Hi there!
[tex]\large\boxed{x \approx 19.6}[/tex]
We can use right triangle trigonometry to solve.
We are given the angle's adjacent side and are trying to solve for the hypotenuse, so:
Use cosine: cos Ф = A / H
Thus:
cos 30° = 17 / H
Simplify:
0.866 = 17 / H
Isolate for H:
H · 0.866 = 17
H = 17 / 0.866
H = 19.63 ≈ 19.6
Answer:
x = 19.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = 17/x
x cos 30 = 17
x = 17/cos 30
x=19.62990
To the nearest tenth
x = 19.6
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:
Answer:
Babies learn to crawl between age of 6 to 10 months.
Step-by-step explanation:
It may take longer for babies to crawl in winter season since the climate restricts the babies movement due to extra clothes. The babies who are born in summer will learn crawling earlier than those who are born in winter season.
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.
Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?
Answer:
The answer is "0.6368 and 0.773".
Step-by-step explanation:
The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]
For point a:
Therefore the Probability =0.6368
For point b:
[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]
The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?
Point A represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively
The reason the above values of the points of the complex conjugate are correct is as follows:
Definition:
The complex conjugate of a complex number is a complex number that
having equal magnitude in the real and imaginary part as the complex
number to which it is a conjugate, but the imaginary part of the complex
conjugate has an opposite sign to the original complex number
Graphically, the complex conjugate is a reflection of the
original complex number across the x-axis because the transformation for
a reflection of the point (x, y) across the x-axis is given as follows;
Preimage (x, y) reflected across the x-axis give the image (x, -y)
In a complex number, x + y·i. we have;
x = The real part
y = The imaginary part
The reflection of z₁(1, -2) across the x-axis gives the point A(1, 2), while the
reflection of z₂(6, -7) across the x-axis gives the point L(6, 7)
To summarize;
Point A(1, 2) is the reflection and therefore represents the complex
conjugate of z₁(1, -2) and point L(6, 7) is the reflection and therefore
represents the complex conjugate of z₂(6, -7)
Learn more about complex numbers here;
https://brainly.com/question/20365080
necesito la respuesta, entre a b c o d
Answer:
a)a^4 + 19a^2 -12ab - 3b^4 +6b...
Gant Accounting performs two types of services, Audit and Tax. Gant’s overhead costs consist of computer support, $267000; and legal support, $133500. Information on the two services is:
(See screenshot)
Answer:
$240,300
Step-by-step explanation:
Given :
Overhead cost :
Computer support = $267000
legal support = $133500
Overheads applied to audit services = (Number of CPU minutes used by Audit services * activity rate per CPU minute)
+
(number of legal hours used by Audit services * activity rate per legal hour)
The overhead applied to audit is thus :
40,000 * (267,000 / (40,000 + 10,000)) +
200 * (133500 / (200 + 800)
(40000 * 5.34) + (200 * 133.5)
= $240,300
1.2 Write the ratio 1:2 in the simplest form.
ty
This graph shows a portion of an even function.
Use the graph to complete the table of values.
6
f(x)
-1
4
-3
-5
-6
2
DONE
2
4.
6
Answers:
first box = 1second box = 1third box = 3fourth box = 3Refer to the graph below.
==========================================================
Explanation:
If f(x) is an even function, then f(-x) = f(x) for all x in the domain.
What this means is that we have symmetry about the y axis. We can reflect that given curve over the y axis to generate the missing left side.
The graph shows that (1,1) is on the orange curve. It reflects over to (-1,1). This means 1 goes in the first box.
Use the rule [tex](x,y) \to (-x,y)[/tex] to apply a y axis reflection. We simply just change the sign of the x coordinate from positive to negative, while keeping the y coordinate the same.
---------------
We can also see that (3,1) is also on the orange curve. It reflects over to (-3, 1) using that rule mentioned earlier.
1 goes in the second box
---------------
The graph your teacher gave you shows that if we plugged in x = 5, then we get y = 3. In other words, the point (5,3) is on the orange graph.
It reflects over to (-5, 3) to show that x = -5 leads to the output y = 3
3 goes in the third box
----------------
Lastly, the point (6,3) reflects to (-6,3) when reflecting over the y axis.
3 goes in the fourth box.
See the graph below.
HELP! PLEASE!!
Simplify the expression.
9514 1404 393
Answer:
D
Step-by-step explanation:
Regrouping the factors, we have ...
The dotplot below displays the difference in scores for 18 games between a high school soccer team and its opponent.
A dotplot titled difference in Score. A number line going from negative 2 to 4 is labeled Team score minus opponent score. Negative 2, 1; negative 1, 2; 0, 2; 1, 3; 2, 6; 3, 3; 4, 1.
Which of the following is the best explanation for the dots at –1?
In one game, the team beat the opponent by 1 goal.
In two games, the team beat the opponent by 1 goal.
In one game, the team lost to the opponent by 1 goal.
In two games, the team lost to the opponent by 1 goal.
Answer: Choice D
In two games, the team lost to the opponent by 1 goal.
========================================================
Explanation:
Negative scores indicate the team lost, and the absolute value of those values represent how much of a loss.
So a difference of -1 means the team lost by 1 point.
We have 2 dots over this value, so there are 2 occasions where the team lost to the opponent by 1 goal.
An example would be that say the team scored 3 goals and the opponent scored 4 goals. So we have a differential of 3-4 = -1. The order is important because we would not say 4-3 = 1.
Answer:
d
Step-by-step explanation:
took the test
which is more 1 ton or 2,884 pounds?
This semester, the tuition fee increased to $5,871. If this represents an increase by 14%, what was the original fee?
Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings?
FINAL ANSWER: D
Given : Molly and Lynn both set aside money weekly for their savings.
Molly already has $650 set aside and adds $35 each week.
Lynn already has $825 set aside but adds only $15 each week.
To Find : inequality to determine how many weeks, w, it will take for Molly’s savings to exceed Lynn’s savings
Solution:
Molly already has $650
adds $35 each week.
=> added in w weeks = 35w
After w weeks = 650 + 35w
Lynn already has $825
adds $15 each week.
added in w weeks = 15w
After w weeks = 825 + 15w
Molly’s savings to exceed Lynn’s savings
⇒ 650 + 35w > 825 + 15w
⇒ 20w > 175
⇒ 4w > 35
⇒ w > 35 /4
At least 9 weeks
Answer:
D
Step-by-step explanation:
First, to eliminate some answers you can figure out which way the sign should go. The question wants to know when Molly's savings will be larger so the sign should open towards her side of the equation. Since her savings are represented on the left the sign should be a greater than, >.
Then, figure out where the variables belong. The variable represents the number of weeks that have passed, so they should be multiplied by the number that is affected by the passing of weeks. This is the amount each person saves, aka the independent variable. So the "w" variable should be next to the 35 and 15.
I really need the help please and thank you
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(-5/2) divide 13/7 x 9/7
Help :(
Answer:
-45/26
Step-by-step explanation:
(-5/2)÷(13/7)×(9/7)
(-5/2)×(7/13)×(9/7)
-45/26
Answered by Gauthmath must click thanks and mark brainliest
Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
perpendicular to
7y = x − 4
and passes through the point
(−2, 1)
Answer:
[tex]y = -7x -13[/tex]
Step-by-step explanation:
Given
Perpendicular to
[tex]7y = x -4[/tex]
Passes through
[tex](-2,1)[/tex]
Required
The equation
First, we calculate the slope of:
[tex]7y = x -4[/tex]
Divide through by 7
[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]
A linear function is:
[tex]y=mx + c[/tex]
Where;
[tex]m \to slope[/tex]
So:
[tex]m = \frac{1}{7}[/tex]
For the perpendicular line; the slope is:
[tex]m_2 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_2 = -\frac{1}{1/7}[/tex]
[tex]m_2 = -7[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = -7(x - -2) + 1[/tex]
[tex]y = -7(x +2) + 1[/tex]
Open bracket
[tex]y = -7x -14 + 1[/tex]
[tex]y = -7x -13[/tex]
The graph shown below expresses a radical function that can be written in
17
the form f(x) = a(x + k)!
C. What does the graph tell you about the
value of k in this function
Answer:
C. [tex]k[/tex] is greater than zero.
Step-by-step explanation:
We know that graph is obtained from the function of the form [tex]f(x) = a\cdot (x+k)^{1/n} + c[/tex]. According to the graph and if [tex]x + k = 0[/tex], we find that:
[tex]x = -k[/tex] (1)
[tex]x < 0[/tex] (2)
By (1) and (2):
[tex]-k < 0[/tex]
[tex]k > 0[/tex]
Hence, correct answer is C.
What is the largest value of x for which the following equation has a real solution (x,y)?
Answer:
x = 9/2
Step-by-step explanation:
x^2+7x+y^2+4y=191/4
Complete the square: (x+7/2)^2-(49/4)+(y+2)^2-4 = 191/4
Simplify: (x+7/2)^2+(y+2)^2=191/4+49/4+4
(x+7/2)^2 + (y+2)^2 = 64
(x+7/2)^2 + (y+2)^2 = (8)^2
Center of circle -> (-7/2, -2)
Radius -> 8
-7/2 + 8 = 9/2
x = 9/2
Find the measure of the missing angles.
Answer:
e = 41 , f = 139 and d = 90
Step-by-step explanation:
?
We know that vertically opposite angles are equal.
So, e = 41° [Vertically opposite angles]
We know that linear pair of angles are supplementary (180°).
So, f + 41° = 180° [Linear pair of angles]
=> f = 180° - 41°
=> f = 139°
and d + 90° = 180° [Linear pair of angles]
=> d = 180° - 90°
=> d = 90°
Which side is the “adjacent” side to θ?
Answer:
third answer "a"
Step-by-step explanation:
Let T:R²->R² be a linear transformation ,and assume that T (1,2)=(-1,1) and T(1,-1)=(2,3)
compute T(3,3) pls help me
Answer:
(-4,-1)
Step-by-step explanation:
We are given T(1,2)=(-1,1) and T(1,-1)=(2,3) and T is a linear transformation.
This implies for scalars a and b that
T(a(1,2)+b(-1,1))=aT(1,2)+bT(-1,1)
T((a,2a)+(-b,b))=a(-1,1)+b(2,3)
T((a-b,2a+b))=(-a,a)+(2b,3b)
T((a-b,2a+b))=(-a+2b,a+3b)
This means we should be able to solve the system below to find a and b for T(3,3):
a-b=3 and 2a+b=3
Add equations to eliminate b and solve for a:
3a=6
Divide 3 on both sides:
a=2
If a-b=3 and a=2, then b=-1.
Plug in a=2, b=-1:
T((a-b,2a+b))=(-a+2b,a+3b)
T((2--1,2×2+-1)=(-2+2×-1,2+3×-1)
T(3,3)=(-4,-1).
Which is the sum of the sequence {5*1, 5*8, 5*27, 5*64, 5*125, 5*216}?
Answer:
2160
Step-by-step explanation:
I find that it is easier to split the sequence into smaller, more manageable sections. For numbers beyond 13, the simplest way is to split it up into place values.
Note: * is a multiplication symbol
5*1 = 5
5*8 = 40
5*27 = (5*20) + (5*7) = 100+35 = 135
5*64 = (5*60) + (5*4) = 300+20 = 320
5*125 = (5*100) + (5*20) + (5*5) = 500+100+25 = 625
5*216 = (5*200) + (5*10) + (5*6) = 1000+50+30=1080
Now you can add all of the totals up!
135+320+625+1080 = 2160
Theta Company has the following variances at the end of February:
Material Price Variance $40 Unfavorable
Material Usage Variance $225 Unfavorable
Labor Rate Variance $110 Unfavorable
Labor Efficiency Variance $335 Unfavorable
What is the journal entry to be passed by Theta Company at the end of the month of February to close the variances?
Answer:
Debit Cost of Goods Sold $710
Credit Material Price Variance $40
Credit Material Usage Variance $225
Credit Labor Rate Variance $110
Credit Labor Efficiency Variance $335
Step-by-step explanation:
Preparation of the journal entry to be passed by Theta Company at the end of the month of February to close the variances
Debit Cost of Goods Sold $710
($40+$225+$110+$335)
Credit Material Price Variance $40
Credit Material Usage Variance $225
Credit Labor Rate Variance $110
Credit Labor Efficiency Variance $335
(To close the variances)