Answer:
x = 48
Step-by-step explanation:
Pythagorean thm:
a² + b² = c²
Given:
a = x
b = 36
c = 60
Work:
a² + b² = c²
x² + 36² = 60²
x² + 1296 = 3600
x² = 3600 - 1296
x² = 2304
√x² = √2304
x = 48
If f(x) = 4x + 5 and fog(x) = 8x + 13 then find g(x).
Answer:
given
f(x).4x+5
fog(x).8x+13
now
fog(x):8x+13
4x+5(g(x)):: 8x+13
g(x):: 8x+13/4x+5
Answer:
g(x) = 2x + 2
Step-by-step explanation:
One is given the following information:
f(x) = 4x + 5f o g (x) = 8x + 13One is asked to find the following:
g(x)Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:
f(g(x)) = 8x + 13
Substitute the given infromation into the equation:
4(g(x)) + 5 = 8x + 13
Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:
4(g(x)) + 5 = 8x + 13
Inverse operations,
4(g(x)) + 5 = 8x + 13
4(g(x)) = 8x + 8
g(x) = (8x + 8) ÷ 4
g(x) = 2x + 2
plz help brainliest to correct answer
Answer:
-2 would be right next to -3 because its negative and -1 would be right next to -2, 2 would be two points away from 0 bc its a whole number
formula of a square minus b square
Answer:
(a+b)(a-b)
Step-by-step explanation:
[tex]\\ \sf\longmapsto (a+b)(a-b)[/tex]
[tex]\\ \sf\longmapsto a(a-b)+b(a-b)[/tex]
[tex]\\ \sf\longmapsto a^2-ab+ba-b^2[/tex]
[tex]\\ \sf\longmapsto a^2-ab+ab-b^2[/tex]
[tex]\\ \sf\longmapsto a^2-b^2[/tex]
[tex]\large\bf{\orange{ \implies}} \: \tt \: {a}^{2} \: - \: {b}^{2} [/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: (a + b) \quad \: (a - b)[/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: a \: (a - b) \quad \: b \: (a - b)[/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: ab \: + \: ba \: - \: {b}^{2} [/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: ab \: + \: ab \: - \: {b}^{2} [/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: \cancel{ab} \: + \: \cancel{ab} \: - \: {b}^{2} [/tex]
[tex]\large\bf{\pink{ \implies}} \: \tt \: {a}^{2} \: - \: {b}^{2} [/tex]
HELP NEEDED PLEASE!!!!!
Answer:
1^1 + 0^1 =1
Step-by-step explanation:
sin^2 theta + cos^2 theta = 1
sin^2 (pi/2) + cos^2 (pi/2) =1
1^1 + 0^1 =1
A local rental car agency has 200 cars. The rental rate for the winter months is 60%. Find the probability that in a given winter month fewer than 140 cars will be rented. Use the normal distribution to approximate the binomial distribution.
Answer:
[tex]P(Z\leq2.89)=0.9981[/tex]
Step-by-step explanation:
Sample size [tex]n=200[/tex]
Rental Rate [tex]R=60\%[/tex]
Probability =(P<140)
Generally the equation for mean of distribution is mathematically given by
[tex]\mu=nR\\\\\mu=200*0.60\\\\\mu=120[/tex]
Generally the equation for Standard deviation of distribution is mathematically given by
[tex]\sigma=\sqrt{npq}[/tex]
[tex]\sigma=\sqrt{200*0.60*0.40}[/tex]
[tex]\sigma=6.9[/tex]
Therefore
Z-score for x=140 is
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]Z=\frac{140-120}{6.9}[/tex]
[tex]Z=2.89[/tex]
From table
[tex]P(Z\leq2.89)=0.9981[/tex]
11z/(z+3) = 13 - i , z∈C please solve it
[tex]\frac{11z}{z+3}=13-i,z\in\mathbb{C}[/tex]
First, multiply both sides by [tex]z+3[/tex],
[tex]11z=(13-i)(z+3)[/tex]
[tex]13z+39-iz-3i=11z[/tex]
Collect terms and put z on the left,
[tex]2z-iz=3i-39[/tex]
[tex]z(2-i)=3i-39[/tex]
[tex]z=\frac{3i-39}{2-i}[/tex]
Division of complex numbers is defined by multiplying both denominator and numerator with complex conjugate of the denominator,
[tex]z=3\frac{(i-13)(2+i)}{(2-i)(2+i)}[/tex]
Multiply out,
[tex]z=3\frac{2i-1-26-13i}{5}[/tex]
[tex]z=3\frac{-11i-27}{5}[/tex]
The result is,
[tex]z=-\frac{81}{5}-\frac{33}{5}i[/tex]
Hope this helps :)
Social media is popular around the world. Statista provides estimate of the number of social media users in various countries in as well as the projections for . Assume that the results for surveys in the United Kingdom, China, Russia, and the United States are as follows.
Use Social Media United Kingdom China Russia United States
Yes 480 215 343 640
No 320 285 357 360
Required:
a. Conduct a hypothesis test to determine whether the proportion of adults using social media is equal for all four countries. What is the p-value? Using a .05 level of significance, what is your conclusion?
b. What are the sample proportions for each of the four countries? Which country has the largest proportion of adults using social media?
c. Using a 0.05 level of significance, conduct multiple pairwise comparison tests among the four countries. What is your conclusion?
Answer:
Kindly check explanation
Step-by-step explanation:
The data table :
Use of SM _UK _China _ Russia _US _ col total
Yes ______480 __215 ___343 __640 _ 1678
No _______320 _ 285 ___357__ 360 _ 1322
Row Total__ 800 _500 __ 700_ 1000_ 3000
H0 : p1 = p2 = p3 = p4
H1 : p1 ≠ p2 ≠ p3 ≠ p4
Test statistic :
χ² = Σ(observed - Expected)² / Expected
Expected value of each cell = (Row total * column total) / N
N = grand total
Expected Values:
447.467 _279.667 _ 391.533 _ 559.333
352.533 _ 220.333 _ 308.467 _ 440.667
χ²=(2.36536+14.9527+6.01605+11.6337+3.00232 18.9793+7.63611+14.7665) = 79.352
Degree of freedom, df = (row-1)*(column-1) = (2 - 1) * (4 - 1) = 1 * 3 = 3
Using the Pvalue from Chisquare calculator :
Pvalue(79.352, 3) = 0.00000000001
Decision region :
Reject H0 ; If Pvalue < α
α = 0.05
Since 0.000000001 < 0.05 ; Reject H0 and conclude that not all population proportion are equal.
Sample proportion :
Phat = number of yes, x / total
For UK, Phat = 480/800 = 0.6
For China , Phat = 215/500 = 0.43
For Russia , Phat = 343/700 = 0.49
For US, Phat = 640/1000 = 0.64
Suppose $12,000 is deposited into an account paying 5.5% interest, compounded continuously.
How much money is in the account after five years if no withdrawals or additional deposits are
made?
Answer:
$15798.4
Step-by-step explanation:
We will have to use this formula A = Peᵃᵇ
A = Final amount
P = Initial amount (12,000)
e = Mathematical constant: 2.7183
a = Interest rate (5.5% or 0.055)
b = Years
So our equation will look like this
A = 12,000e⁵ ⁰·⁵⁵
A = 12,000(2.7183)·²⁷⁵
A = 12,000(1.316533)
A = 15798.396
Select the correct answer.
Given the following formula, solve for l.
A.
B.
C.
D.
Answer:
c
Step-by-step explanation:
took the test so i assume its this question
If (x+2) is a Factor x^3 + 2x^2 + 2x + k then find the value of K.
Answer:
4
Step-by-step explanation:
if x+2 is a factor of the above expression then,
x=-2
so putting the value of x in above expression we get,
(-2)^3+2×(-2)^2+2×(-2)+k=0
or,-8+8-4+k=0
k=4
Answer:
Step-by-step explanation:
If (x + 2) is a factor of a polynomial then ( - 2 ) is the zero of that polynomial ⇒ ( - 2 )³ + 2( - 2 )² + 2( - 2 ) + k = 0 ⇒ k = - 4
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answer:
1/3
Step-by-step explanation:
common ratio is
9÷27=1/3
3÷9=1/3
1÷3=1/3
therefore common ratio is 1/3
Answer: 1/3
Step-by-step explanation:
Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.
The equation ^2 −4+^2 +2=−4
a. Is a parabola
b. Is an ellipse
c. Is a hyperbola
d. Is a circle
e. None of the above
Answer:
Step-by-step explanation:
None. Your notation is unclear.
I need help completing this problem ASAP
4/(√x - √(x - 2)) × (√x + √(x - 2))/(√x + √(x - 2))
= 4 (√x + √(x - 2)) / ((√x)² - (√(x - 2))²)
= 4 (√x + √(x - 2)) / (x - (x - 2))
= 4 (√x + √(x - 2)) / (x - x + 2)
= 4 (√x + √(x - 2)) / 2
= 2 (√x + √(x - 2))
Mary is thinking of a mystery number. She reduces it by 15% then subtracts 5. The result is 29. Determine the mystery number
Answer:
40
Step-by-step explanation:
Let x represent the mystery number.
Create an equation to represent the situation, then solve for x:
0.85x - 5 = 29
0.85x = 34
x = 40
So, the mystery number is 40.
81×81+68×68-2×81×68
Answer:
First by "BODMAS" we will sove multiplication
81×81+68×68-2×81×68
now first we will solve addition
=6561+4624-11016
=11185-11016
=169
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Please help with this just tell me A B C or D.
Answer:
The answer is D.
[tex]3x {}^{2} - 10x - 1 = 0[/tex]
Step-by-step explanation:
[tex]x = \frac{5 + 2 \sqrt{7} }{3} [/tex]
Divide each term of 5+2√7 by 3 to get 5/3 + 2/3√7.
[tex]x = \frac{5}{3} + \frac{2}{3} \sqrt{7} [/tex]
[tex]x = \frac{2 \sqrt{7 + 5} }{3} [/tex]
or
[tex]x = 3.43[/tex]
Solve for x^2=18
Please help
i provided the question
Answer:
(0, 3)
Step-by-step explanation:
y = 3 is the horizontal tangent to y = x^2+3, and passes the parobala at (0, 3)
12. Convert 30.283° into a degree-minute-second format.
O A. 18° 16' 98"
B. 18° 28' 30"
C. 30° 16' 58"
D. 30° 28' 30"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The angle is given below.
⇒ 30.283°
Convert 30.283° into a degree-minute-second format. Then we have
⇒ 30° (0.83 x 60')
⇒ 30° 16.98'
⇒ 30° 16' (0.98 x 60'')
⇒ 30° 16' 58"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
More about the conversion link is given below.
https://brainly.com/question/9414705
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What is the shape of the cross section?
Answer:
Step-by-step explanation:
Triangular cross-section.
Answer:
it is a triangle cross-section
hope this answer helps you
Plz make me a brainlist
From the observation deck of a skyscraper, Isabella measures a 67
angle of depression to a ship in the harbor below. If the observation deck is 824 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
The horizontal distance from the base of the skyscraper out to the ship is 349.8feet
Angle of elevation and depressionThe angle situated above the hill is known as the angle of depression
Given the following parameters
Height of the harbor = 824 feet
Angle of depression = 67degrees
According to SOH CAH TOA identity:
tan 67 = opp/adj
tan 67 = 824/d
d = 824/tan67
d = 349.8 feet
Hence the horizontal distance from the base of the skyscraper out to the ship is 349.8feet
Learn more on angle of depression here: https://brainly.com/question/12483071
Carol is having a hard time understanding the central limit theorem, so she decides to do her own experiment using the class data survey collected at the beginning of class on the number of hours a student takes during her Spring 2019 BUSI 2305 course. The data file has a total number of 54 students where the average is 10.8 with a standard deviation of 3.15. She sets out to collect the mean on 8 samples of 6 students. Based on this what are the total possible samples that could occur based on the population
Answer:
25827165
Step-by-step explanation:
from the question that we have here
the total population = 54 students
the sample size = 6 students
So given this information carol has to pick the total samples from the 54 students that we have here
the total ways that she has to do this
= 54 combination 6
= 54C6
= [tex]\frac{54!}{(54-6)!6!}[/tex]
= 25827165
this is the total number of possible samples that could occur given the total population of 54 students.
find the scale factor and ratio of perimeters for a pair of similar octagons with areas 49 ft^2 and 64 ft^2
Answer:
scale factor: 1.16
perimeters: 21.84 ft and 25.36 ft
Solve for x, Correct to one decimal place where 0°<x<90°
Sin2x=0,291
Answer:
Step-by-step explanation:
Sin2x=0,291
Sin2x = 2Sinx * Cosxsolve the expression -|6+(-2)|+9
The simplification of the given expression -|6+(-2)|+9 is 5.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
Given expression;
-|6+(-2)|+9
Solve the modules;
-|4|+9 = 5
Thus, the simplification of the given expression is 5.
Learn more about simplification;
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- 2/3 (2 - 1/5) use distributive property
Answer:
-6/5
Step-by-step explanation:
- 2/3 (2 - 1/5)
Distribute
-2/3 *2 -2/3 *(-1/5)
-4/3 + 2/15
Get a common denominator
-4/3 *5/5 +2/15
-20/15 +2/15
-18/15
Simplify
-6/5
Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answer:
-
Step-by-step explanation:
-
The scale on a map is
1:25 000
(a) On a map, a distance
measures 5cm. What is this
in real life? Give your
answer in kilometres.
(b) In real life a distance is
2.2km. What would this be in
the map in centimetres?
Answer:
Step-by-step explanation:
a) 5 cm(25000)(1 m/100 cm)(1 km/1000 m) = 1.25 km
b) 2.2 km (1000 m/km)(100 cm/m) / 25000 = 8.8 cm
Rewrite the polynomial in the form ax+by+c and then identify the values of a, b, and c.
x -- 1 -- 2y
Answer:
a=1, b=-2,c=-1
Step-by-step explanation:
1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1
9. If a card is selected from a standard 52 card deck. What is the probability of selecting a face card or an Ace?