Simplify the LHS by using the identities above to get the RHS:
(cot A - tan A)cosA = (cosA/sinA - cosA/sinA)cosA = Identities 2 and 3(cosA/sinA)cosA - (cosA/sinA)cosA = Distributecos²A/sinA - sinA = Simplify/cancel(1 - sin²A)/sinA - sinA = Identity 11/sinA - sin²A/sinA - sinA = Distribute1/sinA - sinA - sinA = Simplify/cancel1/sinA - 2sinA = cosecA - 2sinA Identity 4Proved
A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Street Journal, October 14, 2010). A year later, a researcher samples 200 Americans and finds that 51 of them use only cell phones for making phone calls. Test whether the proportion of Americans who solely use cell phones to make phone calls differs from 23%. Use the .05 level of significance.
Using the z-distribution, it is found that since the p-value is greater than 0.05, the proportion does not differ from 23%.
What are the hypotheses tested?At the null hypotheses, it is tested if the proportion is of 23%, that is:
[tex]H_0: p = 0.23[/tex]
At the alternative hypotheses, it is tested if the proportion differs from 23%, hence:
[tex]H_1: p \neq 0.23[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters are given as follows:
[tex]p = 0.23, n = 200, \overline{p} = \frac{51}{200} = 0.255[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.255 - 0.23}{\sqrt{\frac{0.23(0.77)}{200}}}[/tex]
z = 0.84.
Using a calculator and considering a two-tailed test, as we are testing if the proportion is different of a value, with z = 0.84, the p-value is of 0.4.
Since the p-value is greater than 0.05, the proportion does not differ from 23%.
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5. The graph of F(x), shown below, resembles the graph of G(x)=x2, but it has been
flipped over the x-axis, stretched vertically by a factor of 3, shifted down 4 units, and
left 1 unit.
-6
F(X)
Part I: Write the equation of F(x).
Using translation concepts, the equation of F(x) is given as follows:
-3(x + 1)² - 4.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The effect of the transformations on G(x) = x² is given as follows:
Reflection over the x-axis: F(x) = -G(x) = -x².Vertical stretch by a factor of 3: F(x) = -3G(x) = -3x².Shift down of 4 units: F(x) = -3G(x) - 4 = -3x² - 4.Shift left of 1 units: F(x) = -3G(x + 1) - 4 = -3(x + 1)² - 4.More can be learned about translation concepts at https://brainly.com/question/4521517
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Evaluate a=5 and y= -7 for y-2a
Answer: -17
Step-by-step explanation:
y - 2a
= -7 - 2(5)
= -7 - 10
= -17
The graph of the function f(x) = (x-4)(x + 1) is shown
below.
4-2
64
Mark this and return
6
2
T
6
2
6
X
Which statement about the function is true?
The function is increasing for all real values of x
where
x<0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1 < x < 4.
O The function is decreasing for all real values of x
where
x < 1.5.
Answer: The function is decreasing for all real values of x where x < 1.5.
Step-by-step explanation:
The axis of symmetry is [tex]x=\frac{4-1}{2}=1.5[/tex]
Since the coefficient of [tex]x^2[/tex] is positive, the graph opens upwards.
So, the function is decreasing for all real values of x where x < 1.5.
What is the area of a sector when r = 2 and 0 = 1.75 radians? [?] sq units Round your answer to the nearest tenth. Enter
Answer:
Step-by-step explanation:
The area of a sector in terms of radians as opposed to degrees is
[tex]A=\frac{\theta}{2\pi }*\pi r^2[/tex]
Filling in the formula accordingly gives us
[tex]A=\frac{1.75rad}{2\pi rad}*\pi (2)^2[/tex]
The radians cancel out, the pi's cancel out, the 2 in the denominator cancels out (divides into 2-squared once), leaving us with
A = 1.75(2) so
A = 3.5 units squared
32y+54x+56=y what is y
Tamika has a spinner with 5 equal sections – red, blue, green, yellow, and purple. She plans to spin it 150 times. Predict how many times she should expect the pointer to land on either green or yellow.
Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.
What is Probability?
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Total number of sections on the spinner = 5
Number of sections with green or yellow sections = 2
Number of trials = 150
Now, the number of times Tamika should expect the spinner to land on green or yellow is,
Expected Number of lands on green or yellow = 150 × (2/5) = 60
Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.
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You roll a fair six-sided die twice. Find the probability of rolling a 2 the first time and a number greater than 4 the second time.
Answer:
1/18
Step-by-step explanation:
So to find the probability of two independent events, you simply multiply the two probabilities. So the probability of rolling any individual number is 1/6 because there's 6 possibilities, and there are no duplicate numbers. So the probability of rolling a 2 the first time is 1/6. The probability of rolling a number greater than 4 has a probability of 2/6, since the numbers 5 and 6 are both greater than 4. This can be further simplified to 1/3. Multiplying these two probabilities gives you 1/18
Perimeter and area
What is the area of the square, circle, and shaded region?
A)
B)
C)
(a) The side length of the square is 8 m, so its area is 64 square m.
(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.
(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.
just do it for the point's my next one will have 69 points
thanks
:) 888888888888888888888888888888888888888888888888888
what is the average rate of change if this function interval x = -3 to x = 0
The average rate of change of the function, over the given interval is 2.
This question is incomplete, the complete question is:
What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.
What is the average rate of change over the interval?The average rate of change of f(x) over the interval [a,b] is expressed as;
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given that;
f(x) = 2x + 10Interval: [ -3, 0 ], a = -3 and b = 0We substitute our values into the expression above.
[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2[/tex]
Therefore, the average rate of change of the function, over the given interval is 2.
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Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?
R0,90° ∘ T5,0(x, y)
T–5,0 ∘ R0,90°(x, y)
T5,0 ∘ R0,90°(x, y)
R0,90°(x, y) ∘ T–5,0
The transformations rule for changing DEF into D"E"F is
(b) T-5,0-RO. 90° (x,y)
Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?To transform a shape is to alter its dimensions and relative placement.
To convert from DEF to D"E"F, use this rule:
(b) T-5,00 RO, 90°(x, y)
From the complete question,
When DEF is spun 90 degrees counterclockwise, it becomes GH.
Then, 5 units were subtracted from the right and translated to the left.
Assume a rotation of 90 degrees counterclockwise, and write it as:
RO, 90°(x,y)
As a symbol, the leftward translation of 5 units looks like this:
T-5,0(x,y)
When both transformations are combined, we have:
T-5,0 R0.90° (x. y)
In conclusion, the transformations rule for changing DEF into D"E"F is
(b) T-5,0-RO. 90° (x,y)
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9. Find the value of the
underlined digit in the
following number.
739,485
Answer:
There's no underlined digit
Answer:
See below
Step-by-step explanation:
3 is in the 10 000 place = 30 000
( just put zeroes in place of all of the following numbers)
5% dextrose infused over 8 hours. how many ml of iv fluid is infused after 6 hours?
The nurse prepares a 1,000 ml IV of 5% dextrose and water to be infused over 8 hours.
We have given that,
5% dextrose infused over 8 hours.
We have to determine the ml of iv fluid is infused after 6 hours.
What is the mixture problem?
A value mixture problem involves combining two ingredients that have different prices into a single blend.
The infusion set delivers 10 drops per milliliter.
The nurse should regulate the IV to administer approximately 21 drops per minute.
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Consider the following sample of fat content of n=10 randomly selected hot dogs
The average fat content of the ten hot dog samples is: 21.91
How to calculate the average fat of hot dog samples?To calculate the average fat of the hot dog samples we must add all the values and divide the result by the number of values as shown below:
25.2 + 21.3 + 22.9 + 17.0 + 29.8 + 21.0 + 25.5 + 16.0 + 20.9 + 19.5 = 219.1219.2 ÷ 10 = 21.91Note: This question is incomplete because there is some information missing. Here is the complete information:
Question: What is the average fat of the hot dogs?
Hot Dogs' fat
Sample 1: 25.2
Sample 2: 21.3
Sample 3: 22.9
Sample 4: 17.0
Sample 5: 29.8
Sample 6: 21.0
Sample 7: 25.5
Sample 8: 16.0
Sample 9: 20.9
Sample 10: 19.5
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Part III: Find the unknown side lengths, AB and BC. HINT: Use either the Pythagorean Theorem or special right triangle properties.
The measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.
What is a right-angle triangle?If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.
From the given triangle, it is observed that one of the angles is 90°, showing the given triangle is a right-angle triangle.
From the Δ ABC we found;
tan 45° = AB/BC
1=AB/BC
AB=BC
sin 45° = AB/AC
(1/√2)=AB/AC
AC = √2 AB
From the graph, it is observed that
AB=BC =3 units
AC= √2 AB
AC = 3√2 units
Hence, the measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.
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Question 3
B
16 cm
38°
-C
Calculate the length of AB to 2 decimal places.
The question was incomplete. Below you can find the missing content.
ABC is a right-angled triangle.
b=16 cm
∠C=38°
Calculate the length of AB. Give your answer correct to 2 decimal places.
The picture is also attached below.
The length of the side AB is 9.85 cm.
From the triangle, it is given that
b= AC=16 cm
∠C=38°
Given that ΔABC is a right-angled triangle.
where ∠B=90°
So, here we can apply the SOH CAH TOA identity
As we know the value of sinθ is the ratio of the opposite side and the hypotenuse of the angle θ.
So, sinθ = opposite side/ hypotenuse
In triangle ΔABC
⇒ sin 38°= AB/AC
⇒ sin 38°= AB/16
⇒ AB= 16 sin 38°
⇒ AB= 9.85 cm
Therefore the length of the side AB is 9.85 cm.
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Sketch the graph of the relation function
[tex] h(x) = \frac{ {x}^{2} + 6x + 8}{ {x}^{2} + 8x + 15} [/tex]
by listing all the intercepts, asymptotes,and the behaviour of the graph with respect to the asymptotes.
Step-by-step explanation:
1) X-intercept: -2; -4;
Y-intercept: 0.533;
2) asymptotes: x= -3 and x= -5;
3) if x→ -5(-0), then y→+∞;
if x→ -5(+0), then y→-∞;
if x→ -3(-0), then y→-∞;
if x→ -3(+0), then y→+∞;
Find the measure of ∠2.
72°
60°
36°
54°
Answer:
(c) 36°
Step-by-step explanation:
We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.
Angle 1Angle 1 is one of 5 congruent central angles, so its measure is ...
∠1 = 360°/5 = 72°
Angle 2Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:
∠2 = 72°/2 = 36°
The measure of angle 2 is 36°.
Angle 3Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...
∠3 = 90° -∠2 = 90° -36° = 54°
If f(x)...............
Answer:
The inverse is 5x-6
Step-by-step explanation:
To find the inverse of a function
y = ( x+6) /5
Exchange x and y
x = ( y+6)/5
Solve for y
Multiply each side by 5
5x = (y+6)/5 *5
5x = y+6
Subtract 6 from each side
5x-6 = y+6-6
5x-6 =y
The inverse is 5x-6
Step-by-step explanation:
[tex]f(x) = \frac{x + 6}{5} [/tex]
[tex] \: [/tex]
[tex]y = \frac{x + 6}{5} [/tex]
[tex] \frac{y + 6}{5} = x[/tex]
[tex]y + 6 = 5\times x[/tex]
[tex]y + 6 = 5x[/tex]
[tex]y = 5x - 6[/tex]
[tex] {f}^{ - 1} (x) = 5x - 6[/tex]
The answer is D.
4. 1/37 of 111 + 1/3 of ? = 0
(1) 3
2) 9
3) 1
4) can not be determined
Answer:
4
Step-by-step explanation:
1/37 of 111+1/3 of 3= 4
1/37 of 111 +1/3 of 9=6
1/37 of 111 +1/3 of 1=3.3
Write each phrase as a mathematical expression.
The quotient of 8 more than the radius, r, and 4
Answer: (r+8)/4
Step-by-step explanation:
Not much really to explain...
10) Bill found a pair of running shoes for $57. The regular price was $68.99. He also found a sweat suit that was
originally $37.80. It was marked down 25%. Find his total SAVINGS.
Oa.) $20.46
Ob.) $21.84
Oc.) $20.45
Od.) $21.44
Answer:
$21.44 or answer D
Step-by-step explanation:
68.99-57=11.99
37.80 x 25/100=9.45
9.45+11.99=21.44
hope this helps you
Complete the following questions. 2 x 4² x 2 = (6 x 3²) ÷ 9 =
Answer:
4 ^x27
3
Step-by-step explanation:
2x4^2x2(6x3^2)
9
Simplifies to:
4 ^x27
3
=
4 ^x27
3
In how many ways can a 7 person committee be chosen from a group of 10 people?
[tex]\displaystyle\\\binom{10}{7}=\dfrac{10!}{7!3!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=4\cdot3\cdot10=120[/tex]
Pls help! Geometry
What is the perimeter and area of the shape above?
Perimeter of the shape = 27.15 units.
Area = 32.3 units²
How to Find the Perimeter and Area of a Composite Shape?The Perimeter of the shape = 1/2(perimeter of circle) + hypotenuse and height of the triangle
Perimeter = = 1/2(2π(5/2)) + [√(9² + 5²)] + 9 = 7.85 + 10.3 + 9 = 27.15 units.
Area = 1/2(area of circle) + area of triangle = 1/2(πr²) + 1/2(bh)
Area = 1/2(π2.5²) + 1/2(5)(9)
Area = 9.8 + 22.5
Area = 32.3 units²
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write the slope intercept form of the equation or each line
The slope intercept equation is 3y+ 2x = -4.5,
What is slope intercept equation?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
let the two points from the graph is (4, -4) and (-2, 0)
then
m= 4/ -6= -2/3
and the intercept is 1.6 as the line intersects the y- axis.
So, the slope intercept is
y= -2/3x - 1.6
3y= -2x - 4.5
3y+ 2x = -4.5
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find x and y.
pls pls help
Answer:
x = 65 , y = 64
Step-by-step explanation:
y - 16 and 2y + 4 are same- side interior angles and sum to 180° , that is
y - 16 + 2y + 4 = 180
3y - 12 = 180 ( add 12 to both sides )
3y = 192 ( divide both sides by 3 )
y = 64
then
2y + 4 = 2(64) + 4 = 128 + 4 = 132
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
2y + 4 is an exterior angle of the triangle , then
x + 67 = 132 ( subtract 67 from both sides )
x = 65
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 36 hours and the median is 32.2 hours. Twenty-four of the families in the sample turned on the television for 21 hours or less for the week. The 11th percentile of the data is 21 hours.
Step 1 of 5 : Based on the given information, determine if the following statement is true or false.
The 54th percentile is greater than or equal to 31 hours.
true or false
Using the median concept, it is found that the statement is true.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, we have that the 50th percentile is of 33.2 hours, hence the 54th percentile has to be above 33.2 hours = above 31 hours, hence the statement is true.
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
395.84
Step-by-step explanation:
V=πr2h=π·3^2·14