Answer:
0
Step-by-step explanation:
[tex]\lim_{x \to 0} (csc(x)-cot(x))\\= \lim_{x \to 0}(\frac{1}{sin x}-\frac{cos(x)}{sin (x)} )\\=\lim_{x \to 0}(\frac{1-cos x}{sin x} )\\=\lim_{x \to 0}(\frac {2 sin ^2 \frac{x}{2}}{2sin \frac{x}{2} cos\frac{x}{2} } )\\=\lim_{x \to 0}(tan \frac{x}{2} )\\=\lim_{x \to 0}\frac{tan \frac{x}{2} }{\frac{x}{2} } \times \frac{x}{2} \\=1 \times 0\\=0[/tex]
Suppose that 67.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 500 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 317 suffered from hypertension.
The researchers want to use a one‑sample z ‑test for a population proportion to see if the proportion of type
2 diabetics who have hypertension while taking their new drug, p, is different from the proportion of all type
2 diabetics who have hypertension. They decide to use a significance level of ???? = 0.05.
A. Determine the p value for this test.
B. Determine the value of the z test statistic.
Answer: A. p-value = 0.04
B. z = - 1.77
Step-by-step explanation: To calculate z test statistic or z-score for a population proportion, first find the proportion (p-hat):
[tex]p_{hat}[/tex] = [tex]\frac{317}{500}[/tex] = 0.634
Then determine the standard deviation:
[tex]\sigma = \sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]
[tex]\sigma = \sqrt{\frac{0.634(0.366)}{500} }[/tex]
[tex]\sigma = \sqrt{0.00046 }[/tex]
[tex]\sigma[/tex] = 0.0215
Calculating z-score:
[tex]z=\frac{p_{hat}-p}{\sigma}[/tex]
[tex]z=\frac{0.634-0.672}{0.0215}[/tex]
[tex]z=-1.77[/tex]
Z-test for the population proportion is z = - 1.77
P-value is the probability describing the data if null hypothesis is true, i.e.:
P(z< -1.77)
Using z-score table, the probability is:
P(z< -1.77) = 0.04
p-value = 0.04
P-value for this test is p-value = 0.04.
Hey guys! I have this problem and I dont really understand how to solve it, could you guys help me? :' )
Answer:
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
Pregnancy length in horses. Bigger mammals tend to carry their young longer before giving birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution, with mean 336 days and standard deviation 3 days. Use the 68–95–99.7 rule to answer the following questions.Required:What percent of horse pregnancies are longer than 339 days?
Answer:
16%
Step-by-step explanation:
The difference between the time of interest (339 days) and the mean (336 days) is 3 days, which is exactly 1 standard deviation.
The 68-95-99.7 rule tells you that 68% of pregnancies will be within 1 standard deviation. The remaining 32% will be evenly split between pregnancies that are longer than 339 days and ones that are shorter than 333 days. So, half of 32%, or 16%, will be longer than 339 days.
Christina's time for a race was 22.3 seconds. Another runner's time was 4.41 seconds faster. Write and evaluate an equation with a variable to find the difference between Christina's time and the other runner's time.
Answer:
[tex]Difference = 4.41[/tex]
Step-by-step explanation:
Given
Represent Christina's time with C and the other runner's time with R
C = 22.3
R = 4.41 + C
Required
Determine the difference using an equation
The difference between both runner's time is as follows;
[tex]Difference = R - C[/tex]
Substitute 4.41 + C for R
[tex]Difference = 4.41 + C - C[/tex]
[tex]Difference = 4.41[/tex]
Hence, the difference is 4.41 seconds
Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?
After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
What is a quadratic equation?"It is a polynomial equation with degree two."
What is completing the square method?"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "
For given example,
We have been given a quadratic equation.
[tex]3x^{2} -12x-15=0[/tex]
First we divide above quadratic equation by 3,
[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex] ................(i)
Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]
[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]
Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),
[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]
Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].
Learn more about completing the square here:
https://brainly.com/question/4822356
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WHY CAN'T ANYONE HELP ME PLEASE?A 40% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
40% solution = 20 gallons
80% solution = 60 gallons
Step-by-step explanation:
x = gallons of 40% solution
y = gallons of 80% solution
Total volume is:
x + y = 80
Total amount of fertilizer is:
0.40 x + 0.80 y = 0.70 (80)
Solve by substitution.
0.40 x + 0.80 (80 − x) = 0.70 (80)
0.40 x + 64 − 0.80 x = 56
0.40 x = 8
x = 20
y = 60
Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)
Answer:
x = -4
Step-by-step explanation:
2 - (7x + 5) = 13 - 3x
add the binomial (7x +5) to both sides
2 = (7x + 5) + 13 - 3x
combine like terms
2 = 4x + 18
subtract 18 from both sides
-16 = 4x
divide by 4
x = -4
Answer:
-4
Step-by-step explanation:
Distribute the negative signs to the values in the parentheses
2 -7x - 5 = 13 - 3x
Add like terms:
-7x - 3 = 13 - 3x
Add 3x to both sides:
-4x - 3 = 13
Add 3 to both sides:
-4x = 16
Divide both sides by -4:
x = -4
A cubical water tank is 80 cm broad. find the volume of tank?
Answer:
512000
Step-by-step explanation:
l=80cm
v=l^3
=80^3
=512000cm^3
Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses
Answer:
24Step-by-step explanation:
Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]
[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;
[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]
Hence, the value of the logarithm expression is 24
find the length of the arc . round your answers to the nearest tenth
Answer:
10.2
Step-by-step explanation:
Length of arc=(2*pi*r)*(theta/360)
Length of arc=(2*pi*3)*(195/360)=10.2
You drive 15 miles in 0.1hours . How fast did you travel if 8=d/t
Answer:
150Step-by-step explanation:
[tex]distance = 15 miles\\time = 0.1 hours\\\\Speed = \frac{Distance}{time}\\ Speed = \frac{15}{0.1}\\ Speed =150[/tex]
Answer:
[tex]150mph[/tex]
Step-by-step explanation:
Given:
s=15miles
t=0.1hours
Required:
v=?
Formula:
[tex]v = \frac{s}{t} [/tex]
Solution:
[tex]v = \frac{s}{t} = \frac{15m}{0.1h} = \frac{150m}{1h} = 150mph[/tex]
Hope this helps ;) ❤❤❤
Geometry please help me!!!!
Answer:
Step-by-step explanation:
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE answer thoroughly. Chapter 9 part 2
4. How can you determine the maximum number of solutions for a polynomial? How are these counted on the graph?
9514 1404 393
Answer:
a) the degree of the polynomial
b) count the x-intercepts, with attention to multiplicity
Step-by-step explanation:
The Fundamental Theorem of Algebra tells you the number of zeros of a polynomial is equal to the degree of the polynomial. That is, for some polynomial p(x), the number of solutions to p(x)=0 will be the degree of p.
__
On a graph, a real zero of the polynomial will be an x-intercept. The "multiplicity" of a zero is the degree of the factor giving rise to that zero. When the multiplicity is even, the graph does not cross the x-axis at the x-intercept. The greater the multiplicity, the "flatter" the graph is at the x-intercept.
If all solutions (zeros) are distinct, then the number of real solutions can be found by counting the number of x-intercepts of the graph.
_____
By way of illustration, the attached graph is of a 6th-degree polynomial with 6 real zeros. From left to right, they are -1 (multiplicity 1), 1 (multiplicity 2), 4 (multiplicity 3). The higher multiplicities are intended to show the flattening that occurs at the x-intercept, and the fact that the graph does not cross the x-axis where the multiplicity is even.
How many different 6-digit phone numbers do not contain the digit 8? Assume that any digit in the phone number can be any of the remaining numbers.
please help. urgent. calculate the value of: E= x^3+1/x^3 if 1/x+x=4
(picture below)
Answer:
52
Step-by-step explanation:
1. We see if we cube both sides of the second equation, then it looks more similar to the first equation (E = x^3 + 1/x^3)
(1/x + x)^3 = 4^3
1/x^3 + 3/x + 3x + x^3 = 64
2. Now we rearrange, because we see x^3 + 1/x^3 in the first equation in this equation
x^3 + 1/x^3 + 3x + 3/x = 64
3. We look at 3x + 3/x and see that it looks like the second equation, so we try factoring it
x^3 + 1/x^3 + 3(x + 1/x) = 64
we know x + 1/x = 4, so 3(x + 1/x) = 12
x^3 + 1/x^3 +12 = 64
4. Now we subtract and get our answer
x^3 + 1/x^3 = 52
To divide a whole number or decimal by 10, move the decimal point
place(s) to the left.
Answer:
you simply have to move one left. It thats decimal you can simply remove one zero
Answer:
You just have to move to the left once
Step-by-step explanation:
Which of the following theorems verifies that ANPO- AXYZ?
How many three-letter (unordered) sets are possible that use the letters q, u, a, k, e, s at most once each? (No Response) 20 sets
Answer:
20sets
Step-by-step explanation:
Since we are to select 3 unordered letters from the word q, u, a, k, e, s, we will apply the combination rule.
For example if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.
nCr = n!/(n-r)!r!
Since the total number of letter in the word q, u, a, k, e, s is 6letters and we are to form 3 letters from it unordered, this can be done in 6C3 number of ways.
6C3 = 6!/(6-3)!3!
6C3 = 6!/3!3!
6C3 = 6×5×4×3×2×1/3×2×1×3×2×1
6C3 = 6×5×4/3×2
6C3 = 120/6
6C3 = 20
Hence 20sets of selection are possible
the value of 2√4-3√27+√16+√225 is
Answer:
hope this help you
sorry if it is mistake
what is the area of the triangle ://
Answer:
The area of a triangle is:
Area = 1/2(bh)
Area = 1/2(70)
Area = 35 square inches
Let me know if this helps!
According to the number line, what is the distance between points A and B?
А
B
VX
- 16 - 14 -12 -10 -8 -6 4-2
0 2
4
6
8 10 12 14 16
U6 units
X 7 units
12 units
14 units
Answer:
Below!
Step-by-step explanation:
Please provide the two points (A & B) so I can help you out with the question or...
use the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where the first point = [tex](x_1,y_1)[/tex] & the second point: [tex](x_2,y_2)[/tex]
(-3.8)+(-21.14)+(-0.55)
please mark this answer as brainlist
Find the particular solution to a differential equation whose general solution and initial condition are given. (C is the constant of integration.) x(t)
Write the null and alternative hypotheses you would use to answer this question. Are Americans getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 190 pounds. Ten years ago, the average weight was 185 pounds.
Answer:
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
Step-by-step explanation:
The null and alternative hypotheses for this experiment would be
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
This is a one tailed test .
If the results are such that we reject the null hypothesis and accept the alternative hypothesis it means that the Americans are getting fatter as the mean weight is increasing day by day.
The null hypothesis deals with all the values equal to or less than 185 pounds and the alternative with all the values greater than 185 pounds.
how many feet is in one centimeter and how many inches is in 1 feet?
Answer:
12 inches r in a foot
0 feet r in a centimeter
Step-by-step explanation:
Answer:
0.032 feet in a centimeter and 12 inches in 1 foot
Step-by-step explanation:
hope it helps pls mark as brainliest!
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answer:
Option (3)
Step-by-step explanation:
From the picture attached,
Bar graph sketched shows the grades earned by the students in an exam.
Number of students who achieved the grade A = 17
Number of students who achieved grade B = 14
Number of students with grade C = 5
Number of students with grade D = 9
Total students who took the exam = 17 + 14 + 5 + 9 = 45
Option (1)
"[tex]\frac{1}{5}[/tex] of the students earned a C"
Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]
= [tex]\frac{5}{45}[/tex]
= [tex]\frac{1}{9}[/tex]
Therefore, this option is incorrect.
Option (2)
"3% more students earned an A then B"
Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{17}{45}\times 100[/tex]
= 37.78%
Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{14}{45}\times 100[/tex]
= 31.11%
Difference in percentage = 37.78 - 31.11
= 6.67%
Therefore, this option is not correct.
Option (3)
"20% of the students earned a D"
Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{9}{45}\times 100[/tex]
= 20%
Option (3) is the correct option.
Option (4)
" [tex]\frac{1}{4}[/tex] of the class earned a B"
Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]
= [tex]\frac{14}{45}[/tex]
Therefore, Option (4) is not correct.
find the slope of the joining pairs of points (1/a, 1/b) (b,a)
Answer: m = 1/b
Step-by-step explanation: Unfortunately, I can't give you a picture of the slope, but take that formula I gave you and enter it into a graphing calculator and it will show you the slope. I recommend desmos online calculator, good luck
What unit of measurement would you use to measure the capacity of a juice box?
Juice in a juice box is usually measured in ounces.
How many cabinets must he sell to break even?
Answer: He must sell 7 cabinets.
Step-by-step explanation:
So it gives us the equations y= 400x + 1400 and the equations y=600x and to find the break even point we need to set the two equations equal each other to solve for x.
400x + 1400 = 600x
-400x -400x
1400 = 200x
x = 7