Answer:Sqrt(8^2 + 3^2)
Step-by-step explanation:
Today, the waves are crashing onto the beach every 4.8 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.8 seconds. 61% of the time a person will wait at least how long before the wave crashes in?
Answer:
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Uniform distribution from 0 to 4.8 seconds.
This means that [tex]a = 0, b = 4.8[/tex]
61% of the time a person will wait at least how long before the wave crashes in?
This is the 100 - 61 = 39% percentile, which is x for which [tex]P(X \leq x) = 0.39[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]0.39 = \frac{x - 0}{4.8 - 0}[/tex]
[tex]x = 4.8*0.39[/tex]
[tex]x = 1.872[/tex]
61% of the time a person will wait at least 1.872 seconds before the wave crashes in.
Prime factorization of 45
A. 2³×5
B. 3²×5
C. 5²×3
D. 5²×9
Answer:
Hello, your answer is:
B. 3²×5
Step-by-step explanation:
Prime factorization of 45 is:
45 = 9 x 5
= 3²×5
Hope this helps you.. Good Luck
Answer:
B. 3² × 5
Step-by-step explanation:
45 can be written as a product of its prime factors.
45 = 3 × 3 × 5
45 = 3² × 5
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the given function.
Answer:
to determine the inverse of the given function, change f(x) to y, switch [tex]\boxed{x}[/tex] and y and solve for [tex]\boxed{y}[/tex]
The resulting function can be written as
[tex]f^{-1}(x)=x^2+\boxed{4}[/tex] where [tex]x\geq\boxed{0}[/tex]
Step-by-step explanation:
Hello,
f is defined for [tex]x\geq 4[/tex] as x-4 must be greater or equal to 0
and [tex]f(x)\geq 0[/tex]
so [tex]f^{-1}[/tex] is defined for [tex]x\geq 0[/tex]
and then we can write
[tex]x=(fof^{-1})(x)=f(f^{-1}(x))=\sqrt{f^{-1}(x)-4} \ so\\f^{-1}(x)-4=x^2 <=> f^{-1}(x)=x^2+4[/tex]
hope this helps
1) Which statement contains an exact number? A) A gross of paper contains 144 sheets. B) One sheet of paper is 0.0042 inches thick. C) One sheet of paper measures 8.5 x 11 inches. D) A ream of medium weight paper weighs 20 pounds. Answer: A
Answer:
B) One sheet of paper is 0.0042 inches thick
Step-by-step explanation:
All the other values are not give from just a sheet of paper, and/or they are either a cumulative value, or values that will be used to calculate another value
Only option B defines a value for a unit of paper, and the value is definite.
Option A indicates the number in a group (gross)
Option C shows two values that can be used to calculate one value; the area.
Option D indicates an accumulated value of weight.
Using the diagram below, solve the right triangle. Round angle measures to the
nearest degree and segment lengths to the nearest tenth.
Answer:
m∠A = 17 degrees m∠B = 73 degrees m∠C = 90 (given) a = 12 (given) b = 40 c = 42 (given)
Step-by-step explanation:
Use sin to solve m∠A
sin x = 12/42 Simplify
sin x = 0.2857 Use the negative sin to solve for x
sin^-1 x = 17 degrees
Add together all of the angle measures to solve for m∠B
17 + 90 + x = 180 Add
107 + x = 180
-107 -107
x = 73 degrees
Use Pythagorean Theorem to solve for b
12^2 + x^2 = 42^2 Simplify
144 + x^2 = 1764
-144 -144
x^2 = 1620 Take the square root of both sides
x = 40
What are the angle measurements of 1,2,3 & 4 for #3 & the measurements for 1 &2 on #4?
Step-by-step explanation:
iii=90
41+i=90(opposite angle)
i=90-41
i=49
26+ii+49+41=180(straight line angle)
116+ii=180
ii=180-116
ii=64
50+25+iv=26+64(opposite angle)
75+iv=90
iv=90-75
iv=15
55+i+55=180(straight line angle)
110+i=180
i=180-110
i=70
ii=55(alternative angle)
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130
x = 69; 90% confidence
a. 0.463 < p < 0.599
b. 0.458 < p < 0.604
c. 0.461 < p < 0.601
d. 0.459 < p < 0.603
Answer:
d. 0.459 < p < 0.603
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.531.
[tex]p=X/n=69/130=0.531[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.531*0.469}{130}}\\\\\\ \sigma_p=\sqrt{0.001916}=0.044[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.044=0.072[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.531-0.072=0.459\\\\UL=p+z \cdot \sigma_p = 0.531+0.072=0.603[/tex]
The 90% confidence interval for the population proportion is (0.459, 0.603).
Suppose that early in an election campaign, a telephone poll of 800 registered voters shows that 460 favor a particular candidate. Just before Election Day, a second poll shows that 520 of 1,000 registered voters now favor that candidate. At the 0.05 significance level, is there sufficient evidence that the candidate's popularity has changed?
Answer:
Yes. At the 0.05 significance level, there is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion that support the candidate has significantly changed.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=800 has a proportion of p1=0.58.
[tex]p_1=X_1/n_1=460/800=0.58[/tex]
The sample 2, of size n2=1000 has a proportion of p2=0.52.
[tex]p_2=X_2/n_2=520/1000=0.52[/tex]
The difference between proportions is (p1-p2)=0.05.
[tex]p_d=p_1-p_2=0.58-0.52=0.05[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{464+520}{800+1000}=\dfrac{980}{1800}=0.54[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.54*0.46}{800}+\dfrac{0.54*0.46}{1000}}\\\\\\s_{p1-p2}=\sqrt{0.00031+0.000248}=\sqrt{0.000558}=0.02[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.05-0}{0.02}=\dfrac{0.05}{0.02}=2.33[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]\text{P-value}=2\cdot P(z>2.33)=0.02[/tex]
As the P-value (0.02) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion that support the candidate has significantly changed.
There is no overlap between the graphs of y< x+ 2 and y> x-2.
True or False
Someone help please
Answer:I think it's TRUE not sure
Step-by-step explanation:
A surveyor is trying to find the height of a hill. He/she takes a ‘sight’ on the top of the hill and find that the angle of elevation is 40°. He/she move a distance of 150 metres on level ground directly away from the hill and takes a second ‘sight’. From this point, the angle of elevation is 22°. Find the height of the hill, correct to 1 d.p.
Answer:
The height of the hill is 116.9 meters.
Step-by-step explanation:
The diagram depicting this problem is drawn and attached below.
From Triangle ABC
[tex]\tan 22^\circ=\dfrac{h}{150+x}\\\\h=\tan 22^\circ(150+x)[/tex]
From Triangle XBC
[tex]\tan 40^\circ =\dfrac{h}{x}\\\\h=x\tan 40^\circ[/tex]
Therefore:
[tex]h=\tan 22^\circ(150+x)=x\tan 40^\circ\\150\tan 22^\circ+x\tan 22^\circ=x\tan 40^\circ\\x\tan 40^\circ-x\tan 22^\circ=150\tan 22^\circ\\x(\tan 40^\circ-\tan 22^\circ)=150\tan 22^\circ\\x=\dfrac{150\tan 22^\circ}{\tan 40^\circ-\tan 22^\circ} \\\\x=139.30[/tex]
Therefore, the height of the hill
[tex]h=139.3\times \tan 40^\circ\\=116.9$ meters( correct to 1 d.p.)[/tex]
The height of the hill is 116.9 meters.
What is the solution to the equation below? Round your answer to two decimal places. 4+4•log2 x=4
Answer:
Option (C)
Step-by-step explanation:
Given expression is,
[tex]4+4\times \text{log}_2(x)=14[/tex]
By subtracting 4 from both the sides of the equation.
[tex]4\times \text{log}_2(x)=14-4[/tex]
Now divide the equation by 4
[tex]\text{log}_2(x)=\frac{10}{4}[/tex]
[tex]\text{log}_2(x)=2.5[/tex]
[If [tex]\text{log}_ab=x[/tex] , then [tex]b=a^{x}[/tex]]
[tex]x=(2)^{2.5}[/tex]
[tex]x = 5.657[/tex]
x ≈ 5.66
Therefore, Option C will be the correct option.
4+4•log2 x=14
x= 5.66
what is the the square route of 98985947875875847688748687587865758 add 9547589777778747 to the answer.
Answer:
800090908988
Step-by-step explanation:
Find the value of x that makes A||B
Answer:
For lines A and B to be parallel, the Same Side Interior angles must be supplementary which means:
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15°
Pls help me I’ll mark brainLiest
Answer:y times 20 p
Step-by-step explanation:
3) BRAINLIEST & 10 + POINTS! :)
Answer:
33,175.21/radians/sec
Step-by-step explanation:
22 rev/sec x 60sec/1 min x 4ft x2 pi/1 rev
22 x 60 = 1320
1320 x 4 = 5280
2 x pi = 6.2831853072
5280 x 6.2831853072= 33,175.218421884
The mean of 100 numerical observations is 51.82 what is the value of all 100 numbers
Answer: 5182
To get the value of all 100 numbers you would need to multiply.
Step-by-step explanation:
51.82x100= 5182
please help me with this
Answer:
Volume = 160 cm³ (Unit = cm³)
Step-by-step explanation:
Length = 4 cm
Width = 4 cm (Because it's a square based cuboid!)
Height = 10 cm
Now, Volume:
Volume = [tex]Length * Width*Height[/tex]
Volume = 4 * 4 * 10
Volume = 160 cm³
Answer:
160 cm³
Step-by-step explanation:
The base is a square. The side length of the base is 4 cm.
The volume of a square-based cuboid is the area of square × height or length.
4² × 10
16 × 10
= 160
The volume of the square-based cuboid is 160 cm³.
[tex]\frac{5x-11}{2x^2+x-6}[/tex] You need to work for your points now!
Answer:
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
Step-by-step explanation:
[tex]\frac{5x-11}{2x^2+x-6}[/tex]
Factor the denominator.
[tex]\frac{5x-11}{\left(2x-3\right)\left(x+2\right)}[/tex]
The fraction cannot be simplified further.
Answer:
[tex] \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]solution,
[tex] \frac{5x - 11}{2 {x}^{2} + x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + (4 - 3)x - 6} \\ = \frac{5x - 11}{2 {x}^{2} + 4x - 3x - 6 } \\ = \frac{5x - 11}{2x(x + 2) - 3(x + 2)} \\ = \frac{5x - 11}{(x + 2)(2x - 3)} [/tex]
Hope this helps..
What is the solution to this inequality -13x> - 39
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form: x < 3
Interval Notation:
( − ∞ , 3 )
Answer:
x<3
Step-by-step explanation:
-13x>-39
-13x>-39 (Divided by Negative Thirteen)
-13>-13
x<3 (The great sign changes to less than when divided or multiplied by a negative number.)
x={...0,1,2}
Hope this helps ❤
What is the answer? ABCD ~ EFGH
Answer:
x = 3.6
Step-by-step explanation:
In similar polygons, corresponding sides are in same ratio
[tex]\frac{AB}{EF}=\frac{AD}{EH}\\\\\frac{3}{2}=\frac{x}{2.4}\\\\\frac{3}{2}*2.4=x\\[/tex]
3 * 1.2 = x
x = 3.6
One-eighth of the students in Martha's class are left handed. One-fourth of the left-handed students wear glasses. What fraction of Martha's class is left-
handed and wears glasses?
Answer:
1/32
Step-by-step explanation:
Multiply the fractions together
1/8 * 1/4 = 1/32
1/32 are left handed glass wearers
Help me plzzzzz!!!!
Answer:124
Step-by-step explanation:
2x + 8 + x - 2 = 180
Add like terms
3x + 6 = 180
Subtract the 6 from both sides
3x + 6 - 6 = 180 - 6
3x = 174
Divide by 3
x = 58
Now we have to find the measure of angle ACD
2(58) + 8 = 124
Planes A and B both intersect plane S. Vertical plane S intersects horizontal plane A and horizontal plane B. Plane S and plane A intersect at line f. Line f contains points N and K. Plane S and plane B intersect at line g. Line g contains points P and Q. Line d intersects plane A at point L. Which statements are true based on the diagram? Select three options.
Answer:
first second third
Step-by-step explanation:
Answer:
A,B,C
Step-by-step explanation:
I took the course
Jimmie invested $13,000 at 5.23% compounded monthly.
What will Jimmie's account balance be in 42 years?
Answer:
116370.197$
Step-by-step explanation:
Jimmie invested $13,000 at 5.23% compounded monthly.
Jimmie's account balance (B) after 42 years:
B = principal x (1 + rate)^time
= 13000 x (1 + (5.23/100)/12)^(42 x 12)
= 116370.197$
Sandy can fold 6 towels in 3 minutes. If she continues at this rate, how many minutes will it take her to fold 36 towels?
Hey there! :)
Answer:
x = 18 minutes.
Step-by-step explanation:
To solve this equation, set up a ratio.
# of towels over time taken:
[tex]\frac{6}{3} = \frac{36}{x}[/tex]
Cross multiply:
6x = 108
Divide both sides by 6:
6x/6 = 108/6
x = 18 minutes.
Answer:
In eighteen minutes she will have folded all 36
A ship traveled at an average rate of 25 miles per hour going west. It then traveled at an average rate of 19 miles per hour heading north. If the ship traveled a total of 145 miles in 7 hours, how many miles were traveled heading west?
Answer:
50 miles
Step-by-step explanation:
hello,
let's note x the number of miles travelled heading west,
it takes 1 hour to travel 25 miles
so it takes x/25 hours to travel x miles
we know that in total it travels 7 hours so it will travel 7-x/25 hours heading North, then heading North it takes 1 hour to travel 19 miles
so in 7-x/25 hours it travels 19(7-x/25) miles
we can write, as the total distance is 145 miles
[tex]x+19(7-\dfrac{x}{25})=145\\<=> 25x+3325-19x=3625\\<=> 6x=300\\<=> x = 50[/tex]
we can verify
50 miles heading West takes 2 hours
in 5 hours it travels 19*5 = 95 miles
the total is 145 miles
so this is correct
hope this helps
a bag contains only red and blue counters the probability that a counter is blue is 0.58 A counter is picked at random What is the probability that it is red
Answer:
0.42
Process:
1 - 0.58
0.42
A triangle with side lengths of 4 , 5 , 6 , what are the measures of it angles to the nearest degree ?
Answer:
41°, 56°, 83°
Step-by-step explanation:
We can find the largest angle from the law of cosines:
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab))
C = arccos((4² +5² -6²)/(2(4)(5))) = arccos(5/40) ≈ 82.8192°
Then the second-largest angle can be found the same way:
B = arccos((4² +6² -5²)/(2·4·6)) = arccos(27/48) ≈ 55.7711°
Of course the third angle is the difference between the sum of these and 180°:
A = 180° -82.8192° -55.7711° = 41.4096°
Rounded to the nearest degree, ...
the angles of the triangle are 41°, 56°, 83°.
What tool is used to draw circles
Answer:
Pair of compasses.
Step-by-step explanation:
These are used to inscribe circles/arcs.
Compasses are used in maths, navigation,e.t.c.
Hope it helps.
Han and Clare are stuffing envelopes. Han can stuff 20 envelopes in one minute, and
Clare can stuff 10 envelopes in one minute. They start working together on a pile of
1,000 envelopes. How long does it take them to finish the pile?
Answer:
33 1/2 min
Step-by-step explanation: