Given :
x² + 5 = 6Subtract 5 from each side :
x² + 5 - 5 = 6 - 5x² = 1Take the root on each side :
√x² = √1x = ±1Hence, the values of x are :
[tex]\fbox {x = 1}[/tex][tex]\fbox {x = -1}[/tex][tex]x^2+5=6\\x^2=1\\x=1 \vee x=-1[/tex]
The gas mileage for a certain model of car is known to have a standard deviation of 6 mi/gallon. A simple random sample of 36 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 98% confidence interval for the mean gas mileage for this car model.
The 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.
The confidence interval of statistical data is computed using the formula:
[tex](\overline{x} - Z\frac{\sigma }{n},\overline{x} + Z\frac{\sigma }{n})[/tex]
where [tex]\overline{x}[/tex] is the mean, Z is the Z-score corresponding to the confidence interval, σ is the standard deviation, and n is the sample size.
In the question, the sample size (n) = 36, the mean of the sample ([tex]\overline{x}[/tex]) = 28.4 mi/gallon, the standard deviation (σ) = 6 mi/gallon.
The confidence interval given to us is 98%.
Z-score corresponding to this (Z) = 2.33.
Thus, the confidence interval can be calculated as:
(28.4 - 2.33{6/√36},28.4 + 2.33{6/√36})
= (28.4 - 2.33,28.4 + 2.33)
= (26.07,30.73).
Thus, the 98% confidence interval for the mean gas mileage for this car model is (26.07,30.73).
Learn more about constructing confidence intervals at
https://brainly.com/question/17030704
#SPJ4
Which function has an average rate of change of -4 over the interval [-2,2]?
Only p(x) has an average rate of change of -4 over [-2, 2].
Find the average rate of change of each given function over the interval [-2, 2]]:
The average rate of change of m(x) over [-2, 2]:
What is the average rate?The average rate of change = [tex]\frac{m(b)-m(a)}{b-a}[/tex]
Where, a = -2, m(a) = -12
b = 2, m(b) = 4
Plug the values into the equation
The average rate of change
[tex]=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}[/tex]
The average rate of change = 4
The average rate of change of n(x) over [-2, 2]:
The average rate of change = [tex]\frac{n(b)-n(a)}{b-a}[/tex]
Where, a = -2, n(a) = -6
b = 2, n(b) = 6
Plug the values into the equation
The average rate of change
[tex]=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}[/tex]
The average rate of change = 3
The average rate of change of q(x) over [-2, 2]:
The average rate of change = [tex]\frac{q(b)-q(a)}{b-a}[/tex]
Where, a = -2, q(a) = -4
b = 2, q(b) = -12
Plug the values into the
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
= [tex]\frac{-16}{4}[/tex]
The average rate of change = -2
The average rate of change of p(x) over [-2, 2]:
The average rate of change = [tex]\frac{p(b)-p(a)}{b-a}[/tex]
Where, a = -2, p(a) = 12
b = 2, p(b) = -4
Plug the values into the equation
The average rate of change = [tex]\frac{-4-12}{2-(-2)}[/tex]
[tex]=\frac{-16}{4}[/tex]
The average rate of change = -4
The answer is D.
Only p(x) has an average rate of change of -4 over [-2, 2].
To learn more about the average rate of visit:
https://brainly.com/question/8728504
#SPJ1
Two of them are drawn simultaneously from a deck of 48 cards.
Calculate the probability that:
a) both are cups
b) At least one cup
c) One is a cup and the other is a sword
The required probability is
a) both are cups is 0.05
b) At least one cup is 0.19
c) One is a cup and the other is a sword is 0.06
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
a) for both are cups
P= 12*11/48*47
p = 0.05
b) for At least one cup
p = 12*36/48*47
p = 0.19
c) for One is a cup and the other is a sword
p = 12*12/48*47
p = 0.06
Thus, the required probability is 0.05, 0.19, 0.06
Learn more about probability here:
brainly.com/question/14290572
#SPJ1Find the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity.
The polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0. This can be obtained by finding factors and multiplying them.
What is the required polynomial ?
Given that zeroes, 2 of multiplicity 2, and i of single multiplicity, that is, (x - 2), (x - i) and (x + i) are the factors of the polynomial.
Thus the polynomial can be written as
(x - 2)²(x - i)(x + i) = 0 ((x - 2) is squared as multiplicity is 2)
(x² - 4x + 4)(x²-i²) = 0
(x² - 4x + 4)(x²+1) = 0
x⁴ - 4x³ + 4x² + x² - 4x + 4 = 0
⇒ x⁴ - 4x³ + 5x²- 4x + 4 = 0
Hence the polynomial function with real coefficients of a least possible degree having zero 2 of multiplicity 2, and zero i of single multiplicity is x⁴ - 4x³ + 5x²- 4x + 4 = 0.
Learn more about forming polynomial here:
brainly.com/question/20038740
#SPJ4
The root rafter of a house has been raised to a height of 18 yards at the ridge. Half of the length of the run measures 14 yards. Find the length of the rafter.
The length of the rafter as detailed in the question is approximately; 22.80 yards
How to use Pythagoras theorem?
The formula for Pythagoras theorem is;
a² + b² = c²
where;
a and b are adjacent and opposite sides of the triangle formed
c is the hypotenuse
Now, a rafter is a sloped member of a roof structure. Thus, if the rafter is raised to a height of 18 yeards, it means that is the vertical height of the top of the rafter to the bottom of the kingpost.
Now, if half the length run is 14 yards, it means that half of the tie beams is 14 yards. Thus, from the base of the rafter to the center of the tie beams is 14 yards. Thus, we will use Pythagoras theorem to find the length of the rafter.
c = √(14² + 18²)
c = √520
c = 22.80 yards
Read more about Pythagoras Theorem at; https://brainly.com/question/231802
#SPJ1
A squared garden has area 1764m2. Find its length and perimeter?
Answer:
length = 42 mperimeter = 168 mStep-by-step explanation:
A squared garden has area 1764m2. Find its length and perimeter?
Area = l²
inverse formulal = √Area
length√1764 = 42 m
Perimeter l × 442 * 4 = 168 m
Answer:
length=42m
perimeter=168m
Step-by-step explanation:
Area=L^2
L^2=1764
L=√1764
L=42m
Perimeter=42+42+42+42 which equals to 168m
the sum of seven odd consecutive is 217. Find the middle number
Answer:
x + x+1 + x+2 + x+3 + x+4 + x+5 + x+6 =217
7x+21=217
7x=196
x=28
Middle Number will be:
x+3
28+3
=31
Therefore, the middle number is 31.
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
Let's put this into equation form.
n + (n + 1) + (n+2) + (n+3) + (n+4) + (n + 5) + (n+6) = 217
Each number is increasingly getting farther away from n (the first number) by 1.
If we simplify, by adding all of the numbers and the n's. We get:
7n + 21 = 217
Let's subtract 21 from both sides to start the process of isolating x.
7n = 196
Now we can divide both sides by 7, to isolate x.
n = 28.
That looks like the answer, but it is not. Remember n is the first number, we want the middle, which out of 7 is the 4th number.
The 4th number is equal to (n+3) or (28 + 3)
The 4th number is 31.
Let's check if this is correct.
28 + 29 + 30 + 31 + 32 + 33 + 34 = 217.
The problem is complete.
A number line goes from negative 5 to positive 5. Point D is at negative 4 and point E is at positive 5. A line is drawn from point D to point E.
What is the location of point F, which partitions the directed line segment from D to E into a 5:6 ratio?
Negative one-eleventh
One-eleventh
Two-fifteenths
Fifteen-halves
Directed numbers are numbers that have either a positive or negative sign, which can be shown on a number line. Therefore, point F is Fifteen-halves of line segment DE.
A number line is a system that can show the positions of positive or negative numbers. It has its ends ranging from negative infinity to positive infinity. Thus any directed number can be located on the line.
Directed numbers are numbers with either a negative or positive sign, which shows their direction with respect to the number line.
In the given question, the distance between points D and E is 9 units. So that dividing 9 units in the ratio of 5 to 6, we have;
[tex]\frac{5}{6}[/tex] x 9 = [tex]\frac{45}{6}[/tex]
= [tex]\frac{15}{2}[/tex]
Therefore, the location of point F, which partitions the directed line segment from d to E into a 5:6 ratio is [tex]\frac{15}{2}[/tex]. Thus the answer is Fifteen-halves.
For further clarifications on a number line, visit: https://brainly.com/question/23379455
#SPJ1
Answer:
1/11
Step-by-step explanation:
Got it right on assignment
Out of 54 jelly beans, two were found to be defective. What is the experimental probability a jelly bean is defective?
26/27
1/27
2/27
24/27
Answer:
1/27
Step-by-step explanation:
To find the probability of a defective jelly bean
P(defective) = number defective/ total
=2/54
= 1/27
Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding One-third the length of the directed line segment?
The ratio given is part to whole, but fractions compare part to part.
The ratio given is part to part. The total number of parts in the whole is 3 – 1 = 2.
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
The ratio given is part to whole, but the associated fraction is One-third.
The reason why partitioning and fractioning are different is because; The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Why is partitioning different from fractioning?It follows from the task content that a close analysis of the statement of ratios; 1:3 implies that the whole is divided into four parts; 1+3 = 4.
On the contrary, one-third simply means 1 out of 3 equal parts of the line.
Read more on fractions;
https://brainly.com/question/17220365
#SPJ1
Answer: OPTION C
Step-by-step explanation:
(LOOK AT IMAGE)
A robot can be programmed to draw any regular polygon.
The instructions seen in the example below are used to draw a regular 10- sided polygon with side lengths of 3 cm.
By changing the numbers in the program below, write down the simplest set of instructions needed to make the robot draw a regular 12-sided polygon with side lengths of 5 cm.
Repeat the following 12 times:
> Move forward 5 cm
> Turn clockwise 30°
Want to know how I found this out? Well, let me tell you.
First, they gave us the information that a 12-sided polygon is to be modeled with side lengths 5 cm. So, that basically gives us our first step. That was easy!
Well, now this is a bit harder. How many degrees do we move? There're so many possibilities! Well, not quite.
According to the Polygon Exterior Angle-Sum Property, the exterior angles of any polygon is always 360 degrees. So, we just divide 360 by how many sides there are in the polygon.
There are 12 sides in this polygon, so, [tex]\frac{360}{12}[/tex] is equal to 30 degrees per side. Well, now we have the second step! We're all done. Congratulations!
Which equation is equivalent to log3 (x+5) = 2 ?
Answer:
the anwer is x= -3
Step-by-step explanation:
(3+5)=2
PLEASE help answer all 5 questions
[tex]p(r) = \frac{2}{9} [/tex]
2)We have 3 blue marbles and 9 marbles in total, so the probability of drawing a blue marble, is the number of blue marbles over the total number of marbles.[tex]p(b) = \frac{3}{9} = \frac{1}{3} [/tex]
3)Since we put the marbles back, the sample space stays 9 balls,so we have to multiply the probability of drawing a red marble then a blue one. Since order matters (red before blue) we do not account for permutations.4)Putting the marbles back in the bag makes this these events independent, as the sample space does not change.5)[tex]p(r \: then \: b) = \frac{2}{9} \times \frac{1}{3} = \frac{2}{27} [/tex]I am studying geometry this summer but can’t solve this question what would be the correct answer
Answer: F
Step-by-step explanation:
Bisectors of an angle split the angle in half which you can visually see from the image. So, the answer is F.
Which phrases describe the graph of f(x) = |x| ? Check all that apply
The phrases which describe the graph are;
The domain of the graph is the set of all real numbers.The range of the graph is the set of all real numbers greater or equal to zero.The graph in the task content is increasing over the interval (0, ∞).The graph in the task content is decreasing over the interval (-∞, 0).What is the graph of the absolute function?The absolute function in the task conten is;
f(x) = |x|, Hence, the domain and range of the graph are as described above.
Read more on absolute function;
https://brainly.com/question/2473412
#SPJ1
A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It
is determined that the height of the frog as a function of time can by modeled
by h (t) = -16t² +64t + 3. How many seconds will it take for the frog to
land on the ground?
Considering the given quadratic function, it is found that it will take 4.05 seconds for the frog to land on the ground.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The height after t seconds is given by:
h(t) = -16t² + 64t + 3.
it hits the ground when h(t) = 0, hence:
-16t² + 64t + 3 = 0
16t² - 64t - 3 = 0.
The coefficients are a = 16, b = -64, c = -3, hence:
[tex]\Delta = (-64)^2 - 4(16)(-3) = 4288[/tex][tex]t_1 = \frac{64 + \sqrt{4288}}{32} = 4.05[/tex][tex]t_2 = \frac{64 - \sqrt{4288}}{32} = -0.05[/tex]Time has to be positive, hence the frog lands on the ground after 4.05 seconds.
More can be learned about quadratic functions at https://brainly.com/question/24737967
#SPJ1
Can someone help.
Triangle not drawn to scale
Given: m = 53°, a = 18, and c = 14. Find me to the
nearest whole number.
Answer:
m∠C = 38° (nearest whole number).
Step-by-step explanation:
To find the missing angle, use the Sine Rule.
Sine Rule (for angles)
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
where:
A, B and C are the anglesa, b and c are the sides opposite the anglesGiven:
A = 53°a = 18c = 14To find m∠C, substitute the given values into the formula and solve for C:
[tex]\implies \sf \dfrac{\sin 53^{\circ}}{18}=\dfrac{\sin C}{14}[/tex]
[tex]\implies \sf \sin C= \dfrac{14 \sin 53^{\circ}}{18}[/tex]
[tex]\implies \sf C= \sin^{-1} \left( \dfrac{14 \sin 53^{\circ}}{18}\right)[/tex]
[tex]\implies \sf C= 38.40096301...^{\circ}[/tex]
Therefore, m∠C = 38° (nearest whole number).
Learn more about the sine rule here:
https://brainly.com/question/27089170
https://brainly.com/question/27704834
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Here is the completed table:
Hours Weeks
168 1
1008 6
840 5
How to complete the table?The mathematical operation that would be used to determine the missing values are division and multiplication. In order to convert hours to weeks, divide by 168 hours. To convert weeks to hours, multiply by 168.
1008 hours to weeks = 1008 / 168 = 6 weeks
5 weeks to hours = 5 x 168 = 840 hours
To learn more about division, please check: https://brainly.com/question/194007
#SPJ1
Please help for 50 points with solution
Answer:
(d) 60°
Step-by-step explanation:
Theorems
Interior angles of a triangle sum to 180°Angles on a straight line sum to 180°Therefore, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.
⇒ (a + 20) + (a + 10) = (a + 90)
⇒ a + 20 + a + 10 = a + 90
⇒ 2a + 30 = a + 90
⇒ 2a + 30 - a = a + 90 - a
⇒ a + 30 = 90
⇒ a + 30 - 30 = 90 - 30
⇒ a = 60
Answer:
a = 60
Step-by-step explanation:
→ Find the sum of all the angles
2a + 30 + 90 - a = 180
→ Collect the a terms
a + 120 = 180
→ Find a
a = 60
Of the houses in Lucia's neighborhood, 1/10 are teal and another 7/10 are red. What
fraction of the houses are either teal or red?
(D) Write your answer as a fraction or as a whole or mixed number.
Answer:
the answer is 8/10
Step-by-step explanation:
The reason is that both of the denominators are the same so that you can add the two numerators and then get the answer.
Select the correct answer. Consider the following system of equations. Use this graph of the system to approximate its solution. A diagonal curve rises through (negative 5, 1) through (6, 6). A diagonal curve declines through (negative 6, 5) through (7, negative 6) on the x y coordinate plane. A. B. C. D.
The approximate solution to the given system of equations, considering the graph, is given as follows:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex].
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:
D. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Answer:
d
Step-by-step explanation:
A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s. How many possible sequences of rolls could there have been
The possible sequences of rolls could there have been Sequence = 120
Given
6 rolls of a die;
Required
Determine the possible sequence of rolls
From the question, we understand that there were three possible outcomes when the die was rolled;
The outcomes are either of the following faces: 1, 2 and 3
Total Number of rolls = 6
Possible number of outcomes = 3
The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;
Sequence = \frac{6!}{3!}
Sequence = \frac{6 * 5 * 4* 3!}{3!}
Sequence = 6 * 5 * 4
Sequence = 120
Hence, there are 120 possible sequence.
Learn more about Sequences:
https://brainly.com/question/12246947
#SPJ4
Geometry help please
7
Answer:
you should download AIR MATH
For each of the following a) identify the inverse function needed to solve for the indicated angle and b) solve for the angle (round to the nearest tenth of a degree).
The angle is the cosine inverse function because base over hypotenuse. Then the angle will be 37°.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The triangle with base of 4 units and hypotenuse of 5 units.
We know that the angle is given by the cosine inverse function because base over hypotenuse. Then we have
⇒ cos⁻¹ (4/5)
Then the angle will be
⇒ 36.869 ≈ 37°
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ1
According to the data in the figure, find the value of x and y.
Answer:
This is a educated guess, but x is 80 and y is 100.
Step-by-step explanation:
My logic here is that the triangles are the same because of all the congruent lines and stuff. But from there, you know that both the right and the left side are 40 degrees. You know the total degree of a triangle is 180 so 180 - 40 - 40 is 100. So the final angle is 100. If you look at x, its on the outside, but on a line. If you can imagine a circle, its half, so its a 180 degrees total. Then its 180 = x + 100. So x is 80. And then by that same logic its y = 100.
PLEASE HELP ME ASAP. I REALLY NEED THIS DONE
Answer:
x = 65
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)
x² = 25 × 169 = 4225 ( take square root of both sides )
x = [tex]\sqrt{4225}[/tex] = 65
is the number there three? if you answer to me i will give you twenty Points.
Answer:
2
Step-by-step explanation:
3 x 2 = 6
1 x 2 = 2
hope it helps
sorry if I'm wrong
Use the data in the table below and a graphing calculator to describe how a linear model compares to a quadratic model. Analyze the "parameters" (as they are called in Desmos) a, b, c for the quadratic model and m & b for the linear model. Write a sentence or two that explains why both graphs look the same, even if you zoom out very far.
PLEASE HELP ME
The quadratic model and the linear model of the table of values are the same
The linear model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
Sum of X = 0Sum of Y = 113Mean X = 0Mean Y = 22.6Sum of squares (SSX) = 10Sum of products (SP) = 28The regression equation is
y = mx + b
Where
m = SP/SSX = 28/10 = 2.8
b = MY - bMX = 22.6 - (2.8*0) = 22.6
So, we have:
y = 2.8x + 22.6
See attachment for graph (1)
The quadratic model of the dataTo do this, we make use of a graphing calculator.
From the graphing calculator, we have the following summary:
a = 0b = 2.8c = 22.60 X^2 +2.8 X +22.6
The regression equation is
y = ax^2 + bx + c
So, we have:
y = 0x^2 + 2.8x + 22.6
See attachment for graph (1)
Why both graphs look the sameThe graphs look the same because when the quadratic model is simplified, it gives the linear model.
This in other words mean that:
The quadratic model and the linear model of the table of values are the same
Read more about regression at:
https://brainly.com/question/7656407
#SPJ1
Fill in the missing statements and reasons in this proof. Number your reasons 1 through 5 as they would be shown in the chart below.
Given: m∠LOM = m∠JKI;
m∠MON = m∠IKH
Prove: m∠LON = m∠HKJ
would rlly appreciate ur help
From the given condition m ∠LOM = m ∠JKI, m ∠MON = m ∠IKH it is proved that m ∠LON = m ∠HKJ as they are congruent angles.
What are congruent angles?Congruent angles are defined as angles with equal measure. According to the question,
m ∠LOM = m ∠JKI (given congruent angles) _____(1)
m ∠MON = m ∠IKH (given congruent angles) _______(2)
Add both the side angle m ∠MON in (1) we get m ∠LOM + m ∠MON = m ∠JKI + m ∠MON
Replace angle m ∠MON = m ∠IKH from (2) on right-hand side we get,
m ∠LOM + m ∠MON = m ∠JKI + m ∠IKH ____(3)
m ∠LOM + m ∠MON = m ∠LON ( M is the interior point of ∠LON) ___(4)
m ∠JKI + m ∠IKH = m ∠HKJ ( I is the interior point of ∠HKJ) ___(5)
Form (3), (4), and (5) we get, m ∠LON = m ∠HKJ (Congruent angles)
Hence, from the given condition it is proved that m ∠LON = m ∠HKJ, are congruent angles.
Learn more about congruent angles on:
brainly.com/question/24887947
#SPJ1
A student received test grades of 83, 90, and 88. What was her grade on a fourth test if the average for the four tests is 84
Her grade on a fourth test is 75.
The average of e for the four tests is 84.
By substituting the given data in the equation, we get
Let the fourth test marks be x
83 + 90 + 88 + x / 4 = 84
261 + x / 4 = 84
261 + x = 336
x = 336 - 261
x = 75
An average may be described as the sum of all numbers divided by means of the whole quantity of values.
A mean can be defined as an average of the set of values in a sample of data. In different words, a median is also called the mathematics mean.
Learn more about mean here: https://brainly.com/question/20118982
#SPJ4