Answer:
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Step-by-step explanation:
The trigonometric identity is :
[tex]\sec^2\theta-\tan^2\theta=1\\\\or\\\\\sec^2\theta=1+\tan^2\theta[/tex]
We need to express secθ in terms of tanθ.
The above equation becomes,
[tex]\sec\theta=\sqrt{1+\tan^2\theta}[/tex]
Hence, this is the required solution.
Mary has three baking pans. Each pan is 8" × 8" × 3". Which expression will give her the total volume of the pans?
Answer: An expression [tex]3 \times (8 \times 8 \times 3)[/tex] will give her the total volume of the pans.
Step-by-step explanation:
Given: Length = 8 inch
Width = 8 inch
Height = 8 inch
Formula to calculate the volume of rectangular pans is as follows.
[tex]Volume = length \times width \times height\\[/tex]
Substitute the values into above formula as follows.
[tex]Volume = length \times width \times height\\= 8 \times 8 \times 3 in^{3}\\= 192 in^{3}[/tex]
Therefore, volume of each pan is 192 cubic inch. As there are three baking pans so total volume of the pans is as follows.
[tex]3 \times 192 in^{3}\\= 576 in^{3}[/tex]
Thus, we can conclude that an expression [tex]3 \times (8 \times 8 \times 3)[/tex] will give her the total volume of the pans.
3. A bicycle has wheels with a diameter of 622 mm. The
bicycle rolls forward and the wheel turns 5 radians.
How many millimeters forward did the bicycle move?
Distance = ( ) (622) = (15.708) ()
= (2.618)
וחתן
Answer:
1553.6mm
Step-by-step explanation:
Given data
Diameter = 622mm
Radius= 622/2= 311mm
Circumference= 2πr
Circumference= 2*3.142*311
Circumference= 1954.32
Each revolution the wheels will turn 1954.32mm
Now let us convert radian to turns
1 radian= 0.159155 turns
5 radians= x turns
cross multiply
x= 5*0.159155
x=0.795 turns
If 1 turn will give 1954.32mm
0.795 turn will give x
cross multiply
x= 0.795*1954.32
x=1553.6mm
The Coordinate Plane
BRE
-2
В
The midpoint of AB = ([?],[ ])
Answer:
0,0
Step-by-step explanation:
find the measure of one interior angle in a regular 23-gon
Answer: A polygon with 23 sides has a total of 3780 degrees. total interior angles = (n - 2)180°, where n is the number of sides.
The measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees
How to calculate the sum of the interior angle of a regular polygon?The formula which is used to calculate the sum of the angle of regular polygon is given by
sum of the interior angles = ( n - 2 ) × 180 degrees
Where,
n is the number of sides
According to the given question.
We have a regular polygon with 23 sides.
⇒ n = 23
Therefore,
The sum of the interior angles of the given regular polygon
= (23-2) × 180
= 3,780 degrees
So, the measure of one interior angle = [tex]\frac{3780}{23} = 164.3 degrees[/tex]
Hence, the measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees.
Find out more information about interior angle of a regular polygon here:
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Find the value of x in each case:
Answer:
x = 19
Step-by-step explanation:
∠ YWX = ∠ ZYW = 2x ( alternate angles )
The sum of the 3 angles in Δ WXY = 180° , that is
3x - 5 + 2x + 90 = 180
5x + 85 = 180 ( subtract 85 from both sides )
5x = 95 ( divide both sides by 5 )
x = 19
6x+2y=
6x+2y=
\,\,16
16
2x-2y=
2x−2y=
\,\,32
32
Answer:
x = 6, y = -8
Step-by-step explanation:
First we take the equations side by side and put them like this:
6x + 2y = 16
+ 2x - 2y = 32
8x = 48
Then solve for x.
x = 6
Then insert x back into either equation
2(5) - 2y = 32
10 - 2y = 32
solve for y,
y = -10
in a class of 30 students, 5 have a brother and 23 have a sister. there are 2 students who have a brother and a sister. what is the probability that a student has a sister also has a brother
Answer:
2/23
Hope this helps!
Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,463]. The population standard deviation used for the analysis is known to be $14,300.
a. What is the point estimate of the mean salary for all college graduates in this town?
Point estimate
b. Determine the sample size used for the analysis.
Sample size
Answer:
a. The point estimate was of $44,600.
b. The sample size was of 16.
Step-by-step explanation:
Confidence interval concepts:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
a. What is the point estimate of the mean salary for all college graduates in this town?
Mean of the bounds, so:
(38737+50463)/2 = 44600.
The point estimate was of $44,600.
b. Determine the sample size used for the analysis.
First we need to find the margin of error, so:
[tex]M = \frac{50463-38737}{2} = 5863[/tex]
Relating the margin of error with the sample size:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.64.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
For this problem, we have that [tex]\sigma = 14300, M = 5863[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]5863 = 1.645\frac{14300}{\sqrt{n}}[/tex]
[tex]5863\sqrt{n} = 1.645*14300[/tex]
[tex]\sqrt{n} = \frac{1.645*14300}{5863}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2[/tex]
[tex]n = 16[/tex]
The sample size was of 16.
A quantity P is an exponential function of time t. Use the given information about the function P = P0e^{kt} to find values for the parameters k and P0.
P=40 when t=4 and P=50 when t=3.
Answer:
P = 40 x 4
= 160
P = 50 x 3
= 150
Please help someone! Very important!
Answer:
OH NO
Step-by-step explanation:
Step-by-step explanation:
oh srr, I'm Vietnamese and I don't know your
country's solution
but i think my answer is correct :((
This circle is centered at the origin, and the length of its radius is 8. What is the circle's equation? 5 A. X+ y = 8 B. x2 + y2 = 64 O c. x2 + y2 = 8 D. X8+ y = 64
Answer:
Step-by-step explanation:
A circle centered in [tex]P(x_o,y_o)[/tex] an radius [tex]r[/tex] has a equation:
[tex](x-x_o)^2+(y-y_o)^2=r^2[/tex]
So, your equation wold be:
[tex](x-0)^2+(y-0)^2=8^2\Rightarrow x^2+y^2=64[/tex]
The correct circle's equation with radius 8 is,
⇒ x² + y² = 64
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
This circle is centered at the origin, and the length of its radius is 8.
Since, The general equation of circle with center (h, k) and radius r is,
⇒ (x - h)² + (y - k)² = r²
Here, Center = (0, 0)
Radius = 8
Hence, The correct circle's equation with radius 8 is,
⇒ (x - h)² + (y - k)² = r²
⇒ (x - 0)² + (y - 0)² = 8²
⇒ x² + y² = 64
Thus, The correct circle's equation with radius 8 is,
⇒ x² + y² = 64
Learn more about the circle visit:
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Which is the solution to the equation below? 4n+5=25-3n
Answer:
[tex]n = \frac{20}{7}[/tex]
Step-by-step explanation:
[tex]4n + 5 = 25 - 3n\\4n + 3n = 25 - 5 \\7n = 20\\\\n = \frac{20}{7}[/tex]
Answer:
n = 20/7
Step-by-step explanation:
4n+5=25-3n
Add 3n to each side
4n+3n+5=25-3n+3n
7n +5 = 25
Subtract 5 from each side
7n+5-5=25-5
7n = 20
Divide by 7
7n/7 = 20/7
n = 20/7
Translate the sentence into an equation. The quotient of a number and 8 is 16. What is the solution to the equation? One-half 2 128 164
Answer:
128
Step-by-step explanation:
I did the math
Answer:
it's 2 :)
Step-by-step explanation:
quotient is a term used in division so you divide
16 divided by 8 is 2 <3
don't forget to say thanks if you got it right ! :)
Let Q(x, y) be the predicate "If x < y then x2 < y2," with domain for both x and y being R, the set of all real numbers.
a) When x = −2 and y = 1, is Q(x, y).
a. true
b. false
The hypothesis of Q(−2, 1) is__, which is___. The conclusion is___, which is____. Thus Q(−2, 1) is a conditional statement with a____hypothesis and a_____conclusion. So Q(−2, 1) is____.
b) Give values different from those in part (a) for which Q(x, y) has the same truth value as in part.
c) Give values different from those in part (c) for which Q(x, y) has the same truth values as in part.
Answer:
a) Q(-2,1) is false
b) Q(-5,2) is false
c)Q(3,8) is true
d)Q(9,10) is true
Step-by-step explanation:
Given data is [tex]Q(x,y)[/tex] is predicate that [tex]x<y[/tex] then [tex]x^{2} <y^{2}[/tex]. where [tex]x,y[/tex] are rational numbers.
a)
when [tex]x=-2, y=1[/tex]
Here [tex]-2<1[/tex] that is [tex]x<y[/tex] satisfied. Then
[tex](-2)^{2}<1^{2}[/tex]
[tex]4<1[/tex] this is wrong. since [tex]4>1[/tex]
That is [tex]x^{2}[/tex][tex]>y^{2}[/tex] Thus [tex]Q(x,y)[/tex] [tex]=Q(-2,1)[/tex]is false.
b)
Assume [tex]Q(x,y)=Q(-5,2)[/tex].
That is [tex]x=-5, y=2[/tex]
Here [tex]-5<2[/tex] that is [tex]x<y[/tex] this condition is satisfied.
Then
[tex](-5)^{2}<2^{2}[/tex]
[tex]25<4[/tex] this is not true. since [tex]25>4[/tex].
This is similar to the truth value of part (a).
Since in both [tex]x<y[/tex] satisfied and [tex]x^{2} >y^{2}[/tex] for both the points.
c)
if [tex]Q(x,y)=Q(3,8)[/tex] that is [tex]x=3[/tex] and [tex]y=8[/tex]
Here [tex]3<8[/tex] this satisfies the condition [tex]x<y[/tex].
Then [tex]3^{2} <8^{2}[/tex]
[tex]9<64[/tex] This also satisfies the condition [tex]x^{2} <y^{2}[/tex].
Hence [tex]Q(3,8)[/tex] exists and it is true.
d)
Assume [tex]Q(x,y)=Q(9,10)[/tex]
Here [tex]9<10[/tex] satisfies the condition [tex]x<y[/tex]
Then [tex]9^{2}<10^{2}[/tex]
[tex]81<100[/tex] satisfies the condition [tex]x^{2} <y^{2}[/tex].
Thus, [tex]Q(9,10)[/tex] point exists and it is true. This satisfies the same values as in part (c)
In the video, you saw that Michael used a budget to make sure he pays bills when they’re due. What are some other reasons someone would want to create a budget?
anyone know the answer to this question ?
Question:
c=3x+80
R=12x- 0.02x^2
R= revenue
C=cost
X=items sold
A) 9x-(0.2x^2+80)
B) x(9-0.2x)-80
C) x(9-0.02x)
D) 9x-0.02x^2+80
Answer:
c) x(9-0.2x)
is the correct answer
PLZ MARK BRAINLIEST
someone asap
A small factory has 3 machines for producing protractors. The high speed machines produces 61% the protractors but 6% of its output is defective. The medium speed machine produces 24% of the protractors, of which 4%o are defective. The low speed machine, which has a defective rate of 2% produces the remainder.
{a) Draw a tree diagram.
(b) What is the probability of a protractor not being defective given it came from a low speed machine?
(c). Knowing that a protractor is defective, what ls the probability it came from the high speed machine?
please help me
if don't know don't answer, if you answer i will report
Answer:
A.) m = 1.5 | B.) p = -1 | C.) t = 2
Step-by-step explanation:
A.)
[tex]4(m+3)=18\\4m+12=18\\4m=6\\m=3/2=1.5[/tex]
B.)
[tex]-2(p+5)+8=0\\-2p-10+8=0\\-2p-2=0\\-2p=2\\p=-1[/tex]
C.)
[tex]3+5(t-1)=8\\3+5t-5=8\\5t-2=8\\5t=10\\t=2[/tex]
Answer:
(a)=
4(m+3)=18
4m+12=18
4m=18-12
4m=6
m=
[tex] \frac{6}{4} [/tex]
(b)=
-2(p+5)+8=0
-2p-10+8=0
-2p=0+10-8
-2p=2
p=
[tex] \frac{2}{ - 2} = - 1[/tex]
(c)=
3+5(t-1)=8
3+5t-5=8
5t=8-3+5
5t=10
t=
[tex] \frac{10}{5} = 2[/tex]
[tex]please \: mark \: as \: brainliest \: because \: i \: spent \: much \: time \: on \: this \: question[/tex]
What is the area of the triangle in centimeters squared?
prove by factorization √16×81=√16×√81
Answer:
√16×81 = 4×9 or √1296 = 36
√16×√81 = 4×9 = 36
Step-by-step explanation:
√81×16
We simplify 81 and 16 by prime factorisation (expressing a number as a product of its prime factors).
√81 = √3×3×3×3 = √9×9 = √9² = 9
√16 = √2×2×2×2 = √4×4 = √4² = 4
Express it in slop-intercept form
Answer:
y = ½x -3
Step-by-step explanation:
_____________________
what are the domain and range of this function?
Answer:
domain: all real numbers
range: {y | y ≥ 0}
which number represents 4%
Answer:
4
Step-by-step explanation:
there are 750 spectator in the stadium of which 420 are women and the rest are men
Complete Question:
There are 750 spectator in the stadium of which 420 are women and the rest are men. What percent of the spectators are women?
Answer:
Percentage = 56%
Step-by-step explanation:
Given the following data;
Total number of people = 750
Number of women = 420
To find the percentage of women;
First of all, we would determine the number of male spectators (men);
Number of men = Total number of people - Number of women
Number of men = 750 - 420
Number of men = 330
Next, we find the percentage of women;
[tex] Percentage = \frac {420}{750} * 100 [/tex]
[tex] Percentage = \frac {42}{75} * 100 [/tex]
[tex] Percentage = 0.56 * 100 [/tex]
Percentage = 56%
Therefore, the percentage of the spectators that are women is 56%.
Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1.2 Australian dollars equals 1 US dollar
Answer: 26.4
Step-by-step explanation: 1.2x22=
Round 263.492 to the nearest tenth.
Answer:
260.
because 263 is below 265 so it wont change to 270.
Find the value of angle x to the nearest degree:
COS X = 0.5505
Answer:
x = 57°
Step-by-step explanation:
Cos(x) = 0.5505
x = Cos⁻¹(0.5505)
x = 56.59
Rounding to the nearest degree;
x = 57°
Hope this helps!
One side of a REGULAR OCTAGON is 19 ft.
What is the PERIMETER of this octagon?
feet.
I
Answer:
152 ft.
Step-by-step explanation:
19*8 = 152
Write the missing power of 10 in each equation.
0.80 × [ ] = 8
[ ] × 0.002 = 20
0.04 × [ ]= 4
[ ]× 0.5 = 500
Find the volume of the composite solid. Round your answer to the nearest
tenth.
Answer:
452.4 in³
Step-by-step explanation:
Volume half sphere = 1/2 volume sphere
Volume sphere = 4/3πr²
Volume = 4/3*3.14*27 Radius = 1/2(6) . 3³ = 27
Volume ≈ 113.1
Volume Cylinder = Area circle x hieght
Area circle = πr²
Area circle = 3.14 * 9
Area circle = 28.26
Volume cylinder = 28.26 * 12 = 339.12
339.12 + 113.1 = 452.22
Because of rounding it would be ≈ 452.4
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K