? Question
A slingshot launches a water balloon into the air. Function f models the height of the balloon, where x is the horizontal
distance in feet:
f(x) = -0.05x2 +0.8x + 4.
From what height did the slingshot launch the balloon, and what was the balloon's maximum height? How far from the
slingshot did the balloon land?
The balloon's maximum height was____
The slingshot
launched the balloon from a height of _____
The balloon landed_____
from the slingshot.
Answers
Answer:
4 ft
7.2 ft
20 ft
Step-by-step explanation:
When the balloon is shot, x = 0.
y = -0.05(0)² + 0.8(0) + 4
y = 4
The balloon reaches the highest point at the vertex of the parabola.
x = -b / 2a
x = -0.8 / (2 × -0.05)
x = 8
y = -0.05(8)² + 0.8(8) + 4
y = 7.2
When the balloon lands, y = 0.
0 = -0.05x² + 0.8x + 4
0 = x² − 16x − 80
0 = (x + 4) (x − 20)
x = -4 or 20
Since x > 0, x = 20.
The slingshot launched the ballon from a height of 4 feet. The balloon's maximum height was 72 feet. The balloon landed 20 feet from the slingshot.
To determine the height from which the slingshot launched the balloon, we need to evaluate the function f(0) because when x is zero, it represents the starting point of the balloon's trajectory.
f(x) = -0.05x² + 0.8x + 4
f(0) = -0.05(0)² + 0.8(0) + 4
f(0) = 4
Therefore, the slingshot launched the balloon from a height of 4 feet.
To find the maximum height of the balloon, we can observe that the maximum point of the parabolic function occurs at the vertex.
The x-coordinate of the vertex can be calculated using the formula x = -b / (2a).
In our case, a = -0.05 and b = 0.8.
Let's calculate the x-coordinate of the vertex:
x = -0.8 / (2×(-0.05))
x = -0.8 / (-0.1)
x = 8
Now, substitute this x-coordinate into the function to find the maximum height:
f(x) = -0.05x² + 0.8x + 4
f(8) = -0.05(8)² + 0.8(8) + 4
f(8) = -0.05(64) + 6.4 + 4
f(8) = -3.2 + 6.4 + 4
f(8) = 7.2
Therefore, the balloon reached a maximum height of 7.2 feet.
To determine how far from the slingshot the balloon landed, we need to find the x-intercepts of the quadratic function.
These represent the points where the height is zero, indicating the balloon has landed.
Setting f(x) = 0, we can solve the quadratic equation:
-0.05x² + 0.8x + 4 = 0
x² - 16x - 80= 0
x=-4 or x=20
We take the positive value, so the balloon landed 20 feet from the slingshot.
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Related Questions
A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 70 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answers
Answer:
42 gallons 45% antifreeze
28 gallons 95% antifreeze
Step-by-step explanation:
If x is volume of 45% antifreeze, and y is volume of 95% antifreeze, then the total volume is:
x + y = 70
And the total amount of antifreeze is:
0.45 x + 0.95 y = 0.65 (70)
Solving by substitution:
0.45 x + 0.95 (70 − x) = 0.65 (70)
0.45 x + 66.5 − 0.95 x = 45.5
21 = 0.5 x
x = 42
y = 28
Which equation represents a population of 250 animals that decreases at an annual rate of 21%
Answers
Answer:
y= 250( 1-0.21)^x
Step-by-step explanation:
This represents exponential decay
The equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
What is an exponential function?The mathematical expression f(x)=[tex]e^t[/tex] denotes the exponential function. The term typically refers to the positive-valued function of a real variable, unless otherwise specified.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
It is given that a population of 250 animals is decreasing at an annual rate of 21%.
p = a x b[tex].^t[/tex]
p = a x (1+r)[tex].^t[/tex]
p = 250 x (1+(-0.21))[tex].^t[/tex]
p = 250(0.79)[tex].^t[/tex]
Note that r = -0.21 is negative to indicate we have exponential decay.
Hence, the equation represents a population of 250 animals that decreases at an annual rate of 21% will be p = 250(0.79)[tex].^t[/tex] The correct option is C.
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The equation to the graph is y = -1/2 x - 3
Answers
Answer:
Hope it helps <3
━━━━━━━☆☆━━━━━━━
▹ Answer
Use a graphing calculator. Attached is an image.
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
.If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3; however, if '
you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4. For what fraction is this true?
Answers
Answer:
The fraction that this is true for = 7/13
Step-by-step explanation:
From the above question
Let the numerator be represented by a
Let the denominator be represented by b
If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
Cross Multiply
3(a + 5) = 2(b + 5)
3a + 15 = 2b + 10
Collect like terms
3a - 2b = 10 - 15
3a - 2b = -5..........Equation 1
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
Cross Multiply
4(a - 5) = 1(b - 5)
4a - 20 = b - 5
Collect like terms
4a - b = 20 - 5
4a - b = 15..........Equation 2
b = 4a - 15
3a - 2b = -5..........Equation 1
4a - b = 15..........Equation 2
Substitute 4a - 15 for b in equation 1
3a - 2b = -5..........Equation 1
3a - 2(4a - 15) = -5
3a - 8a + 30 = -5
Collect like terms
3a - 8a = -5 - 30
-5a = -35
a = -35/-5
a = 7
Therefore, the numerator of the fraction = 7
Substitute 7 for a in Equation 2
4a - b = 15..........Equation 2
4 × 7 - b = 15
28 - b =15
28 - 15 = b
b = 13
The denominator = b is 13.
Therefore,the fraction which this is true for = 7/13
To confirm
a) If you add 5 to both the numerator and the denominator of a fraction, you obtain 2/3
This means:
a + 5/b + 5 = 2/3
7 + 5/ 13 + 5 = 2/3
12/18 = 2/3
Divide numerator and denominator by of the left hand side by 6
12÷ 6/ 18 ÷ 6 = 2/3
2/3 =2/3
If you subtract 5 from both the numerator and the denominator of the same fraction, you obtain 1/4
This means:
a - 5/b - 5 = 1/4
7 - 5/13 - 5 = 1/4
2/8 = 1/4
Divide the numerator and denominator of the left hand side by 2
2÷2/8 ÷ 2 = 1/4
1/4 = 1/4
From the above confirmation, the fraction that this is true for is 7/13
Please answer this correctly without making mistakes Please simplify the correct answer
Answers
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
In 2012, entering freshmen at the UA have an average ACT score of 25.4 with a standard deviation of 2.1. 1. What is the probability a student has an ACT score more than 24.1
Answers
Answer:
P [ Z > 24,1 ] = 72,24 %
Step-by-step explanation:
P [ Z > 24,1 ] = 1 - P [ Z < 24,1 ]
P [ Z < 24,1 ] = ( Z - μ₀ ) / σ
P [ Z < 24,1 ] = ( 24,1 - 25,4) / 2,1
P [ Z < 24,1 ] = - 1,3/ 2,1
P [ Z < 24,1 ] = - 0,6190 ≈ - 0,62
We look in z-table and find for z(score) -0,6190
P [ Z < 24,1 ] = 0,27763
Then
P [ Z > 24,1 ] = 1 - 0,27763
P [ Z > 24,1 ] = 0,72237 ⇒ or P [ Z > 24,1 ] = 72,24 %
easy math please help!
Answers
Answer:
[tex]\boxed{ \sf 41.81}[/tex]
Step-by-step explanation:
The triangle is a right triangle.
We can use trigonometric functions.
[tex]\sf sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]\sf sin(?)=\frac{2}{3}[/tex]
[tex]\sf ?=sin^{-1}(\frac{2}{3})[/tex]
[tex]\sf ?= 41.81031489...[/tex]
Answer:
[tex]\boxed{41.81}[/tex]
Step-by-step explanation:
∠B is opposite of side AC, which has a length of 2 units. The hypotenuse of the triangle is equivalent to 3 units.
The trigonometric function that uses the opposite side and the hypotenuse is sine function. This is represented by [tex]sin = \frac{opposite}{hypotenuse}[/tex]. The side that is opposite to the angle being solved for is the opposite side (it does not border the angle and it is not the hypotenuse).
However, you are solving for an angle. So, you need to use the inverse sine function ([tex]sin^{-1}[/tex]) to solve this question properly.
Simply type into a calculator [tex]sin^{-1} (\frac{2}{3})[/tex] and it will evaluate the answer to approximately 41.81°.
HEREEEEEEEEEEEEEElollll
Answers
Answer:
Hey there!
Your answer would be 4/50. The total times she drawed a purple tile was 4, and she drawed 50 times.
Hope this helps :)
What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0? radius = units
Answers
Answer:
8 units
Step-by-step explanation:
We need to rewrite an equation in the standard for a circle form.
r is radius.
(x−h)²+(y−k)²= r²
x² + y² – 2x + 8y – 47= 0
x² - 2x + y² + 8y - 47 = 0
x² - 2*x *1+ 1 ²- 1² + y² + 2*4*y + 4² - 4² - 47 = 0
(x - 1)² + (y + 4)² - 1 - 16 -47 =0
(x - 1)² + (y + 4)² - 64=0
(x - 1)² + (y + 4)² = 8²
Radius is 8.
The radius of the circle is 8 units
What is radius?The radius of a circle is a line drawn from the center to the circumference of the circle
The equation of the circle is given as;
[tex]x^2 + y^2 - 2x + 8y - 47 = 0[/tex]
Rewrite the equation as:
[tex]x^2 - 2x + y^2 + 8y = 47[/tex]
Next, we rewrite the equation in the standard form
So, we have:
x^2 - 2x + 1^2 - 1^2 + y^2 + 8y + 4^2 - 4^2 = 47
Evaluate the exponents
x^2 - 2x + 1 - 1 + y^2 + 8y + 16 - 16 = 47
Rewrite the equation as follows:
x^2 - 2x + 1 + y^2 + 8y + 16 = 47 + 1 + 16
Express as perfect squares
(x - 1)² + (y + 4)² = 64
(x - 1)² + (y + 4)² = 8^2
The radius of the circle is calculated as:
r^2 = 8^2
By comparison, we have:
r = 8
Hence, the radius of the circle is 8 units
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Identify the percent, amount, and base in this problem What is 15% of 60?
Answers
Answer:
9
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
1/6•4•(-1/3)•9•(-1/2)•5
Answers
Answer:
Step-by-step explanation:
its 5
1/6 *2 *3 *5=
1/3*3*5=
5
Lines $y=(3a+2)x-2$ and $2y=(a-4)x+2$ are parallel. What is the value of $a$?
Answers
Answer:
-8/5Step-by-step explanation:
Given two lines y=(3a+2)x-2 and 2y=(a-4)x+2, Since both lines are parallel to each other, this means that the slope of both lines are the same
Let's get the slope of both equation. For the first equation;
y=(3a+2)x-2
We can see that the equation is written in this form y = mx+c where m is the slope of the line. On comparison, the slope of the given line is 3a+2
Similarly for the second line;
2y=(a-4)x+2
Re-writing in the standard format we will have;
y = (a-4)x/2+2/2
y = (a-4)x/2 + 1
The slope of the second line is (a-4)/2
On equating the slope of both lines to get the value of 'a' we will have;
3a+2 = (a-4)/2
Cross multiplying
2(3a+2) = a-4
6a+4 = a-4
Collecting like terms;
6a-a = -4-4
5a = -8
a = -8/5
Hence the value of a is -8/5
Select all the correct coordinate pairs and the correct graph. Select the correct zeros and the correct graph of the function below.
Answers
Answer:
(0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
First graph in top row is the answer.
Step-by-step explanation:
The given function is, f(x) = x⁴ - 4x³ + x² + 6x
For zeros of the given function, f(x) = 0
x⁴ - 4x³ + x² + 6x = 0
x(x³ - 4x² + x + 6) = 0
Therefore, x = 0 is the root.
Possible rational roots = [tex]\frac{\pm 1, \pm 2, \pm 3, \pm 6}{\pm1}[/tex]
= {±1. ±2, ±3, ±6}
By substituting x = -1 in the polynomial,
x⁴ - 4x³ + x² + 6x = (-1)⁴ - 4(-1)³+ (-1)² + 6(-1)
= 1 + 4 + 1 - 6
= 0
Therefore, x = -1 is also a root of this function.
For x = 2,
x⁴ - 4x³ + x² + 6x = (2)⁴ - 4(2)³+ (2)² + 6(2)
= 16 - 32 + 4 + 12
= 0
Therefore, x = 2 is a root of the function.
For x = 3,
x⁴ - 4x³ + x² + 6x = (3)⁴ - 4(3)³+ (3)² + 6(3)
= 81 - 108 + 9 + 18
= 0
Therefore, x = 3 is a root of the function.
x = 0, -1, 2, 3 are the roots of the given function.
In other words, (0, 0), (-1, 0), (2, 0), (3, 0) are the zeros.
From these points, first graph in top row is the answer.
write the equation for taking away 5 from x gives 10
Answers
Answer:
[tex]\boxed{\sf x - 5 = 10}[/tex]
Step-by-step explanation:
Taking away 5 from x ⇒ subtracting 5 from x
[tex]\large {\sf x - 5[/tex]
Gives 10 ⇒ result is 10
[tex]\large {\sf x - 5 = 10[/tex]
What additional information do you need to prove △ABC ≅ △DEF by the SSS Postulate? A. BC = EF B. AB = DE C. AC = DF
Answers
Answer:
AC = DF
Step-by-step explanation:
The SSS Postulate occurs when all three corresponding pairs of sides are congruent, therefore, the only missing pair is AC = DF.
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Find the percentage of buyers who paid:
between $150,000 and $152,400 if the standard deviation is $1200.
Answers
Answer:
The percentage is [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 150000[/tex]
The standard deviation is [tex]\sigma = \$ 1200[/tex]
The prices we are considering is [tex]x_1 = \$150000 \to \ x_2 = \$ 152400[/tex]
Given that the price is normally distributed , the percentage the percentage of buyers who paid between $150,000 and $152,400 is mathematically represented as
[tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } < \frac{X - \mu}{\sigma } < \frac{x_2 - \mu}{\sigma })[/tex]
So [tex]\frac{X - \mu}{\sigma }[/tex] is equal to z (the standardized value of X )
So
[tex]P(x_1 < X < x_2) = P(\frac{x_1 - \mu}{\sigma } <Z < \frac{x_2 - \mu}{\sigma })[/tex]
substituting values
[tex]P(x_1 < X < x_2) = P(\frac{150000 - 150000}{1200 } <Z < \frac{152400 - 150000}{1200 })[/tex]
[tex]P(x_1 < X < x_2) = P(0<Z < 2)[/tex]
[tex]P(x_1 < X < x_2) = P( Z < 2) - P( Z < 0 )[/tex]
From the standardized normal distribution table [tex]P(Z < 2 ) = 0.97725[/tex] and
[tex]P(Z < 0) = 0.5[/tex]
So
[tex]P(x_1 < X < x_2) = 0.97725 - 0.5[/tex]
[tex]P(x_1 < X < x_2) = 0.47725[/tex]
The percentage is [tex]P(x_1 < X < x_2) = 47.7 \%[/tex]
Below are the jersey numbers of 11 players randomly selected from a football team. Find the range, variance, and standard deviation for the given sample data.
33 29 97 56 26 78 83 74 65 47 58
What do the results tell us?
A. Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
B. Jersey numbers on a football team vary much more than expected.
C. The sample standard deviation is too large in comparison to the range.
D. Jersey numbers on a football team do not vary as much as expected.
Answers
Answer:
Option(A) is correct
Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Step-by-step explanation:
The given data set in the question are ;33, 29, 97, 56, 26, 78, 83, 74, 65, 47, 58
the range can be determined by finding the highest value and subtract it to the lowest value. In this case the values are:
Highest = 97
Lowest = 71
Range = highest value - Minimum value
Range = 97 - 26 = 71
[tex] Range= 71[/tex]
mean of the data is the summation of all the numbers in the data set divided by the number of given samples.
Mean = (33 + 29 + 97 + 56+ 26 + 78 + 83 74+ 65 + 47 + 58)/11
= 647/11
[tex]Mean value =58.7[/tex]
Now to find the variance of the data set by using below formular
σ²=[ (xᵢ -mean)²]/n-1
[(33-58.7)² +(29-58.7)²+( 97-58.7)²+( 56-58.7)²+( 26 -58.7)²+(78-58.7)²+( 83 -58.7)²+(74-58.7)²+( 65-58.7)²+( 47 -58.7)²+(58 -58.7)²]/10
[tex]Variance=546[/tex]
Now, we will calculate standard deviation by taking square root over variance
σ =√(variance)
σ =√(546)
[tex]Standard deviation= 23.4[/tex]
Hence, the range is 71 ,variance is 546 and standard deviation is 23.4 therefore,
Option A is the answer that is Jersey numbers are nominal data that are just replacements for names, so the resulting statistics are meaningless.
Identify the conclusion in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. There is not sufficient evidence to warrant rejection of the claim.
b. There is sufficient evidence to warrant rejection of the claim.
c. There is sufficient evidence to support the claim.
d. There is not sufficient evidence to support the claim.
Answers
Answer:
C
Step-by-step explanation:
Firstly, we set up the null and alternative hypothesis as follows;
The null hypothesis is;
H0: μ ≥ 12
The alternative hypothesis is;
Ha : μ < 12
Next step is to calculate the test statistic z
Mathematically;
z = (x - μ )/ σ /√n
= (11.58 - 12) /1.93/√(80
Test statistic z = -1.92
Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel
P(z < -1.92) = 0.0274
P-value = 0.0274
alpha = 0.05
From the above, we can see that
P-value < alpha
And because of this, we are going to reject the null hypothesis and therefore accept the alternative.
We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."
What rule (i.e. R1, R2, R3, R4, or R5) would you use for the hawk and for the grizzly bear? a. R2 and R5 b. R1 and R3 c. None of the above d. R1 and R4
Answers
Answer:
I NEED POINTS
Step-by-step explanation:
select the fraction equivalent of 0.06. reduce to the lowest terms
Answers
Answer: 3/50
Step-by-step explanation:
0.06 = 6/100 , 100 would be the denominator because we have two figures after the decimal point. Each figures can also be represented by 10,
Again,
0.06 = 6 × 10-²
Now 0.06 = 6/100
= 3/50.
Therefore, the fractional form = 3/50 in its lowest term.
Help ASAP!!!!
Solve for X. Round to the nearest hundredth if necessary.
Answers
Answer:
11.47Step-by-step explanation:
Given : A right triangle
To do : Solve for x
Solution,
[tex]cos \: 55 = \frac{x}{20} [/tex] ( by definition of cos function, adjacent / hypotenuse )
[tex]0.5736 = \frac{x}{20} [/tex]
multiply both sides of the equation by 20
[tex](0.5736) \times 20 = x[/tex]
Calculate the product
[tex]11.471 = x[/tex]
Swipe both sides of the equation
[tex]x = 11.471[/tex]
Round answer to nearest hundredth
[tex]x = 11.47[/tex]
Hope this helps...
Best regards!!
Question 8(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc DF. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x plus 10 degrees, the measure of angle EGC is 70 degrees, and the measure of arc DF is 11x plus 2 degrees. 50° 90° 100° 140°
Answers
Answer: 90°
Step-by-step explanation:
As known ∡EGC=(arcEC+arcDF)/2
arcEC+arcDF=70°*2
5x+10+11x+2=140
16x+12=140
16x=128
x=128:16
x=8
So arcDF=11*x+2=11*8+2=90°
The measure of arc DF is 90°.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Given, Circle A with chords EF and CD that intersect at point G,
arc EC = 5x + 10°
arc DF = 11x + 2°
∠EGC = 70°
The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite
so
∠EGC=(1/2)[arc EC+arc DF]
substitute the values
70 = 1/2(5x + 10 + 11x + 2)
70 = 1/2(16x + 12)
140 = 16x + 12
16x = 128
x = 128/16 = 8
so ac DF = 11x + 2
arc DF = 11(8) + 2
arc DF= 88 + 2 = 90°
Hence the value of arc DF is 90°.
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Solve for x. please help me its urgent
Answers
14x = 350
x = 25
Answer:
x = 25
Step-by-step explanation:
The sum of the angles of a quadrilateral are 360 degrees
3x+x+10 + 4x+6x = 360
Combine like terms
14x+10 = 360
Subtract 10 from each side
14x +10-10 = 360-10
14x = 350
Divide each side by 14
14x/14 = 350/14
x = 25
If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.
Answers
Step-by-step explanation:
736 / 365 = 2R6
So even if the first 365 students all have different birthdays, and the next 365 students also all have different birthdays, then there are 2 students for every birthday. The last 6 students therefore share a birthday with at least 2 other students. So there are at least 3 students who share a birthday.
Yes, we can prove that at least three students have a birthday on the same day of the year.
What is algebra?
Algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas.
We have,
Total number of students = 736
So,
In a year there are 365 days.
And we have 736 students,
So,
Two students have birthday on same day = 365 × 2 = 730
NOw,
Students left = 736 - 730 = 6
So,
These 6 Students share birthday with othe 6 Students .
So, yes there are at least three students who have a birthday on the same day of the year
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A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No
Answers
Answer:
1. [tex]H_{0}[/tex] : p = 0.70 , [tex]H_{a}[/tex] : p > 0.70
2. Test Statistic : 0.54 , P value : 0.2946
3. Fail to reject null Hypothesis
4. No.
Step-by-step explanation:
1. Null hypothesis is 70% of children receive antibiotics.
Alternative hypothesis is more than 70% of children receive antibiotics.
2. Test statistic is calculated as;
z = [tex]\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }[/tex]
z = [tex]\frac{0.01}{0.0185}[/tex]
z = 0.54
3. p value is calculated as;
1 - right tailed probability
1 - 0.7054 = 0.2946
A humanities professor assigns letter grades on a test according to the following scheme. A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answers
Answer:
Limits for B scores
( 79,2 ; 92 )
Step-by-step explanation:
The interval we are looking for is between 6 % and 59%
p₁ = 6 % p₁ = 0,06
As this point is at the right tail of the bell we better look for
p = 1- 0,06 p = 0,94
In z-table z score for 0,94062 is: z₁ = 1,56 ( 0,94062 ≈ 0,94 )
Doing the same to find z₂ score for 59% or 0,59
In z-table again
p = 0,59
z₂ = 0,023
Now we know
1,56 * σ = x₁ - 79
1,56*8,4 + 79 = x₁
x₁ = 92,10 or x₁ = 92
And
0,023*8,4 + 79 = x₂
x₂ = 79,19 or x₂ = 79,2
01:
Which expression can be used to model the phrase the sum of three and a number?
Answers
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
Determine whether the outcome of the following hypothesis test was a correct decision, a type I error, or a type II error. Claim: "Less than 40% of college students graduate with student loan debt." A hypothesis test of this claim resulted in the decision to reject H0. The actual percentage of college graduates with student loan debt is 45%.
Answers
Answer:
Step-by-step explanation:
The claim: "Less than 40% of college students graduate with student loan debt."
The null hypothesis: more than 40% of college students graduate with student loan debt." p >= 40%
If the actual percentage of college graduates with student loan debt is 45%. The researcher was supposed to fail to reject the null but since he rejected it when it was actually true, it is a type I error.
A type I error occurs when the research rejects the null when it is actually true.
Find f o g if f(x) = 3x^2 - 12 and g(x) = 5x + 3. f(g(x)) = Choices: a. 35x2 - 70 b. 15x2 - 30x + 9 c. 75x2 + 45x - 10 d. 75x2 + 90x + 15
Answers
Answer:
d.
Step-by-step explanation:
[tex]f(g(x))=3(g(x))^2-12=3(5x+3)^2-12=3(25x^2+30x+9)-12=75x^2+90x+27-12=75x^2+90x+15[/tex]
The measure of < A is 45 degree
Answers
We are given [tex]\triangle ABC \cong \triangle EFG[/tex]
The order of the letter sequence is important. The letters pair up based on how they are arranged. We see that A and E are the first letters of the sequences. So this means that angles A and E are the same measure
angle A = angle E
3x+20 = 5x-80
3x-5x = -80-20
-2x = -100
x = -100/(-2)
x = 50
Use this x value to find the measure of angle A
angle A = 3x+20
angle A = 3(50)+20
angle A = 150+20
angle A = 170 degrees
Therefore, the statement "the measure of angle A is 45 degrees" is false.