Hello,
[tex]Speed = \frac{Distance}{Time} = \frac{15 km}{3 h} = \boxed{5 km/h}[/tex]
Stan walked at 5 km/h
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 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.
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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.
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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°
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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]What is the measure of z?
Z
X
y
4
9
z = [ ? ]VI
Answer:
z= [ 5] VI
that is my answer
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).
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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
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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.
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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.
Please help me. Due today. Please show work so I can get it correct!!!!
Based on the inscribed angle theorem, the value of x is: 126°.
What is the Inscribed Angle Theorem?The inscribed angle theorem states that, the measure of inscribed angle (63 degrees) equals half of the measure of central angle (x).
Thus, we would have:
63 = 1/2(x)
2(63) = x
126 = x
x = 126°
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Determine the equation of the parabola shown in the diagram in vertex form. (check picture below)
The equation of the parabola is y - 1 = (2/3) * (x - 3)².
What is equation of the parabola ?The general equation of a parabola is: y-k = a(x-h)²
(h, k) - Coordinates of the vertex.
a - Vertex constant
Here:
(h, k) = (3, 1) and (x, y) = (0, 7).
So,
7 - 1 = C · (0 - 3)²
6 = 9 · C
C = 2/3
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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.
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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]
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Answer:
d
Step-by-step explanation:
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.
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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
isabella and aiden get a reward of $119 in the ratio of 4 3, what fraction of the total reward does isabella get
Using proportions, considering the given ratio, Isabella gets [tex]\frac{4}{7}[/tex] of the total reward.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratio of Isabella and Aiden is 4:3, which means that out of 4 + 3 = 7 items, Isabella gets 4 and Aiden gets 3, hence the fraction is given by:
[tex]\frac{4}{7}[/tex].
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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.
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).
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(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!
Calculate: 6666666x666666/1+2+3+4+5+6+5+4+3+2+1- 777777x777777/1+2+3+4+5+6+7+6+5+4+3+2+1
Answer: 3.8395025e+12
Lol
3839502493910
Step-by-step explanation:
you will multiple the 6 and the 7 digits and the other digits
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
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.
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.
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Answer: OPTION C
Step-by-step explanation:
Which equation is equivalent to log3 (x+5) = 2 ?
Answer:
the anwer is x= -3
Step-by-step explanation:
(3+5)=2
Find 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.
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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
Mario is having a pizza party on Saturday night. He ordered 8 pizzas. if the average person eats 1/3 of a pizza, how many persons will 8 pizzas serve?
Answer:
24 people
Step-by-step explanation:
I pizza will feed 3 people
There are 8 pizza's
8 x 3 = 24
How many x-intercepts does the graph of y=2x^2-4x+2 have?
A.0
B.1
C.2
Answer:
B. 1
Step-by-step explanation:
Please see attachment.
Hope this helps!
If not, I am sorry.
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].
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