Answer:
No, we can't reject [tex]H_0[/tex] at the α = 0.01 level of significance.
Step-by-step explanation:
We are given the sample of five matched pairs below ;
Sample 1 (B) : 20, 20, 23, 18, 22
Sample 2 (A) : 23, 16, 15, 14, 18
Let [tex]\mu_1[/tex] = population mean for first sample
[tex]\mu_2[/tex] = population mean for second sample
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0 {means that there is no difference between the population means of both samples}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0 {means that three is positive difference between the population means of both samples, i.e. population mean of first sample is higher than the population mean of second sample}
The test statistics that will be used here is Paired data test statistics;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_D}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = [tex]\bar B -\bar A[/tex] = 20.6 - 17.2 = 3.4
[tex]s_D=\sqrt{\frac{\sum D_i^{2}-n \bar D^{2} }{n-1}}[/tex] = [tex]\sqrt{\frac{121-5 \times 3.4^{2} }{5-1}}[/tex] = 3.975
n = sample size = 5
So, test statistics = [tex]\frac{3.4-0}{\frac{3.975}{\sqrt{5} } }[/tex] ~ [tex]t_4[/tex]
= 1.913
Now at 0.01 significance level, the t table gives critical value of 3.747 at 4 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 3.747 > 1.913, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the there is no difference between the population means of both samples.
Answer:
No, we can't reject at the α = 0.01 level of significance.
Step-by-step explanation:
the other response is right
PLEASE HELP
What is the volume, in cubic m, of a cube with an edge length of 14m?
Answer:
v = 2744 m³
Step-by-step explanation:
Volume of cube
= length³
= l³
= 14³
= 2744 m³
make as the brainliest
Final answer:
The volume of a cube with an edge length of 14m is 2,744 cubic meters (m³), calculated using the formula V = a³, where a is the edge length.
Explanation:
To find the volume of a cube with an edge length of 14m, we use the formula for the volume of a cube, which is V = a³, where a is the length of an edge of the cube. In this case, each edge is 14 meters long. Therefore, the volume of the cube is calculated as follows:
V = 14m × 14m × 14m = 2,744 m³
This means the volume of the cube is 2,744 cubic meters (m³). It's important to remember that the volume measures the amount of space within the cube, and the unit of measure for volume in the International System of Units (SI) is cubic meters (m³).
"Benny decided to look at the price of new and used vans. Benny found a used van for $3000. Benny found that he paid 20% of the price of a new van. How much would a new van cost?"
Answer:
$15000
Step-by-step explanation:
We have that the value of the truck is $ 3000 and that this payment is equivalent to 20% of the value of a new truck, therefore the value of the new truck would be:
% of value value
20 3000
100 x
x = 100 * 3000/20
x = 15000
therefore the value of the new truck is $ 15000
Which of these equations correctly represents the following scenario: In her prime, 40 million people knew who Britney Spears was, but that number has been decreasing by 10% each year. So, since 90% of people still recognize her each year, how many people still know who Britney is each year?
y = 40,000,000(0.9)x
y = 0.9(40,000,000)x
y = 40,000,000(0.01)x
y = 0.1x + 40,000,000
y = 0.01(40,000,000)x
Answer:
Its the first option
40,000,000(0.9)x.
Step-by-step explanation:
90% recognise her each year so after 1 year so the number (N) is:
N = 40,000,000(0.90)^1 = 36,000,000 recognise her after 1 year.
N = 40,000,000(0.90)^2 = 32,400,000 recognise her after 2 yeas
- and so on.
After x years:
N = 40,000,000(0.90)^x.
Note the x is a power and is best written as ^x.
The correct equation to represent the given scenario is [tex]y = 40,000,000(0.9)^x[/tex]. This equation represents a geometric sequence, with the initial quantity being 40,000,000 and decreasing by 10% each year.
Explanation:The scenario is a geometric sequence, where the number of people who still recognize Britney Spears each year is decreasing by 10%. To represent this situation mathematically, we can use a geometric equation: [tex]y = a \cdot r^x[/tex]where 'a' is the initial quantity, 'r' is the ratio of decrease or increase, and 'x' is the number of time periods.
In this case, 'a' is 40,000,000 (the initial amount of people), 'r' is 0.9 (representing a 10% decrease each year), and 'x' will represent the number of years since her prime. Thus, the correct equation out of the options to represent the scenario is [tex]y = 40,000,000(0.9)^x.[/tex]
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Write 14 as a product of primes.
Answer:
14 = 2*7
Step-by-step explanation:
2 and 7 are prime.
Answer:
14 = 1 x 14 or 2 x 7. Factors of 14: 1, 2, 7, 14. Prime factorization: 14 = 2 x 7
Step-by-step explanation:
Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with standard deviation of 3 ml. A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are:299.4 297.7 301.0 298.9 300.2 297.0Is this convincing evidence that the mean contents of cola bottles is less than the advertised300 ml? Test at the 5% significance level.
Answer:
No because there is sufficient statistical evidence to suggest that the mean contents of cola bottles is equal to 300 ml as advertised
Step-by-step explanation:
Here we have the measured contents as
299.4
297.7
301.0
298.9
300.2
297.0
Total = 1794.2
∴ Mean = 299.03
Standard deviation = 1.5
We have
[tex]z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]
Where:
[tex]\bar x[/tex] = Mean of sample = 299.03 ml
μ = Mean of population = 300 ml
σ = Standard deviation of population = 3 ml
n = Sample size = 6
α = 5% = 0.05
We set our null hypothesis as H₀ = 300 ml
Our alternative hypothesis is then Hₐ < 300 ml
Therefore, z = -0.792
The probability from z table is P = 0.2142
Since the P value, 0.2142 is > than the 5% significance level, 0.05 we accept the null hypothesis that the mean contents of cola bottles is 300 ml.
Identifying Characteristics of the Exponential Function y = bx (b > 1)
The domain of an exponential function is . The range of an exponential function is .
On a coordinate plane, the graph of y = 2 Superscript x is shown. The curve approaches the x-axis in quadrant 2 and then increases quickly into quadrant 1.
Answer:
domain (-∞, ∞)range (0, ∞)Step-by-step explanation:
The domain is the horizontal extent: all real numbers. -∞ < x < ∞.
The range is the vertical extent: all numbers greater than zero. 0 < y < ∞. (The graph never actually touches y=0, but comes arbitrarily close.)
To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52). The order in which the selections is made does not matter. How many different 6-number selections are possible?
Answer:
The answer is 20,358,520
Step-by-step explanation:
Selecting 6 numbers from a collection of 52 numbers regardless of order involves a combination.
Note: if regards was taken into order of selection, this would be a permutation.
Hence, the different 6 number selections out of 52 is
52C6 = 52! / [6!*(52-6)!]
= 52!/(6!*46!)
= 20,358,520
An amusement park charges an admission fee of 20 dollars for each person. Let C be the cost (in dollars) of admission for P people. Write an equation relating to C to P. Then use this equation to find the cost of admission for 17 people.
Answer:
20 x 17 = 340
Step-by-step explanation:
C= cost
P=people
Equation- 20p=c
20 x 17 (people) = cost
:) would appreciate anything
Can someone help solve for X
Answer:
x = 2sqrt(5)
Step-by-step explanation:
We can use the Pythagorean theorem to solve
The legs are x and 8/2 =4
and the hypotenuse is 6
a^2 + b^2 = c^2
x^2 +4^2 = 6^2
x^2 +16 = 36
Subtract 16 from each side
x^2 +16-16=36-16
x^2 = 20
Take the square root of each side
sqrt(x^2) = sqrt(20)
x = sqrt(4*5)
x = sqrt(4) sqrt(5)
x = 2sqrt(5)
Answer:
Step-by-step explanation:
Is it A)50 degrees, B) 60 degrees C) 74 degrees or D) 78 degrees
Each month, Jeremy adds the same number of cards to his baseball card collection. In Jeremy, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April
Jeremy will have 72 baseball cards in April.
What is a consecutive pattern?A consecutive pattern refers to a sequence or order of numbers, letters, or other objects in which each follows in direct and uninterrupted succession from the one that precedes it.
We have,
To solve this problem, we need to determine the pattern of how many cards Jeremy adds to his collection each month.
To do this, we can find the difference between consecutive months:
February minus January: 48 - 36 = 12
March minus February: 60 - 48 = 12
We can see that Jeremy is adding 12 cards to his collection each month.
So to find out how many cards he will have in April, we can add 12 to the number he had in March:
April
= 60 + 12
= 72
Therefore,
Jeremy will have 72 baseball cards in April.
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For five days, several hikers walk the distance and direction described by the vector
⟨5, –2⟩ each day. The next day, they walk the distance and direction described by the vector ⟨–1, 8⟩. At the end of the six-day trip, what is their bearing from their starting location?
Answer:
94.76°
Step-by-step explanation:
Assuming the coordinates are <E, N>, the total distance from the start is ...
5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>
These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...
arctan(24/2) = 85.24°
The bearing is 180° -85.24° = 94.76°.
Ryan charges his neighbors $17.50 to wash their car. How many cars must he wash next summer if his goal is to earn at least $1,500?
Answer:
86 cars
Step-by-step explanation:
1,500/17.50=85.71 so you just round it a little
He must wash 86 cars.
What is division?The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. It is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.
Example: 4 / 2 = 2.
Given, Ryan charges his neighbors $17.50 to wash their car.
So, he earns $17.50 per car.
Let Ryan washes x cars to earn $1500
$17.50(x)=$1500
x = $1500/$17.50
x = 85.71 ≈ 86
Hence, Ryan needs to wash 86 cars to earn at least $1500.
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Suppose your new business made a profit during the first year of $3000. If the profit increased 12% per year, find the total of all profit earned by the end of the first 5 years.
Answer:
Therefore the total of all profit earned by the end of of the the first 5 years is $19,058.542.
Step-by-step explanation:
To find total profit earned per year, we need to use the compound growth formula.
The compound growth formula:
[tex]A= P(1+r)^t[/tex]
A= Amount after t years
P= initial amount
r= rate of growth
t= time in year.
Given that,
New business made a profit during the first year of $3000.
If the profit increased 12% per year.
Here P= $3,000 and r =12%=0.12 , t=1 years
Plugging all value in the above formula:
[tex]A=3000(1+0.12)^1[/tex]
=3000(1.12)
=$3360
Profit after 2 year is $3,360.
Now, P= $3,000 and r =12%=0.12 , t=3 years
[tex]A=3000(1+0.12)^2[/tex]
=3000(1.12)²
=$3763.2
Similar the profit at 4 year is
[tex]A=3000(1+0.12)^3[/tex]
=3000(1.12)³
=$4214.784
The profit at 5th year is
[tex]A=3000(1+0.12)^4[/tex]
=3000(1.12)⁴
=$4720.558
Therefore the total of all profit earned by the end of of the the first 5 years is=$(3,000+3360+3763.2+4214.784+4720.558)
=$19,058.542
Zad.1 12 pracowników spytano o liczbę dni wykorzystanego urlopu. Oto odpowiedzi: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Podaj dominantę i medianę. Zad. 2 13 pracowników spytano o liczbę dni wykorzystanego urlopu. Oto odpowiedzi: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Podaj dominantę i medianę. Zad.3 Oblicz dominantę i medianę a)Odległość zamieszkania w km. b) Liczba pracowników a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15
Answer:
Taak 1.12
Mediaan is 5 en het gemiddelde is 5,67
Taak 2 13
De mediaan is 6
Het gemiddelde is 6
Standaarddeviatie is 3,32
Variantie is 11
Aantal werknemers is 13
Step-by-step explanation:
Taak.1 12 medewerkers is gevraagd naar het aantal verlofdagen. Hier zijn de antwoorden: 2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8. Geef de dominante en de mediaan. Taak 2 13 medewerkers is gevraagd naar het aantal vakantiedagen. Hier zijn de antwoorden: 2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9. Geef de dominante en mediaan. Zad.3 Bereken de dominante en de mediaan a) Verblijfsafstand in km. b) Aantal werknemers a) b) 0-5 5 5-10 25 10-15 30 15-20 55 20-35 30 25-30 20 30-35 15
Taak. 1 12, wordt de mediaan gegeven door
2, 5, 14, 3, 6, 5, 8, 2, 5, 4, 6, 8 herschikken, we krijgen
2, 2, 3, 4, 5, 5, 5, 6, 6, 8, 8, 14
Daarom is de mediaan 5 en het gemiddelde 5,67
Taak 2 13
2, 4, 14, 3, 6, 7, 8, 2, 5, 4, 6, 8, 9 herschikken, we krijgen
2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 14
De mediaan is het zevende nummer in de rij = 6
Het gemiddelde is ook = 6
Standaarddeviatie = 3,32
Variantie = 11
Aantal werknemers = som van frequentie of aantal gegevens = 13.
The regular price of a computer is $1200 and the regular price of a printer is $300. The regular price of a computer is 1200 dollars and the regular price of a printer is 300 dollas. An electronics store has a promotion that offers a 40% 40 percent discount on the printer when the computer is purchased at the regular price. What is the total cost of the computer and the printer at the promotional price?
Answer:
$1380
Step-by-step explanation:
The regular price of a computer is $1200The regular price of a printer is $300.The electronics store offers a 40% discount on the printer only when the computer is purchased at the regular price.
Discount on the Printer = 40% of $300 =0.4 X 300 =120
Promotional Price of the Printer = $300-120 =$180
Therefore, the total cost of the computer and the printer at the promotional price
=Regular price of a computer + Promotional Price of the Printer
=1200+180
=$1380
For a research project on rodents, 60 groundhogs were tagged and released. Later, researchers
counted 700 groundhogs, 12 of which had tags. To the nearest whole number, what is the best
estimate for the groundhog population?
The estimated size of the lemur population can be calculated using the mark and recapture technique.
Explanation:The estimated size of the lemur population can be calculated using the mark and recapture technique. The formula to estimate population size is:
N = (M * C) / R
where N is the estimated population size, M is the number of marked individuals in the second capture, C is the total number of individuals in the second capture, and R is the number of marked individuals recaptured in the second capture.
In this case, the number of marked individuals in the second capture is 11, the total number of individuals in the second capture is 49, and the number of marked individuals recaptured is 11. Plugging these values into the formula:
N = (11 * 49) / 11 = 49
Rounding to the nearest whole number, the estimated size of the lemur population is 49.
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If the slope of the linear function y=-2x-4 was changed to 3, what would the new equation be? *
A. y=2x-3
B. y=3x-4
C. y=2x+3
D. y=3x+4
Answer:
b
Step-by-step explanation:
-2 is the slope so change -2 to 3
A box of cereal has a volume of 336 cubic inches. If the width of the box is 4 inches and the length is 7 inches, what is the height of the box
I'm confused
Answer:
12 inches
Step-by-step explanation:
Volume = length × width × height
336 = 4 × 7 × height
height = 12
Answer:
12 cubic inches.
Step-by-step explanation:
Since volume is length x width x height, you just do 7 x 4 (28) and then the total, 336 and divide that by 28. So, 12 cubic inches!
Mrs. Garcia has two kinds of flowers in her garden. The ratio of lilies to daisies in the garden 3:2 if there are 15 lilies, what is the total number of flowers in her garden?
Answer:
The total number of flowers in Mrs. Garcia's garden is 25.
Step-by-step explanation:
The ratio of lilies to daisies is 3:2 and there are 15 lilies. We need to compute the number of daisies first and then add both the number of daisies and lilies to compute the total number of flowers. Using the ratio method:
Lilies : Daisies
3 : 2
15 : x
By cross multiplying we get:
3x = 15*2
3x = 30
x = 10
Hence, the total number of flowers in the garden are:
10 + 15 = 25
The total number of flowers in Mrs. Garcia's garden is 25.
Answer:
25
Step-by-step explanation:
Given that the number of lilies = 15
Given ratio = 3:2
Let the total number of flowers be X
Let the number of daisies be 'a'
3/2 = 15/a
3×a = 2×15
3a = 30
a = 30/3
a = 10
X = number of lilies + number of daisies
X = 15 + 10
X = 25
At a high school with over 500 students, a counselor wants to estimate the mean number of hours per week that students at the school spend in community service activities. The counselor will survey 20 students in the Environmental Club at the school. The mean number of hours for the 20 students will be used to estimate the population mean.Which of the following conditions for inference have not been met?1. The data are collected using a random sampling method.2. The sample size is large enough to assume normality of the distribution of sample means.3. The sample size is less than 10 percent of the population size. A. II onlyB. III onlyC. II and III onlyD. I, II, and III
Population distribution is probability distribution that measures the frequency of sample provided. For the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.
Given-Total students 500.
Total students surveyed by the counselor is 20.
Population distribution
Population distribution is probability distribution that measures the frequency of sample provided.
I)The data are collected using a random sampling method- All the students surveyed by the counselor is 20 is collected using a random sampling method. Hence the condition I is met for the inference.II) The sample size is large enough to assume normality of the distribution of sample means- The sample size for the given problem is 20. For a large population the sample size must equal to or greater than the 30.Hence the condition II is not met for the inference.III)The sample size is less than 10 percent of the population size- We have total student 500. The 10 percent of the population size is,[tex]P=\dfrac{10\times500}{100}[/tex]
[tex]P=50[/tex]
Here the 10 percent of the population size is 50. Our sample size is 20. Thus the sample size is less than 10 percent of the population size.Hence the condition III is met for the inference.
Hence, for the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.
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f(x) = x4 + x3 + 2x2 + ax + b,
where a and b are constants.
When f(x) is divided by (x - 1), the remainder is 7
(a) Show that a + b = 3
When f(x) is divided by (x + 2), the remainder is -8
(b) Find the value of a and the value of b
Answer:
see explanation
Step-by-step explanation:
The remainder theorem states that if f(x) is divided by (x - h)
The the remainder is f(h)
(a)
Given f(x) is divided by (x - 1) then remainder is f(1), thus
f(1) = [tex]1^{4}[/tex] + 1³ + 2(1)² + a + b = 7, that is
1 + 1 + 2 + a + b = 7
4 + a + b = 7 ( subtract 4 from both sides )
a + b = 3 ← as required → (1)
(b
Given f(x) is divided by (x + 2) then the remainder is f(- 2), thus
f(- 2) = [tex](-2)^{4}[/tex] + (- 2)³ + 2(- 2)² + 2a + b = - 8, that is
16 - 8 + 8 + 2a + b = - 8
16 + 2a + b = - 8 ( subtract 16 from both sides )
2a + b = - 24 → (2)
Multiply (1) by 2
2a + 2b = 6 → (3)
Add (2) and (3) term by term to eliminate the term in a
3b = - 18 ( divide both sides by 3 )
b = - 6
Substitute b = - 6 into (1)
a - 6 = 3 ( add 6 to both sides )
a = 9
Thus a = 9 and b = - 6
Final answer:
To solve for the constants a and b in the polynomial function f(x), we apply the remainder theorem to the given division scenarios. Setting up and solving a system of linear equations using the remainders allows us to find that a is 9 and b is -6.
Explanation:
The given function is f(x) = x^4 + x^3 + 2x^2 + ax + b, and we need to find the constants a and b given that when f(x) is divided by (x - 1), the remainder is 7, and when divided by (x + 2), the remainder is -8.
To find a + b, we apply the remainder theorem. When a polynomial f(x) is divided by (x - p), the remainder is f(p). Therefore, for (x - 1):
f(1) = 1 + 1 + 2 + a + b = 7
4 + a + b = 7
a + b = 3
Similarly, for (x + 2):
f(-2) = (-2)^4 + (-2)^3 + 2(-2)^2 + a(-2) + b = -8
16 - 8 + 8 - 2a + b = -8
16 - 2a + b = -8
We already know that a + b = 3, so we can set up a system of equations:
a + b = 3
-2a + b = -24
Solving for a and b:
Subtracting the first equation from the second: -3a = -27
Divide by -3: a = 9
Substitute a into the first equation: 9 + b = 3
Solve for b: b = -6
The table shows employment status for 1600 adults from five countries. Are the events S = "is Swedish" and E = "is employed"
independent? Why or why not?
Answer:
Yes; because P(S & E)= P(E) • P(E).
Step-by-step explanation:
P(S)=530/1600 = 0.33, P(E)= 1523/1600= 0.95, and P(S & E)= 498/1600= 0.31 = (0.33)(0.95)
For this question please tell me if I'm right or wrong. If I'm wrong please correct me.
Please use the following image below in order to answer the question correctly:
Tell whether NL is best described as a radius, chord, diameter, secant, or tangent of ⊙P.
What can NL be best described as?
Please show all the work on how you got your answer. ( I'm not asking for an explanation. All I want is the work shown so I can understand how you got your answer)
Answer:
You right in this one.
Step-by-step explanation:
Answer:
D) secant
Step-by-step explanation:
NL doesn't pass through the centre, so not radius or diameter
Passes through two points on the circle so not a tangent
Extends to a point outside the circle, so not a chord
Solving Square Roots Worksheet (x - k)^2 : Part 1
1. 2(x + 7)^2 = 16
2. (x - 3)^2 = -12
3. -5(n - 3)^2 = 10
Answer:
1. x = +/- 2[tex]\sqrt{2}[/tex] - 7
2. x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]
3. n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]
Step-by-step explanation:
1. Divide both sides by 2: (x + 7)^2 = 8
Square root both sides: x + 7 = +/- 2[tex]\sqrt{2}[/tex]
Subtract 7 from both sides: x = +/- 2[tex]\sqrt{2}[/tex] - 7
2. Square root both sides: x - 3 = [tex]\sqrt{-12}[/tex]
Since there is a negative inside the radical, we need to have an imaginary number: [tex]i=\sqrt{-1}[/tex] . So, [tex]\sqrt{-12} =i\sqrt{12} =2i\sqrt{3}[/tex]
Add 3 to both sides: x = [tex]3[/tex] +/- [tex]2i\sqrt{3}[/tex]
3. Divide by -5 from both sides: (n - 2)^2 = -2
Square root both sides: n - 2 = [tex]\sqrt{-2}[/tex]
Again, we have to use i: [tex]n-2=\sqrt{-2} =i\sqrt{2}[/tex]
Add 2 to both sides: n = [tex]2[/tex] +/- [tex]i\sqrt{2}[/tex]
Hope this helps!
Answer:
1. x = 2sqrt(2) - 7, -2sqrt(2) - 7
2. No real solutions
x = 3 + 2sqrt(3) i, 3 - 2sqrt(3) i
3. No real solutions
n = 3 + sqrt(2) i, 3 - sqrt(2) i
Step-by-step explanation:
1. 2(x + 7)² = 16
(x + 7)² = 8
x + 7 = +/- sqrt(8) = +/- 2sqrt(2(
x = 2sqrt(2) - 7, -2sqrt(2) - 7
2. (x - 3)² = -12
A perfect square can never be negative for real values of x
(x - 3) = +/- i × sqrt(12)
x - 3 = +/- i × 2sqrt(3)
x = 3 +/- i × 2sqrt(3)
3. -5(n - 3)² = 10
(n - 3)² = -2
A perfect square can never be negative for real values of x
n - 3 = +/- i × sqrt(2)
n = 3 +/- i × sqrt(2)
Which point on the graph shows the reflection of point A across the y-axis?
Answer:
point t
Step-by-step explanation:
to reflect over the y-axis, flip the sign of the x coordinate
(6, -4) to (-6, -4)
point t is located at (-6,-4)
A tower is 1964 feet tall. The angle of elevation from the base of an office building to the top of the tower is 37degrees. The angle of elevation from the roof of the office building to the top of the tower is 19degrees.
To find the height of the office building and the angle of elevation to the top of the tower, we can use the tangent function and solve two equations simultaneously.
To find the height of the office building and the angle of elevation from the base to the top of the tower, we can use the Tangent function.
Tan(angle) = Opposite/Adjacent
For the first angle (37 degrees), the opposite side is the height of the tower (1964 feet) and the adjacent side is the height of the office building.
So, tan(37) = 1964/Adjacent.
For the second angle (19 degrees), the opposite side is again the height of the tower (1964 feet) and the adjacent side is the height of the office building + the height from the roof to the top of the tower.
So, tan(19) = 1964/(Adjacent + Roof Height).
We can solve these two equations simultaneously to find the height of the office building and the height from the roof to the top of the tower.
Learn more about Tangent function here:
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Explain How to find the volume of a cube whose edge length is 1/4 yd. Then find the volume of such a cube
Answer:
[tex]Volume=0.015625\ yd^3[/tex]
Step-by-step explanation:
-A cube is a 3-D object whose height=length=width.
-To find its volume, we multiply its length by width by height dimensions.
#We can calculate the volume of a cube using the formula:
[tex]V=length\times width\times height\\\\=0.25 \ yd\times 0.25\ yd \times 0.25\ yd\\\\=(0.25\ yd)^3\\\\=0.015625\ yd^3[/tex]
Hence, the volume of the cube is [tex]0.015625\ yd^3[/tex]
To find the volume of a cube with an edge length of 1/4 yard, cube the length of the edge. The volume of the cube is 1/64 cubic yards.
Explanation:To find the volume of a cube, you need to cube the length of its edge. In this case, the edge length is 1/4 yard. So, the volume formula becomes (1/4)^3 = 1/4 × 1/4 × 1/4 cubic yards. Simplifying further, we have 1/64 cubic yards as the volume of the cube.
Sistemas de ecuaciones no lineales
Answer:
¿que hay de ellos?
find two numbers that multiply to 17 and add to 18
Answer:
The numbers are 1 and 17
Step-by-step explanation:
The only factors of 17 are 1 and 17 since 17 is a prime number
1*17 =17
1+17 =18
The two numbers that multiply to 17 and add to 18 are 1 and 17.
To find two numbers that satisfy the conditions of multiplying to 17 and adding to 18, we can set up a system of equations based on these criteria.
Let the two numbers be x and y .
1. Set up the equations:
- [tex]\( xy = 17 \)[/tex] (product of the numbers)
- [tex]\( x + y = 18 \)[/tex] (sum of the numbers)
2. Solve the system of equations:
From x + y = 18, express y in terms of x :
[tex]\[ y = 18 - x \][/tex]
Substitute y = 18 - x into [tex]\( xy = 17 \)[/tex]:
[tex]\[ x(18 - x) = 17 \][/tex]
[tex]\[ 18x - x^2 = 17 \][/tex]
[tex]\[ x^2 - 18x + 17 = 0 \][/tex]
3. Find the roots of the quadratic equation:
Use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where a = 1 , b = -18, and c = 17:
[tex]\[ x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot 17}}{2 \cdot 1} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{324 - 68}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm \sqrt{256}}{2} \][/tex]
[tex]\[ x = \frac{18 \pm 16}{2} \][/tex]
So, [tex]\( x = \frac{34}{2} = 17 \)[/tex] or [tex]\( x = \frac{2}{2} = 1 \)[/tex].
4. Determine the corresponding y values:
- If x = 17, then [tex]\( y = 18 - 17 = 1 \)[/tex].
- If x = 1 , then [tex]\( y = 18 - 1 = 17 \)[/tex].
Therefore, the two numbers that multiply to 17 and add to 18 are 1 and 17.
The numbers 1 and 17 satisfy the conditions of multiplying to 17 and adding to 18, providing a clear solution based on the given criteria of the problem.