2 hats are $40, 3 hats are $60, and so on. This is a direct share. If you triple the number of hats, the total amount will triple.
For 1 hut and $30 fee, 2 hut and $50 fee, 3 hut and $70 fee. This is a linear relationship, with each additional hat ordered increases the price by $20. However, due to a one-time processing fee of $10, the total price of 3 hats will not be 3 times the total price of 1 hat.
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the managers of a company are worried about the morale of their employees. in order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. they select the fortunato test of job satisfaction which has a known standard deviation of 24 points. they should sample employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.
90% confidence interval is 82.11 < μ < 93.89
"Information available from the question"
The complete question is this:
The managers of a company are worried about the morale of their employees. In order to determine whether a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.
Due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88 points. What is the 90% confidence interval?
Now, According to the question:
We have :
The confidence level = 0.90
The significance level, [tex]\alpha[/tex] = 0.10
The sample mean, x = 88
The population standard deviation, σ = 24
The sample size, n = 45
Critical value of z using the z - distribution table:
z(critical) = [tex]z_\alpha[/tex] /2
= [tex]z_0_._0_5[/tex]
= ±1.645
90% confidence interval:
μ = x ± z. σ/[tex]\sqrt{n}[/tex]
μ = 88 ± 1.645 x 24 / [tex]\sqrt{45}[/tex]
μ = 88 ± 5.89
82.11 < μ < 93.89
Hence, 90% confidence interval is 82.11 < μ < 93.89
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The production costs, P , for a band to have a concert can be modeled by the equation P=850+5x , where x is the number of concert tickets sold. The band earns $50 for each ticket sold. The band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert. How many tickets does the band have to sell for each concert to meet the goal?
The number of tickets that the band have to sell for each concert to meet the goal is 76 tickets
How many tickets does the band have to sell for each concert to meet the goal?Based on the information given, the production costs, P , for a band to have a concert can be modeled by the equation P=850 + 5x.
x = the number of concert tickets sold.
Since the band earns $50 for each ticket sold. The band’s goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert.
This will be illustrated thus:
Revenue - Cost = Profit
50x - 850 + 5x = 5000
Collect like terms
55x = 5000 - 850
55x = 4150
Divide
x = 4150 / 55
x = 76
The tickets will be 76.
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find the measure of angle B
You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus. How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
The sample required to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence is 158.
Given:
You wish to conduct your own study to estimate the miles per gallon on a 2007 Ford Taurus.
How large a sample would you need to estimate the mean per gallon within 0.5 miles per gallon with 95% confidence = ?
if you read in a previous study that the standard deviation of miles per gallon for a 2007 Taurus is 3.21.
we know that :
z value of 95% is 1.96
Margin of error = E = z × sd/√n
we have:
n = (z×sd/E)²
= 158.33
= 158
Hence we get the sample as 158
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Which is equivalent to ³√8^x?
O ^x√8^3
O 8^3/x
O8^x/3
O8^3x
After solving the given expression it will be equivalent to [tex]8^\frac{x}{3}[/tex]. Hence, option C is correct.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given expression in the question,
[tex]\sqrt[3]{8}^x[/tex]
So, this form is written as power/root
Then, then it can be written as [tex]8^\frac{x}{3}[/tex].
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Show transcribed dataFind the characteristic polynomial of A. Use x for the variable in your polynomial. You do not need to factor your polynomial 12 - 10 0 A = 9 -7 0 0 02 characteristic polynomial of A is: 0
The characteristic polynomial x³ - 7x² + 16x - 12 The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.
Its coefficients include the determinant and the trace of the matrix.
Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A11 + A22 + A33 )x - determinant(A)
Where Aii is the determinant of the matrix obtained by deleting i th row and i th column.
Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7
A11 = -7 × 2 = -14
A22 = 2 × 12 = 24
A33 = ( 12×-7) - (-10×9) = 6
Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12
Substituting these values in above equation , we obtain;
x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.
Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.
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f ( x ) = − 2 x − 3 find f( 2 )
Answer:
The answer is (-7)
Step-by-step explanation:
f(x) = -2x - 3, if f(2)
f(2) = -2(2) - 3 = -4 - 3 = (-7)
Thus, The answer is (-7)
suppose the cost of a car produced in the united states is $20,000. the current exchange rate is us$1= €0.85. What is the cost of the car in euros?
The cost of the car in euros is 17,000 euros
Given that,
Let's say an automobile made in the United States costs $20,000. At this time, one US dollar is worth 0.85 euros. A automobile made in the United States costs $20,000 to construct.
To find : that the car's price in euros ?
The information provided lets us know that,
The car's price in euros= 20,000 * 0.85
= 17,000 euros
Therefore, the car's price in euros is 17,000 euros.
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Raquel is playing a game where she throws a ball that paper called a trash ball into her trashcan the diameter of the top of the trashcan is 20 inches Raquel once the trash ball to have a diameter that is 1/4 the diameter of the top of the trashcan what should the timing of Raquel trash Be?
The diameter of the top of the trash ball is 5 inch.
What is a diameter?A straight line that runs through the middle of a body or figure from the sideways particularly a circle or sphere is called as a diameter of a circle or sphere.
Given that the diameter of top of the trash can is 20 inch.
And the diameter of trash ball is 1/4th of the diameter of trash can.
The diameter of trash ball = 1/4 ( the diameter of trash can )
The diameter of trash ball = 1/4 (20 inch)
The diameter of trash ball = 20/4
The diameter of trash ball = 5 inch.
Therefore, the diameter of the top of the trash ball is 5 inch.
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The complete question is;
Raquel is playing a game where she throws balled-up paper called a “trash ball” into her trash can. The diameter of the top of the trash can is 20 inch . Raquel wants the “trash ball” to have a diameter that is 1/4 the diameter of the top of the trash can. What should the diameter of Raquel's “trash ball” be? .
A 3-gallon container of window cleaner costs $17.76. What is the price per quart?
Answer: $1.48
Step-by-step explanation:
find how much each gallon cost
1. 17.76/3=5.92
Divide by 4 because 4 quarts equal a gallon
2. 5.92/4=1.48
Therefore each quart equals $1.48,
Hope this helps!
let $abc$ be an acute triangle satisfying the conditions $ab > bc$ and $ac > bc$. denote by $o$ and $h$ the circumcenter and orthocenter, respectively, of the triangle $abc$. suppose that the circumcircle of the triangle $ahc$ intersects the line $ab$ at $m$ different from $a$, and the circumcircle of the triangle $ahb$ intersects the line $ac$ at $n$ different from $a$. prove that the circumcenter of the triangle $mnh$ lies on the line $oh$.
In an acute triangle, the circumcenter of the triangle lies on the line O.
Acute triangle.
In geomentry, acute triangle is the type of triangle in which all the three internal angles of the triangle are acute
Given,
Here we need to prove that in the acute triangle ABC, the circumcenter of the triangle MNH lies on the line OH.
Let us consider T be the intersection of σ1 and σ1 other than W.
Now, the Lemma 1: T is on XY.
Now, the Proof is written as We have ∠XTW} = ∠YTW = 90 degres because they intercept semicircles.
Therefore, ∠XTY = ∠XTW + ∠YTW = 180 degrees,
Then XTY is a straight line.
Here we know that NHLB is cyclic because ∠BNH and ∠BLH, opposite and right angles, sum to 180 degree. Furthermore, we are given that NTWB is cyclic.
Therefore, the triangle MNH lies on the line OH.
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Suppose f(x,y,z) = x^2 + y^2 + z^2 and W is the solid cylinder with height 5 and base radius 2 that is centered about the z-axis with its base at z = -1. Enter \theta as theta.
(a) As an iterated integral,
\displaystyle \iiint\limits_{W} f \, dV = \int_A^B \!\! \int_C^D \!\! \int_E^Fdz \, dr \, d\theta
with limits of integration
A =
B =
C =
D =
E =
F =
(b) Evaluate the integral.
If f(x,y,z) = x²+y²+z² and W is the solid cylinder with height 5 and base radius 2 that is centered about z-axis with its base at z=-1 then the integral value is 432π.
They want f inside the integral so your integer and is: (x² + y² + z²) rdzdrdt
Note that you need another r because you are integrating in cylindrical
coordinates.
conversion equations:
x = rcost
y = rsint
x² + y² = r²
(x² + y² + z²)rdzdrdt becomes (r² + z²)rdzdrdt
W is the solid cylinder with height of 3, radius of 4, and centered about the z-axis, starting from z = -1.
Around the z-axis, cylinders take the forms of circles: x² + y² = r²
This cylinder will have the equation: x² + y² = 16
Its height is 3 so from z = -1 to z = 2
z bounds: -1 <= z <= 2
r bounds (based on the circle): 0 <= r <= 4
t bounds (based on the circle): 0 <= t <= 2pi
\(\int_{0}^{2\pi}\int_{0}^{4}\int_{-1}^{2}(r^{2}+z^{2})rdzdrdt\)
(r² + z²)r = r³ + rz²
dz integral gives: r^3*z + (1/3)rz^3 --> 2r^3 + (8/3)r - (-r^3 - (1/3)r)
= 2r^3 + (8/3)r + r^3 + (1/3)r
= 3r^3 + 3r
dr integral gives: (3/4)r^4 + (3/2)r^2 --> 216
dt integral gives: 216t --> 432pi
Hence we get the integral value as 432π
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1 + 1 =
i got to put 20 characters very sadly but get rich quick here!
Answer:
2
Step-by-step explanation:
Hii!
Answer:
2
Step-by-step explanation:
1+1=2
a chain of sport shops catering to beginning skiers, headquartered in aspen, colorado, plans to conduct a study of how much a beginning skier spends on his or her initial purchase of equipment and supplies. based on these figures, it wants to explore the possibility of offering combinations, such as a pair of boots and a pair of skis, to induce customers to buy more. a sample of 44 cash register receipts revealed these initial purchases: $ 180 $ 186 $ 130 $ 263 $ 258 $ 159 $ 127 $ 84 $ 208 180 104 233 92 223 176 216 219 209 205 150 241 110 239 124 173 174 264 232 182 261 216 193 196 223 239 176 261 150 245 84 232 152 95 233 click here for the excel data file required: a. arrive at a suggested class interval. (round your answer up to the next multiple of 5.) b. organize the data into a frequency distribution using a lower limit of $70.
(a) Class interval of a given data is 36.
(b) Frequency distribution is 44.
We have given that,
total frequency = 44
lower limit = $70
number of class = 5
(a) we have to find class interval,
Class interval = [tex]\frac{Max. number - min. number}{no. of classes}[/tex]
here maximum number is 264 and minimum number is 84
Class interval = [tex]\frac{264 - 84}{5}[/tex]
= [tex]\frac{180}{5}[/tex]
Class interval = 36
we have to round our value to the next multiple of 5
so the class interval will be 40.
(b) A frequency distribution is the pattern of frequencies of a variable. It is the number of times each possible value of a variable occurs in a dataset. There are three types of frequency distribution such as Cumulative frequency distribution, Relative frequency distribution, Relative cumulative frequency distribution.
The frequency distribution is as follows:
Class interval Frequency
70 - 110 6
111 - 151 5
152 - 192 10
193 - 233 14
234 - 274 9
Total 44
This is the organize data into a frequency distribution.
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Write an equation of a circle whose
center is (3,-2) and passes through the
point (-5,8).
Answer:
(x-3)^2+(y+2)^2=164
Step-by-step explanation:
radius is
the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of pennsylvania showed a mean annual premium of $1,430 with a standard deviation of s s = $165.
(a)
Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
H0: ???? > 1,503
Ha: ???? ≤ 1,503
H0: ???? < 1,503
Ha: ???? ≥ 1,503
H0: ???? ≤ 1,503
Ha: ???? > 1,503
H0: ???? = 1,503
Ha: ???? ≠ 1,503
H0: ???? ≥ 1,503
Ha: ???? < 1,503
(b)
What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)
$
(c)
At
???? = 0.05,
test for a significant difference.
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Do not reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
Reject H0. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.
The hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium is between -2.064 and 2.064.
Hypothesis testing
The standard formula to calculate the hypothesis testing is given by the z test is
Z = (X – U) / (SD / √n)
Where:
X – Sample Mean
U – Population Mean
SD – Standard Deviation
n – Sample size
Given,
Here we have the the insure website reports that the mean annual premium for automobile insurance in the united states was $1,503 in march 2014. being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. a sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,430 with a standard deviation of is $165.
Here we need to develop the a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.
While we looking into the given question we have identified the values of
Sample mean = 1430
Sample size = 25
Population mean = 1503
Standard deviation = 164
Then the hypothesis testing is calculated as,
=> Z = (1430 – 1503) / (164 / √25)
Therefore, if we reject the null hypothesis and accept the alternative hypothesis. The z score of -2.23 is within the rejection area.
And the 2 critical values (cutoff points) are -2.064 and 2.064. Since the z score, -2.23, is outside this interval, we reject the null hypothesis. We accept the alternative hypothesis.
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A dessert recipe calls for 2 cups of milk and makes 5 servings. How many cups of milk are needed for 8 servings?
5 servings = 2 cups of milk
1 serving = 2/5 cups of milk
do not worry about the fraction of milk for now!!
8 servings = 2/5 × 8 cups of milk
= 3.2 cups of milk
= 3 cups (rounded down)
Which figure has two sets of parallel sides?
Answer: Parallelogram
Step-by-step explanation: [Parallelogram definition]: A parallelogram is a quadrilateral with 2 pairs of parallel sides. In these figures, sides of the same color are parallel to each other. A shape with four sides of equal length.
To see a shape that is a parallelogram, look at the attachment down below:
In a large doll store, 47% of the dolls blink, 56% of the dolls have movable legs and
arms, and 23% of the dolls neither blink nor have movable limbs. Find the probability
that a doll chosen at random will both blink and have movable limb.
This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.
what is probability?There is a 50% chance that the outcome will be heads, thus 50 heads are to be expected. When we really attempt it, though, we might instead get 48 heads, 55 heads, or anything else at all, but in most situations, it will be a figure close to 50.
calculation
If B is a set of moveable arms and legs and A is the number of dolls that can blink, then P(A)=0.47, P(B)=0.56, P(A' and B')=0.23,
therefore P(A or B)=1-0.23=0.77, and
P(both blink and moveable limbs)=P(A and B)=0.47+0.56-0.77=0.26.
This means that the probability that a doll selected at random will blink and have moving limbs is 0.26.
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which statement is true about the graphed function? F(x) < 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) > 0 over the intervals (–[infinity], –2.5) and (–0.75, 0.75).
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, [infinity]).
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, [infinity]).
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
Lets explain the graph to answer the problem
- When we ask about f(x) we means the values of y
- f(x) > 0 means the graph is over the x-axis because over the x-axis
y is positive
- f(x) < 0 means the graph is under the x-axis because under the x-axis
y is negative.
* Lets describe each part of the graph
- The graph intersect the x-axis at :
x = -2.5 , x = -0.75 , x = 0 , x = 0.75
- The graph is over the x-axis between -∞ and -2.5 and between
-0.75 and 0.75
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-∞ , -2.5) and (-0.75 , 0.75)
∴ f(x) > 0 over the intervals (-∞ , -2.5) and (-0.75 , 0.75)
- The graph is under the x-axis between -2.5 and -0.75 and between
0.75 and ∞
At x = -2.5 f(x) = 0 , at x = -0.75 f(x) = 0 , at x = 0.75 f(x) = 0
∴ x = (-2.5 , -0.75) and (0.75 , ∞)
∴ f(x) < 0 over the intervals (-2.5 , -0.75) and (0.75 , ∞)
* The true statement in the answer is;
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
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in general, high scores on the big five factor of ___are associated with less optimal life outcomes.
In general, high scores on the big five factor of Neuroticism are associated with less optimal life outcomes.
Neuroticism is one of the Big Five factors in the study of personality in psychology. Neuroticism is a personality trait characterized by sadness, moodiness, and emotional instability.
High neurotic people frequently experience mood swings, anxiety, impatience, and melancholy. People who score lower on this personality trait tend to be more emotionally stable and resilient. A person may strive to be a perfectionist during their everyday activities, and experience stress as a result of events that are beyond their control.
An individual with neuroticism may choose to concentrate on and dwell on the bad rather than the positive parts of a scenario. When individuals believe they have an advantage over others, they get envious of them and experience jealousy.
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Question is attached
Answer:
56°
Step-by-step explanation:
the measurement of angle O is less than 90°, but not 62°, and angle O is larger than angle R, so angle O is not 28°, so the only other option less than 90° is 56°
if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
If the angle between two vectors is represented by theta and it is equal to zero or 180 degrees then the following angles would mean the vectors are parallel .
Given :
if the angle between two vectors is represented by , tell if the following angles would mean the vectors are orthogonal, parallel or neither.
if two vectors points are given then find the dot product of vectors if the result is equal to zero then the two vectors are orthogonal vectors .
If they were parallel the angle would be 0 or 180 degrees, therefore, the two vectors are not parallel.
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Question 3 (1 point) Use the table below to determine 1) which is the correct graph and 2) answer whether the relationship is proportional or not. Time (mins) 2 3 4 Height of Balloon (meters) Hot Air Balloon Height over Time 123456 Time (minutes) Height (meters) 22 33
Answer:
See below for the graph
It is proportional. The graph is a straight line going through the origin.
Step-by-step explanation:
The equation of the line is
y = 11x
Use quadratic regression and a graphing calculator to find the quadratic function that best fits the data set. Then use the model to forecast the value of the function at the indicated point.(Round your coeffiecients to two decimal places.) Years Abortions Since 1985(per 1000 live births) t3 10 15 16 17 422 389 350 324 325 319 What was the abortion rate in 2005? (Round your answer to the nearest whole number) abortions
The abortion rate in 2005 was 309 per 1000 live births.
Given:
y = Ax²+Bx+C
from calculator : A = 0.13
B = -8.34
C = 423.50
y = 0.13x² - 8.34x + 423.50
Abortion rate in 2005:
x=20
y = 0.13x(20)² - 8.34×20 + 423.50
y = 308.7
y = 309 per 1000 live births.
Hence we get the required answer.
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