Answer:
About 95% of data lies between 15.6 and 32.4
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 2.4
Standard Deviation, σ = 4.2
We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.
Empirical Formula:
Almost all the data lies within three standard deviation from the mean for a normally distributed data.About 68% of data lies within one standard deviation from the mean.About 95% of data lies within two standard deviations of the mean.About 99.7% of data lies within three standard deviation of the mean.We have to find the percentage of data lying between 15.6 and 32.4
[tex]15.6 = 24 - 2(4.2) = \mu - 2\sigma\\32.4 = 24 + 2(4.2) = \mu + 2\sigma[/tex]
Thus, we have to find the percentage of data lying within two standard deviations of the mean. By Empirical formula about 95% of data lies between 15.6 and 32.4
Point O is the center of this circle. What is m∠CAB?
A.
55°
B.
48°
C.
45°
D.
35°
Answer:
48
Step-by-step explanation:
Answer:
b)48
Step-by-step explanation:
Which cone has a volume of 24pie cm³? Need this done asap!
Step-by-step explanation:
volume of a cone is given by
[tex] \frac{\pi {r}^{2}h }{3} [/tex]
1st cone,
B= 25π cm²
πr²=25π
r²=25
r=5
Here, volume = π(5)²×3.5/3
=29.1π cm³
2nd cone,
r=3cm
Here, volume = π(3)²×6.5/3
= 19.5π cm³
3rd cone,
r= 4cm
Volume = π(4)²×4.5/3
=24π cm³
4th cone,
B=4π cm²
r²=4
r=2
volume = π(2)²×7.5/3
= 10π cm³
So, the third cone has vol 24π cm³
Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates (22,2), determine and state the coordinates of P.
The coordinates of P are (12, 2).
Solution:
Given data:
[tex](x_1, y_1)= A (4, 2)[/tex] and [tex](x_2, y_2)=B(22, 2)[/tex]
P(x, y) is the point on the line segment AB.
AP : PB = m : n = 4 : 5.
That is m = 4 and n = 5.
Section formula:
[tex]$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)[/tex]
[tex]$P(x, y)=\left(\frac{4\times 22 + 5\times 4}{4+5}, \frac{4\times 2 + 5\times 2}{4+5}\right)[/tex]
[tex]$P(x, y)=\left(\frac{88 + 20}{9}, \frac{8+10}{9}\right)[/tex]
[tex]$P(x, y)=\left(\frac{108}{9}, \frac{18}{9}\right)[/tex]
P(x, y) = (12, 2)
Hence the coordinates of P are (12, 2).
Help please!!! Find the sum of the series show your work
Answer:
[tex]\sum_{i=1}^{12}(3i-1) = 222[/tex]
Step-by-step explanation:
The given series is
[tex]\sum_{i=1}^{12}(3i-1)[/tex]
The first term is
[tex]f(1) = 3 \times 1 - 1 = 2[/tex]
The last term is
[tex]f(12) = 3 \times 12 - 1 = 35[/tex]
To find the number of terms in the sequence, solve,
[tex]3i - 1 = 35[/tex]
[tex]3i = 36 \\ i = 12[/tex]
The sum of the first i-terms of an arithmetic sequence is:
[tex]S_i = \frac{i}{2} (f(1) + f(2))[/tex]
We substitute the values to get;
[tex]S_ {12}= \frac{12}{2} (2+ 35)[/tex]
[tex]S_ {12}=6(37)[/tex]
[tex]S_ {12}= 222[/tex]
HELP PLEASE !!!!!!!!!!!!!!
What’s the area of this?
Answer:
25.5
Step-by-step explanation:
[tex]A_{t} = \frac{1}{2} * (6 + 3) * (5 + 2) = 31.5\\\\A_{r} = 2 * 3 = 6\\\\A = A_{t} - A_{r} = 31.5 - 6 = 25.5[/tex]
Solve the system of linear equations using elimination. −2x − y = 3 −9x − y = 17
A) (2, 1) B) (2, −1) C) (−2, 1) D) (−2, −1)
Answer:
x = -2 , y = 1
Step-by-step explanation:
Solve the following system:
{-2 x - y = 3 | (equation 1)
-9 x - y = 17 | (equation 2)
Swap equation 1 with equation 2:
{-(9 x) - y = 17 | (equation 1)
-(2 x) - y = 3 | (equation 2)
Subtract 2/9 × (equation 1) from equation 2:
{-(9 x) - y = 17 | (equation 1)
0 x - (7 y)/9 = -7/9 | (equation 2)
Multiply equation 2 by -9/7:
{-(9 x) - y = 17 | (equation 1)
0 x+y = 1 | (equation 2)
Add equation 2 to equation 1:
{-(9 x)+0 y = 18 | (equation 1)
0 x+y = 1 | (equation 2)
Divide equation 1 by -9:
{x+0 y = -2 | (equation 1)
0 x+y = 1 | (equation 2)
Collect results:
Answer: {x = -2 , y = 1
Answer:
C) (−2, 1)
Step-by-step explanation:
Name the property illustrated in this statement. If y - 2 = -8. then y - 2 + 2 = -8 + 2.
10
Step-by-step explanation:
first what is 10 take away 2 is 8 then 10 take away 2 is 8 + 2 equals 10 8 + 2 equals 10 so that's how I got the answer 10
What is the volume of the triangular prism? Round to the nearest tenth.
Answer:
the volume of the triangular prism is 1,185.6 in³
Step-by-step explanation:
To find the volume of these triangular prism, we will, first, find the area of the triangle then multiply by the length
Area of triangle = [tex]\frac{1}{2}[/tex] × b×h
From the diagram ,the height of the triangle is given to be 10.4 in and the base is given to be 12 in.
We will now proceed to insert the values into the formula;
Area of triangle = [tex]\frac{1}{2}[/tex] × b×h
= [tex]\frac{1}{2}[/tex] × 12×10.4
= [tex]\frac{1}{2}[/tex] × 124.8
=62.4
Area of triangle is 62.4 in²
From the diagram is given to be 19 in
Volume of triangular prism = area of triangular prism × l
=62.4 in² × 19 in
=1,185.6 in³
Therefore the volume of the triangular prism is 1,185.6 in³
The total cost of a boat rental includes the price per hour plus the cost of one full tank of gas. The table below represents the boat rental fees.
No. Of Hours 2 4 6 8
Rental Fee $92$150$208 $266
What is the cost for a full tank of gas?
A. $58
B. $266
C. $34
D. $29
Answer:
C. $34
Step-by-step explanation:
$58 is added every 2 hours so you just subtract that from $92 since $92 is the price of 2 hours and a full tank of gas.
a ladder 20 feet long leans against a building, forming an angle of 71° with the level ground. To the nearest foot, how high up the wall of the building does the ladder touch the building?
The wall is 18.79 feet high from the ground.
Data;
Length of ladder = 20ftangle of elevation = 71 degreeslength of the wall = ?Trigonometric RatioTo solve this problem, we need to use trigonometric ratio SOHCAHTOA in which we can find the missing side.
if we draw an illustration of this question, we would get
hypothenuse = 20ftangle = 71 degreesopposite = ?Using the sine angle ratio,
[tex]sin\theta=\frac{opposite}{hypothenuse}\\sin71=\frac{x}{20}\\ x=20sin71\\x=18.79ft[/tex]
The wall is 18.79ft high
Learn more on trigonometric ratios here;
https://brainly.com/question/4326804
To calculate the height the ladder reaches on the wall, we use sine function and find it to be approximately 19 feet.
To find out how high up the wall the ladder touches the building when a 20-foot ladder forms an angle of 71° with the level ground, we can use trigonometry. Specifically, the sine function relates the opposite side to the hypotenuse in a right triangle. The ladder represents the hypotenuse, and the height reached on the wall is the opposite side.
Using the formula:
sin(angle) = opposite/hypotenuse
For this problem:
sin(71°) = height / 20 feet
Now we solve for height:
height = 20 feet × sin(71°)
We can calculate this using a calculator:
height ≈ 20 feet × 0.945
height ≈ 18.9 feet
To the nearest foot, the ladder reaches approximately 19 feet up the wall.
An athlete jumped 5.5 feet which was 1.1 times higher than the previous jumper. How high did the previous athlete jump?
Answer:
5ft
Step-by-step explanation:
1.1j=5.5ft
Divide both sides by 5.5
So: j=5ft. This is the previous jump
Replace the ? in each of these statements with the symbol >, <, or =.
a. 39 ? 38
b. 16 ? 16
c. 11 ? 315
d. 5 ? 4
39>38
16=16
11<315
5>4
Hope this helps you mate
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The graphed line can be expressed by which equation?y+2=23(x+2) y−2=34(x−1) y−1=−34(x−2) y−2=34(x−2)
For this case we have that by definition, the equation of a line in the point-slope form is given by:
[tex]y-y_ {0} = m (x-x_ {0})[/tex]
Where:
[tex](x_ {0}, y_ {0}):[/tex]It is a point through which the line passes
m: It is the slope of the line
According to the graph we have that the line goes through the following points:
[tex](x_ {1}, y_ {1}) :( 4,2)\\(x_ {2}, y_ {2}): (- 2, -2)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-2} {- 2-4} = \frac {-4} {- 6} = \frac {2} {3}[/tex]
We choose a point:
[tex](x_ {0}, y_ {0}): (-2, -2)[/tex]
The equation of the line is:
[tex]y - (- 2) = \frac {2} {3} (x - (- 2))\\y + 2 = \frac {2} {3} (x + 2)[/tex]
ANswer:
[tex]y + 2 = \frac {2} {3} (x + 2)[/tex]
Option A
Is (1, 10) a solution to this system of equations?
y = 9x + 1
y = x + 9
Final answer:
The point (1, 10) satisfies both given equations when substituting x with 1 and y with 10, therefore it is a solution to the system of equations.
Explanation:
To determine if the point (1, 10) is a solution to the given system of equations, we must substitute x with 1 and y with 10 into each equation and see if the equations hold true.
For the first equation y = 9x + 1, substituting gives us:
10 = 9(1) + 1
10 = 9 + 1
10 = 10
This is true, so (1, 10) satisfies the first equation.
For the second equation y = x + 9, substituting gives us:
10 = 1 + 9
10 = 10
This is also true, so (1, 10) satisfies the second equation as well.
Since (1, 10) satisfies both equations, it is indeed a solution to the system of equations.
Let's determine if the point (1, 10) is a solution to the given system of equations by substituting the x and y values from the point into both equations.
The system of equations is:
1. \( y = 9x + 1 \)
2. \( y = x + 9 \)
We are given the point (1, 10), where x = 1 and y = 10.
We'll substitute these values into each equation to check for equality.
First, let's substitute x = 1 and y = 10 into the first equation:
\( y = 9x + 1 \) becomes \( 10 = 9(1) + 1 \), simplifying to \( 10 = 9 + 1 \), which further simplifies to \( 10 = 10 \).
The first equation is satisfied with x = 1 and y = 10.
Next, we'll substitute x = 1 and y = 10 into the second equation:
\( y = x + 9 \) becomes \( 10 = 1 + 9 \), simplifying to \( 10 = 10 \).
The second equation is also satisfied with x = 1 and y = 10.
Since the point (1, 10) satisfies both equations, we can conclude that (1, 10) is indeed a solution to the given system of equations.
About 8% of the U.S. population catches the flu each season. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?
1 in 8
1 in 12
1 in 18
1 in 80
Answer:
The correct answer is B. 1 in 12.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Percentage of the U.S. population that catches the flu each season = 8%
8% = 8/100
2. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?
Let's review together each of the possible answers given:
A. 1 in 8 = 1/2 = 0.125 = 12.5%, this is not the percentage given.
B. 1 in 12 = 1/12 = 0.083 = 8.3%, if we round to 8%, this is the percentage given.
C. 1 in 18 = 1/18 = 0.056 = 5.6%, this is not the percentage given.
D. 1 in 80 = 1/80 = 0.0125 = 1.25%, this is not the percentage given.
The correct answer is B. 1 in 12.
3/4, find the surface area
Answer:
1,350 cm^2
Step-by-step explanation:
It's a cube so all faces/bases are the same.
15 × 15 = 225
225 × 6 = 1,350
10. The length of the hypotenuse of a 30°-60°-90° triangle is 16. What is the perimeter?
64+8 square root 3
24+8 square root 3
16+64 square root 3
8+24 square root 3
Answer:
24+8 square root 3
Step-by-step explanation:
The ratio is x : x radical 3 : 2x
hypotenuse= 2x= 16
x =8
x square root 3 = 8 square root 3
16+8=24
According to the survey described here, what was the sample of the survey? “A recent telephone survey of 900 teenagers aged 16 to 19 from across the state shows 1 out of 4 of them drive themselves to school.”
A. all teenagers aged 16 to 19 in the state
B. 900 teenagers aged 16 to 19 from across the state
C. 1 out of 4 teenagers aged 16 to 19 from across the state
D. teenagers aged 16 to 19 from across the state who own a telephone
Answer:
Step-by-step explanation:
B is correct. This choice accurately describes the sample.
what is y= -3/2x + 4 in standard form
Answer:
2y + 3x = 8
Step-by-step explanation:
Step 1: Add 3/2x to both sides
y + 3/2x = -3/2x + 4 + 3/2x
y + 3/2x = 4
Step 2: Multiply both sides by 2
(y + 3/2x)*2 = 4*2
2y + 3x = 8
Answer: 2y + 3x = 8
What are period and amplitude for the function
PLEASE ANSWER BOTH QUESTIONS I WILL GIVE You the
Answer: Period: 4. Amplitude: 3
Step-by-step explanation: The period is how long it takes for one cycle of the function (one up and down). In this graph, one cycle ends at 4.
The amplitude is how far away the extremes of the graph are from the midline. This graph is a total of 6 units tall, making the amplitude 3. (I usually find total graph height and divide by 2.)
A spinner with four equal quadrants labeled A, B, C, and D is spun. What is the theoretical probability of the spinner NOT landing on the letter C?
Answer:
3/4, 75% chance
Step-by-step explanation:
you have four in total, three of which are not c, so you have a three out of four chance of NOT picking c. 3/4 as a percentage is 75%
Answer:
25%
Step-by-step explanation:
On MobyMax its 25%
Write an equation in slope-intercept form for the line passing through the pair of points. (2, –6), (–4, 3) Question 17 options: y = x + 3 y = x – 3 y = x – 3 y = x + 3
Answer:
No answer choices are correct; y=-9/6x-3
Step-by-step explanation:
Slope=Rise/Run=(3-(-6))/(-4-2)=9/-6=-9/6
y=-9/6x+b
3=-9/6(-4)+b
3=36/6+b
3=6+b
-3=b
So the equation is y=-9/6x-3, so none of your answer choices are correct
Robyn bought the following items in a supermarket. Can you help Robyn round each price to the nearest dollar. Item Actual Price Round to Nearest Dollar $ 34.70 $ $ 278.22 $ $ 45.89 $ 8.38
Answer:
$34.70 rounded to $35, $278.22 rounded to $278, $45.89 rounded to $46, $8.38 rounded to $8.
Step-by-step explanation:
The prism is completely filled with 1750 cubes that have edge length of 15 ft.
What is the volume of the prism?
The volume of the prism = 14 ft³
Solution:
Number of cubes in the prism = 1750
Edge length of each cube (a) = [tex]\frac{1}{5}[/tex] ft
To find the volume of each cube:
Volume of each cube = a³
[tex]$=\left(\frac{1}{5} \right)^3[/tex]
Volume of each cube [tex]$=\frac{1}{125} \ \text{ft}^3[/tex]
To find the volume of the prism:
Volume of the prism = Volume of each cube × Number of cubes
[tex]$=\frac{1}{125} \ \text{ft}^3\times 1750[/tex]
= 14 ft³
The volume of the prism = 14 ft³
Lateral surface area of a cylinder with a radius of 3 and a height of 8
The answer will be 150.8
Answer: AL≈150.8
Step-by-step explanation:
AL=2πrh
AL=2π3(8)
AL=2π24
AL=150.8 Rounded up
Solve the equation:
x² – 2x² – 15x=0
Answer: x=0, x²=0
Step-by-step explanation:
Answer:
x=3 and x=5/2
Step-by-step explanation:
3) Find the value of x. A) 21 B) 27 C) 31 D) 34
Answer:
I will guess 21
Step-by-step explanation:
9+10=21 boi
Answer:
for Usatestprep it is 21
Step-by-step explanation:
i swear 100%
Evaluate n/6 + 2 when n = 12
Answer:
[tex]\frac{(12)}{2} +2\\6+2=8\\8[/tex]
Hope this helped
Answer:
4
Step-by-step explanation:
n/6 + 2 when n = 12
n/6 + 2
Replace n with 12
Therefore,
n/6 + 2 = 12/6 + 2
= 2+2
=4
I hope this was helpful, please rate as brainliest
The Pham family bought 6 bags of cookies . Each bag had 13 cookies . They have since eaten 29 of the cookies . How many cookies do they have left ?
If they had six bags of cookies and each bag has thirteen cookies, then in total they have a total of seventy-eight cookies. If they've eaten twenty-nine cookies, then they now have forty-nine cookies because 78-29=49.