Answer: he made 22 foul shots
Step-by-step explanation:
Let x represent the number of one point shot that he made.
Let y represent the number of two point shots that he made.
Let z represent the number of three point shots that he made.
If the number of two-point shots he made is two less than five times the number of three-point shots made, it means that
y = 5z - 2
he made 104 total shots. It means that
x + y + z = 104- - - - - - - - - - 1
Substituting y = 5z - 2 into equation 1, it becomes
x + 5z - 2 + z = 104
x + 6z = 106- - - - - - - - - - -2
Total number of points scored is 200. It means that
x + 2y + 3z = 200- - - - - - - - - - 3
Substituting y = 5z - 2 into equation 3, it becomes
x + 2(5z - 2) + 3z = 200
x + 10z - 4 + 3z = 200
x + 13z = 204- - - - - - - - - - 4
Subtracting equation 4 from equation 2, it becomes
- 7z = - 98
z = - 98/ - 7
z = 14
Substituting z = 14 into equation 2, it becomes
x + 6 × 14 = 106
x + 84 = 106
x = 106 - 84
x = 22
The average adult gets 7.45 hours of sleep each night, with a standard deviation of 0.65 hours. A pharmaceutical company developing a sleep aid is researching how much sleep the top 1% of adults get each night, on average. Use a calculator to find how many hours of sleep must an adult get each night to be in the top 1% if the company is only basing their initial research on the sleep habits of 30 adults.
Answer:
At least 8.96 hours of sleep to be in the top 1%.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 7.45, \sigma = 0.65[/tex]
How many hours of sleep to be on the top 1%?
The top 1% is the 100 - 1 = 99th percentile, which is X when Z has a pvalue of 0.99. So X when Z = 2.327. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 7.45}{0.65}[/tex]
[tex]X - 7.45 = 0.65*2.327[/tex]
[tex]X = 8.96[/tex]
At least 8.96 hours of sleep to be in the top 1%.
Answer:
2.31
.12
7.73
Step-by-step explanation:
σx¯=0.653–√0=0.12
By plugging all the numbers into the formula z=x¯−μσx¯ we find that
2.31=x¯−7.450.12
0.28=x¯−7.45
7.73=x¯
What is the explicit formula for this sequence?
-1, -4, -16, -64, ...
Answer:
a, ar, ar²,ar³,ar⁴...
a line has an x-intercept of (4,0) and a y-intercept of (0,12).Find the slope of the line
Answer:
m = -3
Step-by-step explanation:
Slope Formula: [tex]m = \frac{y2-y1}{x2 - x1}[/tex]
All you have to do is plug in 4 for x1, 0 for x2, 0 for y1, and 12 for y2 and you should be able to calculate your answer!
Answer:
-3
Step-by-step explanation:
→ Utilise the gradient formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
→ Substitute in the values from the coordinates (4,0) and (0,12)
[tex]\frac{12-0}{0-4}=\frac{12}{-4} =-3[/tex]
→ The gradient of the line is -3
An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A's, 23% B's, 45% C's, 14% D's, and 8% F's. At the end of the semester, she has the following grades.
A 6
B 14
C 22
D 8
E 4
Test her claim at 5% significance level.
Answer:
At a plus or minus 5%
Her claim is wrong
Step-by-step explanation:
Ok..
Let's calculate the total amount of result first.
6 +14+22+8+4= 54.
Let's take the percentage of each.
For A
6/54= 0.11
11.1%
11.1%*5%= 10.5
For B
14/54
=0.25925
= 25.9%
25.9%*5%= 24.605
For C
22/54
0.4074
40.7%
40.7*5%= 42.73%
For D
8/54
= 0.148
14.8%
14.8%*5% = 14.06%
For E
4/54
= 0.074
= 7.4%
7.4%*5%=7.77%
But she suggested
10% A's, 23% B's, 45% C's, 14% D's, and 8% F's
The area of a square is increasing at a rate of 2 square feet a second. If the square started with an area of 4 square feet, how much time passes before the area of the square equals 16 square feet
Answer:
6 seconds
Step-by-step explanation:
The area of interest increases from 4 square feet to 16 square feet, an increase of 12 square feet. Since the area increases by 2 square feet each second, the time required for it to increase 12 square feet is ...
(12 square feet)/(2 square feet/second) = 6 seconds
Find the value : 10a^2b^0 for a=−3, b=−8
What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?
y = 2 x + 33
y= *x+36
y = 4x - 16
y = 4x + 16
Answer:
y = 4x +16
Step-by-step explanation:
The given equation is in "point-slope" form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
The slope of the given line is m=4. This is the same slope as any parallel line.
__
The line you want can be written in the same point-slope form as ...
y -32 = 4(x -4)
Rearranging, we have ...
y = 4x -16 +32 . . . . . add 32, eliminate parentheses
y = 4x +16 . . . . . . . . collect terms
last one haha ill give 20 points
The type of triangle drawn is an isosceles triangle.
Base angles ∠ACB and ∠CAB are equal.
What is an isosceles triangle?This is a type of triangle with base angles and opposite sides equal.
Analysis:
∠DCA = ∠CAB ( alternate angles are equal)
∠CAB + ∠ACB + ∠CBA = 180°( sum of angles in a triangle)
50 + ∠ACB + 80 = 180
130 + ∠ACB = 180
∠ACB = 180 - 130 = 50°
Since ∠ACB = ∠CAB = 50°. The triangle drawn is an isosceles triangle.
In conclusion, the triangle is isosceles because the base angles are equal.
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. Draw a unit circle. A unit circle is a circle whose radius is 1 and whose center is located at the origin of a rectangular coordinate system. On this unit circle let θ be the angle measured from the positive x‐axis to the point P = (x, y). Label the angles 0, 6 , 4 , 3 , 2 , , 2 3 , 2 and the coordinates of the points on the unit circle that correspond to each of these angles. 2. Plot the point 2 3 , 2 1 . How can you check that the point is on the unit circle? (Hint: recall the equation of the unit circle). Plot the points symmetric to it with respect to the y-axis, to the x-axis, and to the origin. Label the coordinates of the points you found. Find positive angles (expressed in radians) which correspond to the points. 3. Explain how symmetry can be used to find the coordinates of points on the unit circle for angles whose terminal sides are in quadrants II, III, and IV. 4. If x, y is a point on the unit circle in quadrant I and if 2 3 x , what is y ? 5. Find two negative and three positive angles, expressed in ra
Answer:
When drawing a rectangle the point of origin is P = xy and the 0 be upon the positive x axis back to P this way we have a rectangle length.
The circle is inscribed in the middle of the rectangle.
Step-by-step explanation:
0,6 as this is 1/6th of circle
9,45 as this is 3/9th of a circle
36, 22.5 as this is 5/10 of a circle
-27, -16.5 as this is 7/10 of a circle
When we join up -27 to 0 with the end line of a rectangle the base, we find it is at point for -16 for y and joined to 6 at y and has formed 10/10 of a circle.
This is not correct but may help as they are in proportion.
Find the equation of the line given
the gradient
Parrallel to the line y= - 2x+4
point ( 1-3)
Answer:
y = -2x - 1
Step-by-step explanation:
Step 1: Find the parallel line
y = -2x + b
Step 2: Solve for b
-3 = -2(1) + b
-3 = -2 + b
b = -1
Step 3: Write parallel equation
y = -2x - 1
Please help! The table below shows the elevations of the three animals that Fernanda can see from her boat.
Answer:
Sea Lion, fish, Bird
Step-by-step explanation:
Find the absolute value of the animals, and then compare them from least to greatest
A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then what is the computed value of the test statistic?
Answer:
Th computed value of the test statistic is 3.597
Step-by-step explanation:
The null and the alternative hypothesis is as follows:
Null Hypothesis:
[tex]\mathbf{H_o:}[/tex] the population correlation coefficient is equal to zero
[tex]\mathbf{H_a:}[/tex] the population correlation coefficient is not equal to zero
The test statistics for Pearson correlation coefficient is thus computed as :
[tex]t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }[/tex]
where;
r = correlation coefficient = 0.60
n = sample size = 25
So;
[tex]t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }[/tex]
[tex]t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }[/tex]
[tex]t =\dfrac{0.60 *4.796} {0.8}[/tex]
t = 3.597
Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069
Decision Rule:
Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.
Conclusion:
We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.
What is the repeating digit in the decimal equivalent of 49?
Answer:
49/99
Step-by-step explanation:
I'm assuming you want to find the fraction that gives the decimal 0.494949...
If that is the case, the 49/99 is your answer.
Answer:
4
Step-by-step explanation:
The 3 by 3 grid below shows nine 1 cm x 1 cm squares and uses 24 cm of wire.
What length of wire is required for a similar 20 by 20 grid?
Answer:
840 cm
Step-by-step explanation:
From the diagram attached, the 3 by 3 grid is made up of nine 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of four rows each row having a length of 3 cm and four columns with each column having a length of 3 cm.
The length of wire required by the 3 by 3 grid = 4 column (3 cm / column) + 4 row (3 cm / row) = 12 cm + 12 cm = 24 cm
The 20 by 20 grid is made up of twenty 1 cm x 1 cm squares. The the length of wire needed to make this grid consist of twenty one rows each row having a length of 20 cm and twenty columns with each column having a length of 20 cm.
The length of wire required by the 20 by 20 grid = 21 column (20 cm / column) + 21 row (20 cm / row) = 420 cm + 420 cm = 840 cm
g Your underground used-book business is booming. Your policy is to sell all used versions of Calculus and You at the same price (regardless of condition). When you set the price at $10, sales amounted to 100 volumes during the first week of classes. The following semester, you set the price at $30 and sales dropped to zero. Assuming that the demand for books depends linearly on the price, what price gives you the maximum revenue?
Answer:
The price that maximizes the revenue is $15 per book.
Step-by-step explanation:
We have a demand that has a linear relation to price.
The two points we will use to calculate the demand function are:
Price p=10, Demand q=100Price p=30, Demand q=0We have the equation:
[tex]q=m\cdot p+b[/tex]
Then, we replace:
[tex]q(30)=0=m(30)+b\\\\q(10)=100=m(10)+b\\\\\\b=-30m\\\\100=10m+(-30m)=-20m\\\\m=-100/20=-5\\\\b=-30(-5)=150\\\\\\q(p)=-5p+150[/tex]
The revenue R can be calculated as the multiplication of price and quantity.
We can maximize R by deriving and equal that to 0:
[tex]R=p\cdot q=p(-5p+150)=-5p^2+150p\\\\\\\dfrac{dP}{dp}=-5(2p)+150=0\\\\\\-10p+150=0\\\\p=150/10=15[/tex]
The price that maximizes the revenue is $15 per book.
The price that will offer the maximum revenue would be as follows:
$15
Find the priceWhat information do we have,
When Price = $10, Q = 100 Units
When Price = $ 30, Q = 0 units
With the above information, we can take the equation:
Q = Maximum (p + b)
by putting the values in both the above situations,
30 = 0 = m30 + b
10 = 0 = m10 + b
we get b = -30m. by putting this, we get
100 = 10m + (-30m) = -20m
∵ q(p) = -5p + 150
Through the equation and putting the above values, we get:
[tex]R = p.q.[/tex]
[tex]= p(-5p + 150)[/tex]
[tex]= -5p^2 + 150p[/tex]
$15 as the maximum price.
Thus, $ 15 is the correct answer.
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Length of Triangles.
Answer:
9
Step-by-step explanation:
Since the scale factor is 12/8 = 1.5, to find LA we have to multiply FI by 1.5 which is 6 * 1.5 = 9.
The city planning commission has been given a budget of 300,000 if the density of concrete is 150 lbs/ft3 determine if the cpc can afford to buy the bridge. The cost of concrete is 0.80/lb
Answer:
Check Explanation
Step-by-step explanation:
The volume of concrete required to build the bridge is missing and should be provided.
In its absence, let us assign a letter to it.
Let the volume of concrete required to build the bridge be V ft³.
And we further assume that the concrete is the only major material needed to build the bridge for the sake of our question.
Density = (mass/volume)
Density = 150 lb/ft³
Mass = ?
Volume = V ft³
Mass = (Density) × (Volume)
Mass of concrete required = 150 × V = (150V) lb
Cost of concrete is 0.80 per lb
1 lb of concrete costs 0.80
150V of concrete will cost 150V × 0.80 = (120V) currency amount.
Now, depending on the value of V, we can now determine if the city planning commission (cpc) can afford the bridge.
If 120V > 300,000 budget, the cpc cannot afford the bridge, but if 300,000 budget > 120V, then the cpc can afford the bridge.
Hope this Helps!!!
Please answer this correctly
Answer:
14.3%
Step-by-step explanation:
There is only one four out of 7 total numbers.
1/7 = 0.142857 = 14.29%
We are given 7 numbers.
4 is only one card in that 7 card set so, 1/7.
1/7 = 0.1428
0.1428 * 100% = 14.28%
Therefore, the answer is roughly 14.3%
Best of Luck!
Hoping to increase the chances fo reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 0.90, 0.80, 0.70 for successfully completing the task in the allotted time. Assuming that the teams work independently, what is the probability that the task will NOT be completed in time
Answer:
P = 0.006
Step-by-step explanation:
If the first team have a probability of 0.9 to complete the task, we can said that the probability to not complete the task in time is 0.1. It is calculated as:
1 - 0.90 = 0.1
At the same way, the probability to not complete the task for the second and third team are 0.2 and 0.3 respectively and they are calculated as:
1 - 0.80 = 0.2
1 - 0.70 = 0.3
Finally, the the probability that the task will NOT be completed in time is the probability that any of the teams completed the task. So, it is equal to:
P = 0.1 * 0.2 * 0.3 = 0.006
Im stuck on this question
Answer:
well the shape is acute so it will be quite low work out the opposite angles and you will find out that the lines are parallels there for meaning the answer is the lowest angle
Step-by-step explanation:
In order to solve for the variable in the equation 2 (4 x + 3) + 4 = 3 x minus (2 x + 4), Giovanni first applies the distributive property. Which equation is a result of this step?
Answer:
8x + 6 + 4 = 3x - (2x + 4)
Step-by-step explanation:
When Gio applies the distributive property, the equation above is the result. Naturally, I look at the 1st parenthesis I see and start the 1st distributive property there first. The 2nd distributive property would be the other parenthesis where you multiply by -1, so you would get 8x + 6 + 4 = 3x - 2x - 4
Answer:
A or 8x + 6 + 4 = 3x - (2x + 4)
Step-by-step explanation:
7. Evaluate 4P2
O
22
O
12
O
14
5
Answer:
12Step-by-step explanation:
To evaluate 4P2, we will use the permutation formula as shown;
nPr = [tex]\frac{n!}{(n-r)!}[/tex]
4P2 = [tex]\frac{4!}{(4-2!}[/tex]
[tex]= \frac{4!}{2!} \\= \frac{4*3*2!}{2!}\\ = 4*3\\= 12[/tex]
4P2 = 12
The royal fruit company produces two types of fruit drinks. the first type is 20% pure fruit juice, and the second is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 35% pure fruit juice. How many pints of each of the two existing types of drinks must be used to make 60 pints of a mixture that is 35% pure fruit juice?
Answer:
We have 20% fruit juice and 70% fruit juice.
We need 60 pints of 35% fruit juice.
We set up 2 equations where t is 20% and s is 70%
t + s = 60 pints
.20t + .70s = (.35 * 60)
We solve for both unknowns
t = 42 s = 18
We need 42 pints of 20% and 18 pints of 70 %
**** DOUBLE CHECK *******************************
42 pints of 20% = 8.40 pints of juice 33.6 pints water
18 pints of 70% = 12.60 pints of juice 5.40 pints water
TOTAL mixture = 21 pints juice 39 pints water = 60 total pints
21 pints juice / 60 = .35 (or 35% fruit juice)
Correct !!!
Step-by-step explanation:
What is the density of a material with a mass of 512 kilograms and a volume of 4 cubic meters?
Answer:
128 kg/m^3
[tex]solution \\ \: mass = 512 \: kg \\ volume = 4 {m}^{3} \\ now \\ density = \frac{m}{v} \\ \: \: \: \: \: \: \: \: \: \: \: \: = \frac{512}{4} \\ \: \: \: \: \: \: \: \: \: = 128 \: kg/ {m}^{3} [/tex]
hope this helps...
Good luck on your assignment
If ABCD is a rectangle, and m∠ADB=55°, what is the value of x?
Answer:
x= 70
Step-by-step explanation:
Rectangles have four right angles (angles of 90 degrees).
The point of intersection of the diagonals divides each one of them into two equal parts.
Knowing this, we can conclude that:
m\angle c=m\angle b=55\°
Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":
x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°
Rata-rata markah matematik untuk Amin, azman dan aziz adalah 73. Tanda Azman lebih 35 berbanding Amin manakala aziz dua kali ganda daripada Amun. Apakah tanda Amin?
Answer:
The Amin's score in math was 46.
Step-by-step explanation:
The question is:
The average math score for Amin, azman and aziz is 73. Azman marks 35 more than Amin while aziz is twice that of Amun. What is Amin's sign?
Solution:
Let us denote that:
x = Amin's score in math
y = Azman's score in math
z = Aziz's score in math.
The average of x, y and z is, 73.
That is:
[tex]\frac{x+y+z}{3}=73\\\\\Rightarrow x+y+z = 219[/tex]
Now it is provided that:
[tex]y=x+35...(i)\\z=2x...(ii)[/tex]
Use the equations (i) and (ii) to determine the value of x as follows:
[tex]x+y+z=219\\\\x+x+35+2x=219\\\\4x=184\\\\x=46[/tex]
Thus, the Amin's score in math was 46.
whats the answers to this ?
Answer:
Hi there!
The correct answers are: A, B, D, E
Step-by-step explanation:
First of all, perpendicular means when two lines intersect to form a 90° angle.
Second ⊥ means perpendicular.
When something is a bisector it means it evenly slices a line in half.
The process used to collect data will __________ of the study.
affect the validity and the bias
affect only the validity
affect only the bias
not affect the validity and the bias
The process used to collect data will affect the validity and the bias of the study.
What is validityThe way data is gathered is very important for making sure a study is accurate and doesn't have any unfair influences. Validity means how well the information collected correctly shows the things the study is trying to find out. If the way data is collected is not done correctly, it can cause incorrect or untrustworthy results, making the study less reliable
Bias means when we make mistakes or go away from the correct value or truth. If the way we collect data is biased, it can lead to unfair outcomes or favor certain groups.
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Please answer this correctly
Answer:
Median
Step-by-step explanation:
I believe this is median, as the mode and median stay the same numbers with and without 26, Mean 26, Mode 45, so the median would change the most as it goes from 23 to 26
Answer:
Median
Step-by-step explanation:
Mean of 10 numbers = 260/10 = 26
Mean of 11 numbers = 286/11 = 26
No change
Median:
Median for 10 numbers
12 , 14, 15 , 17 , 19 , 27, 29 ,37 , 45, 45
Median = 19+27/2 = 46/2 = 23
Median of 11 numbers
12 , 14, 15 , 17 , 19 , 26, 27, 29 ,37 , 45, 45
Median = 26
Median changes the most
Simplify ^36 - ^16 =
Answer:
[tex]x^{36}-x^{16}[/tex] is already at its simplest form
Step-by-step explanation:
You cannot factor or GCF anything out of it, and you cannot just subtract exponents. Therefore, it is simplified already.