Answer:
A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.
Step-by-step explanation:
The relative frequencies given are at most 0.02 apart. This means they are reasonably close.
The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.
However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.
Since the relative frequencies are reasonably close, the number cube is likely to be fair.
Answer:
Option A and C are true.
Step-by-step explanation:
Given : Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.
Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome
Outcome : 1 2 3 4
Relative Frequency : 0.23 0.24 0.26 0.27
To find : Which statements about Dina's experiment are true?
Solution :
Option A - The relative frequencies in the table are reasonably close.
This statement is true, as we see that the relative frequency are all between 0.23 to 0.27 that are reasonably close.
Option B - The theoretical probability of rolling an even number is 0.51.
This statement is not true, as the theoretical probability of rolling even numbers is
2 even numbers from 4, so probability is
[tex]P=\frac{2}{4}=\frac{1}{2}=0.5[/tex]
Option C - The relative probability of rolling an even number is 0.51.
This statement is true, as the relative frequency of an even number is 0.24+0.27=0.51
Option D - The number cube is not likely to be fair.
The statement is not true, as the relative frequency are reasonably close which implies that the number cube is likely to be fair and sum of the relative frequency is 1.
Therefore, Option A and C are correct.
A rectangle has an area of 24 square centimeters. Select the three choices that show pairs of possible side lengths of the rectangle
Answer:
A, B, and C
Step-by-step explanation:
We can use guess-and-check.
A rectangle with the area 24 cm² has the sides that make the product of 24 (A = l * w)
1 * 24 is 24.
2 * 12 is 24.
3 * 8 is 24.
4 * 20 is 80.
12 * 12 is 144.
What is the value of x?
Answer:
x = 12.8
Step-by-step explanation:
To find the value of x, set up a proportion between the two similar triangles. Then solve for x.
[tex]\frac{32}{32+x} = \frac{40}{56}[/tex]
Solve by cross multiplying and isolating x.
32(56) = 40(32+x)
1792 = 1280 + 40x
512 = 40x
12.8 = x
A diagonal path divides a square park in half. If the park is 50 yards on each side, how long is the path?
The length of the diagonal path is approximately 70.71 yards.
To find the length of the diagonal path that divides the square park in half, we can use the Pythagorean theorem. A square park of 50 yards on each side means we are dealing with a right-angled triangle with both legs equal to 50 yards.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
[tex]c^2 = a^2 + b^2[/tex]
Here, both a and b are 50 yards, so the equation becomes:
[tex]c^2[/tex] = 502 + 502 = 2500 + 2500 = 5000
Now we find the square root of 5000 to get the length of the diagonal:
c = √5000 ≈ 70.71 yards
Therefore, the length of the diagonal path is approximately 70.71 yards.
can anyone takes some time and help me with this please I'm struggling and I need help
Answer:
10
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [1, 4 ]
f(b) = f(4) = 4² +5(4) = 16 + 20 = 36
f(a) = f(1) = 1² + 5(1) = 1 + 5 = 6, hence
average rate of change = [tex]\frac{36-6}{4-1}[/tex] = [tex]\frac{30}{3}[/tex] = 10
Find the value of x.
Answer options: 17, 7, 14, 10
Answer:
7
Step-by-step explanation:
Since both chords are congruent and the distance of the x and 7 are equidistant from the center, then the value of x will also be 7.
Left side chord will have a value of y + 10
The right side chord will have a value of y + 10
Now since the right angles on both sides are equal, then x = 7.
The value of x is 7.....
Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph. Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph. Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport. At what time did Frank arrive at the airport?
Answer:
10:00 AM
Step-by-step explanation:
Frank drove at a speed of 50 mph, and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
7 AM + 3 hours = 10 AM
The solution is, at 10:00 AM Frank will arrive at the airport.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
here, we have,
given that,
Frank left his house at 7 a.m. and drove to the airport at a speed of 50 mph.
Lance left his house at 6 a.m. and drove to the same airport at a speed of 55 mph.
Frank's house is 150 miles from the airport and Lance's house is 220 miles from the airport.
so, we get,
Frank drove at a speed of 50 mph,
and traveled a distance of 150 miles. This means he traveled for
150/50 = 3 hours.
Thus, it takes Frank 3 hours to reach the airport.
so, we get,
since he departed at 7:00 AM, he will arrive at the airport at
7 AM + 3 hours = 10 AM
Hence, The solution is, at 10:00 AM Frank will arrive at the airport.
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What is the volume of the sphere?
25.12
75.36
150.72
904.32
Answer:
D
Step-by-step explanation:
Formula
V = 4/3 * pi * r^3
Givens
pi = 3.14
r = 6
Solution
V = (4/3) * 3.14 * 6^3 Expand the cube
V = (4/3) * 3.14 * 216 Multiply by 3.14
V = (4/3) * 678.24 Multiply by 4
V = 2712.96 / 3 Divide by 3
V = 904.32
measure each rectangle to the nearest 1/4 in with your ruler and label the dimensions use the area model to find the area
Answer:
can you attach a picture
Step-by-step explanation:
Do u have a picture so i could solve it
A rectangle’s perimeter and its area have the same numerical value. The width of the
rectangle is 3 units. What is the length of the rectangle in units?
Step-by-step explanation:
6 units.
(3*2)+2x=3x
Set the perimeter equal to the area
x(length)=6 units
HELP QUICK!15 + 100 • [12 – (12 – 3 • 2)] + 6
Answer:
621
Step-by-step explanation:
Use PEMDAS.
15 + 100 * [12 - 6] + 6
15 + 100 * 6 + 6
15 + 600 + 6
621
Answer:
[tex]\boxed{\bold{621}}[/tex]
Step By Step Explanation:
Follow PEMDAS Order Of Operations
[tex]\bold{12-\left(12-3\cdot \:2\right): \ 6}[/tex]
[tex]\bold{15+100\cdot \:6+6}[/tex]
[tex]\bold{100\cdot \:6: \ 600}[/tex]
[tex]\bold{15+600+6}[/tex]
[tex]\bold{15+600+6: \ 621}[/tex]
[tex]\bold{621}[/tex]
I need help with this question I dont get how to do it..
Answer:
If 300 lunches were served, then 90 students choose milk.
Step-by-step explanation:
The graph shows that 30% of students choose milk. So when 300 lunches are served, 300*.30 students choose milk. 300*.3 or 300*30% is equal to 90.
The answer for this question is the first option "if 300 lunches were served then 90 students would have milk".
A) If 300 lunches were served then 90 would chose milk as milk is represented and shown to have a popularity of 30%. 30% of 300 is equivalent to 90 making the statement true
B) If 200 lunches were served then 90 would choose milk however this is false as milk at 30% as votes and 30% of 200 is not 90
C) if if 300 lunches were served then 30 more students would chose water over juice however water has a population of 40% and 40% of 300 is 120 and juice has a population of 10% and 10% of 300 is 30 and 120-30=90 not 30.
D) if 200 lunches were served than 10 more students would choose tea over juice. Tea has a population of 20% and 20% of the 200 is 40 and juice has a population of 10% and 10% of 200 is 20 and 40-20=20 not 10
The only correct statement is If 300 lunches were served then 90 would chose milk.
PLEASE HELP! WILL GIVE BRAINLIEST ANSWER + 100 POINTS!!
(a) Which two points should you use to find the equation of the model? Explain.
(b) Use the two points you chose in Part (a) to find the slope of the linear model, rounded to three decimal places. Show your work.
(c) What is the equation of the linear model in point-slope form?
(d) Rearrange the equation you wrote in part (c) into slope intercept form. Show your work.
A) You would use the two points that are closest to the graphed line
(2,7) and (8,13)
B) Slope = change in Y over the change in X:
Slope = (13-7) / (8-2) = 6/6 = 1
Slope = 1
c) Point slope is written as y -y1 = m(x-x1) where m is the slope y1 is the first Y value and x1 is the first x value.
Equation is: y-7 = x-2
d) To rewrite y -7 = x-2 in slope intercept form, you need to isolate y.
To isolate Y add 7 to both sides:
y = x +5
Step a is (2,7)/(8,13).
Step b is 1
Step c is y-7 = x-2
Step d is y = x +5
Given that √x = -4, what is x?
Square on both sides..
x=16 !!!
[tex] \sqrt{x} = - 4 \\ { \sqrt{x} }^{2} = {( - 4)}^{2} \\ x = 16 [/tex]
(-) +(-) =+
The sign below is located at the start of Pinecone trail and shows the distances from the sign to different points of interest along the trail. Sage hiked from the start of the trail to Lookout Point. She then hiked back to Giant Boulder to camp for the night. What was the total distance, in miles, that Sage hiked?
Answer:
Total distance = 53/4 miles = 13.25 miles
Step-by-step explanation:
Sage hiked from the start of the trail to Lookout Point.
Distance = 8 3/4 miles = 35/4 miles
She then hiked back to Giant Boulder
This means she traveled an additional
8 3/4 miles - 4 1/4 miles = 35/4 mi - 17/4 mi = 18/4 mi = 9/2 mi
The total distance traveled by sage is the sum of both trajectories
Total distance = 35/4 miles + 9/2 miles = 53/4 miles
Total distance = 13.25 miles
What happens to the graph of y=|x| when the equation changes to y=|x+3| - 1
Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. What fraction of the tomatoes did mrs Jenkins use to make the salad?
Answer:
Final answer is 1/3.
Step-by-step explanation:
Given that Mrs Jenkins picked some tomatoes from her garden. She used 5/9 of the tomatoes to make pasta sauce. Then she used 3/4 of the remainder to make a salad. Now we need to find about what fraction of the tomatoes did Mrs Jenkins use to make the salad.
Since she used 5/9 of the tomatoes to make pasta sauce.
Then remaining amount of tomatoes = 1- 5/9 = 9/9 -5/9 = 4/9
Then she used 3/4 of the remainder to make a salad. So fraction of the tomatoes did Mrs Jenkins use to make the salad = (4/9)(3/4)=12/36=1/3
Hence final answer is 1/3.
Area of regular hexagon
Check the picture below.
let's recall that a circle has 360°, so that means every two radii coming from the center of the hexagon, will split those 360° in 6 even pieces, 360/6 = 60, namely those two radii make up a 60° central angle, as you see in the picture.
running a perpendicular from the center, we end up with a 30-60-90 triangle, as you see there, and thus we can use the 30-60-90 rule to get the length of "a".
now, keeping in mind that the perimeter of the polygon is simply 4+4+4+4+4+4 = 24.
[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}dp~~ \begin{cases} d=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ d=2\sqrt{3}\\ p=24 \end{cases}\implies A=\cfrac{1}{2}(2\sqrt{3})(24)\implies A=24\sqrt{3}[/tex]
Solve for X... (-3 + 5) - (6x - 8)
Answer:
10 -6x
Step-by-step explanation:
We cannot solve since there is no equal sign, we can only simplify
(-3 + 5) - (6x - 8)
Combine the like terms in parentheses
(2) - (6x - 8)
Distribute the minus sign
2 -6x --8
2 -6x +8
Combine like terms
2+8 -6x
10 -6x
set it equal to 0
(-3+5)-(6x-8)=0
2-6x+8=0
isolate x
-6x=-2-8
-6x=-10
cancel negatives
6x=10
divide by 6
x= 10/6
reduce:
x = 5/3
If you had 150 subjects to work on and had 28 Days How many per day do you need to do?
Divide the total subjects by total days:
150 / 28 = 5.357 per day. Round the answer as needed.
Answer: Approximately 5 subjects per days.
Step-by-step explanation:
To solve the exercise and calculate the number of subjects you need to do per day you must keep on mind the information given in the problem. You know that:
- The total number of subjects is 150.
- You had 28 days left.
Therefore, you need to divide 150 subjects by 28 days.
Then, you obtain the following result:
[tex]=\frac{150subjects}{28days}=5.35\frac{subjects}{day}[/tex]≈ 5 subjects per days.
3x2 + 7x + 2 how to factor
Answer:
(x+2)(3x+1)
Step-by-step explanation:
the factored form of the quadratic expression 3x² + 7x + 2 is (3x + 1)(x + 2).
To factor the quadratic expression 3x² + 7x + 2, you can use the factoring method or apply the quadratic formula. Let's use the factoring method:
1. Look for two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 2). These numbers should also add up to the coefficient of x (which is 7).
The two numbers that meet these conditions are 1 and 6. They multiply to give 6, and they add up to 7.
2. Rewrite the quadratic expression using the two numbers found in step 1:
3x² + 1x + 6x + 2
3. Group the terms in pairs and factor out the greatest common factor from each pair:
x(3x + 1) + 2(3x + 1)
4. Notice that both pairs have a common factor of (3x + 1). Factor out this common binomial:
(3x + 1)(x + 2)
So, the factored form of the quadratic expression 3x² + 7x + 2 is (3x + 1)(x + 2).
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Suppose a 50-foot ladder is leaning against a wall. Which statements about the base of the ladder are true? Choose two that apply.
A If the base is 24 feet from the wall, the ladder reaches 45 feet up the wall.
B If the base is 30 feet from the wall, the ladder reaches 40 feet up the wall.
C If the base is 27 feet from the wall, the ladder reaches 44 feet up the wall.
D If the base is 14 feet from the wall, the ladder reaches 48 feet up the wall.
Answer: 30-40-50, or B
Step-by-step explanation:
Think of this equation of a right triangle. We know that the hypotenuse is 50 feet and leaning.
Since right triangles follow a formula is 3-4-5, then, 30, 40 and 50 is the answer.
If the 50-foot ladder is leaning against a wall. Statement B about the base of the ladder is true.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that, a 50-foot ladder is leaning against a wall.
Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
The hypotenuse is 50 feet long and slopes, as is known.
Since right triangles have a formula of 3-4-5, the correct response is 30, 40, and 50.
Thus, if the 50-foot ladder is leaning against a wall. Statement B about the base of the ladder is true.
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PLEASE HELP QUICK??!!!
Jordan is saving for a new laptop that costs $325. He uses the equation and table below to show the number of months he has been saving, m, and the total amount he has saved so far, d.
d=80+75m
Which is the first month in which Jordan will have saved enough money to buy the laptop?
Month 2
Month 3
Month 4
Month 5
Answer:
Month 4
Step-by-step explanation:
Given : Jordan is saving for a new laptop that costs $325.
Equation: d=80+75m
To Find: Which is the first month in which Jordan will have saved enough money to buy the laptop?
Solution:
Equation: [tex]d=80+75m[/tex]
where d is the total amount he has saved so far.
m shows the number of months he has been saving.
Now we are given that he needs to save $325.
So, To find the first month in which Jordan will have saved enough money to buy the laptop
Substitute d = 325 in the equation:
[tex]325=80+75m[/tex]
[tex]245=75m[/tex]
[tex]\frac{245}{75}=m[/tex]
[tex]3.266=m[/tex]
Thus,the first month in which Jordan will have saved enough money to buy the laptop is Month 4.
Answer:
Month 4 or C
Step-by-step explanation:
PogChamp
Two numbers have a sum of 18. One number is 4 more than the other. Find the numbers
Bennett spent 4 hours at school today. He attended 3 70 minute classes.There is a 5 minute break between classes.Then he lunch before going home.How long did Bennitt spend eating lunch?
he spent 15 mins for lunch. I wish you used a comma for 3, 70 min classes lol. tripped me up a sec
Final answer:
Bennett spent 20 minutes eating lunch, which was calculated by subtracting the time he spent in classes and during breaks from his total time at school.
Explanation:
To determine how long Bennett spent eating lunch, we need to subtract the time he spent attending classes and the breaks between classes from the total time he was at school. Bennett attended 3 classes, each lasting 70 minutes, so the total class time is 3 classes × 70 minutes/class = 210 minutes. There are 2 breaks between classes, each lasting 5 minutes, adding up to 2 breaks × 5 minutes/break = 10 minutes.
Total time spent on classes and breaks is 210 minutes + 10 minutes = 220 minutes or 3 hours and 40 minutes. Since Bennett was at school for 4 hours (or 240 minutes), the time spent eating lunch can be calculated by subtracting the class and break time from the total time at school: 240 minutes - 220 minutes = 20 minutes.
Therefore, Bennett spent 20 minutes eating lunch.
Which of the following equations represents the graph shown?
Answer:
[tex]y=\frac{3}{2}x[/tex]
Step-by-step explanation:
The given line passes through the origin.
Its equation is of the form;
[tex]y=mx[/tex]
where
[tex]m=\frac{3}{2}[/tex] is the slope of the line.
The required equation is
[tex]y=\frac{3}{2}x[/tex]
Answer: [tex]f(x)=\dfrac{3}{2}x[/tex].
Step-by-step explanation:
Assume one block in the graph takes one value.
From the given graph, it can be seen that the line is passing through two points (0,0) and (2,3).
We know that the equation of a line passing through points (a,b) and (c,d) is given by :-
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Then , the equation of a line passing through points (0,0) and (2,3) is given by :-
[tex](y-0)=\dfrac{3-0}{2-0}(x-0)\\\\\Rightarrow y=\dfrac{3}{2}x[/tex]
Hence, the equations represents the given graph [tex]f(x)=\dfrac{3}{2}x[/tex].
I need to know how to find the mean for 77,82,87,85,32,78?
Answer:
73.5
Step-by-step explanation:
To find the mean, sum the data and divide by the amount of data
mean = [tex]\frac{77+82+87+85+32+78}{6}[/tex]
= [tex]\frac{441}{6}[/tex] = 73.5
The answer is 73.5. Just add all the numbers and divided by how many numbers there are. So you would add all the numbers and then divided by 6 since there are 6 numbers.
Solve the system of linear equations by elimination.
4x+3y= -5
-x+3y= -10
The solution of given system of linear equations are x = 1 and y = -3.
Given system of linear equations are,
[tex]4x+3y=-5 ..........(1)\\\\ -x+3y=-10..............(2)[/tex]
Subtract equation 2 from equation 1.
[tex]4x+3y-(-x+3y)=-5+10\\ \\ 4x+3y+x-3y=5\\ \\ 5x=5\\ \\ x=5/5=1[/tex]
Substituting value of x in equation 1.
[tex]4(1)+3y=-5\\ \\ 3y=-5-4=-9\\ \\ y=-9/3=-3[/tex]
Hence, The solution of given system of linear equations are x = 1 and y = -3.
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Which best describes the relationship between the two triangles below
Answer:
Just took the test test it is A 100%
Step-by-step explanation:
The relationship between the two triangles can be described as ΔMLN ~ ΔFGH by the third angle theorem, ∠M ≅ ∠F, ∠L ≅ ∠G, and ∠N ≅ ∠H.
Given two triangles.
The triangles are named as LMN and FGH.
Also, two of the angles of each triangle is given.
For triangle LMN,
∠L = 36° and ∠M = 51°
Similarly, for triangle FGH,
∠G = 36° and ∠F = 51°
So, for both triangles,
∠L = 36° = ∠G
∠M = 51° = ∠F
Using the angle sum property of triangles,
∠N = ∠H = 180° -(36° + 51°) = 93°
That is, all three angles of triangle LMN is equal to triangle FGH.
So, by the third angle theorem, ΔMLN is similar to ΔFGH.
Hence, the correct option is A.
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If a figure is a square, then it is a regular quadrilateral. True or false? Explain.
Answer:
Yes, because a quadrilateral have four sided figure. So True.
Answer + Explanation:
True, because all quadrilaterals are four-sided figures. Squares have four equal sides, so they are regular quadrilaterals.
Last year Jo paid £245 for her car insurance. This year she has to pay £883 for her car insurance. Work out the percentage increase in the cost of her car insurance.
Answer:
The percentage increase in the cost of her car insurance is 260.4%
Step-by-step explanation:
First, we are going to find by how much the insurance increased:
We know that this year she pays £883 and the last year she paid £245, so
insurance increase = £883 - £245
insurance increase = £638
Now, we are going to find what percentage of the last year price is the insurance increase. So, to find the percentage increase in the cost of the car insurance, we need to divide the insurance increase by the last year price and multiply the result by 100%
percentage increase = [tex](\frac{638}{245} )[/tex](100%)
percentage increase = (2.604)(100%)
percentage increase = 260.4%
We can conclude that Jo's car insurance cost increased 260.4%