Answer:
30.03
Step-by-step explanation:
[(33.7)² - (15.3)²]^½
= [1135.69 - 234.09]^½
= [901.6]^½
= 30.02665483
= 30.03 (4sf)
gordan is twice as old as tony was when gordan was as old as tony is now. combined age of gordan and tony is 112 years. how old are gordan and tony now?
Answer:
Answer
Tony:48
Gordan :64
Step-by-step explanation:
[tex]\begin{array}{c|c|c}Age&Gordon&Tony\\------------------&-------&-------\\now&g&t\\when\ gordan\ was\ as\ old\ as\ tony\ is\ now&t(=g-g+t)&t-g+t=2t-g\\\end{array}\\\\\\\\\left\{\begin{array}{ccc}g&=&2*(2t-g)\\g+t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}3g&=&4t\\g+t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}g&=&\dfrac{4}{3}\\\dfrac{7}{3} t&=&112\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}t&=&48\\g&=&64\\\end {array}\right.\\[/tex]
Proof:
16 years ago, Gordan was 48 and Tony 32.
64=2*32
64+48=112
8 millions =
how many hundred thousands
Answer:
100000
Step-by-step explanation:
100000x80=8m
The graph shows the distribution of the number of text messages young adults send per day. The distribution is approximately Normal, with a mean of 128 messages and a standard deviation of 30 messages.
A graph titled daily text messaging has number of text on the x-axis, going from 8 to 248 in increments of 30. Data is distributed normally. The highest point of the curve is at 128.
What percentage of young adults send between 68 and 158 text messages per day?
34%
47.5%
81.5%
95%
This value is approximate.
====================================================
Explanation:
We have a normal distribution with these parameters
mu = 128 = population meansigma = 30 = population standard deviationThe goal is to find the area under the curve from x = 68 to x = 158, where x is the number of text messages sent per day. So effectively, we want to find P(68 < x < 158).
Let's convert the score x = 68 to its corresponding z score
z = (x-mu)/sigma
z = (68-128)/30
z = -60/30
z = -2
This tells us that the score x = 68 is exactly two standard deviations below the mean mu = 128.
Repeat for x = 158
z = (x-mu)/sigma
z = (158-128)/30
z = 30/30
z = 1
This value is exactly one standard deviation above the mean
-------------------------------------------
The problem of finding P(68 < x < 158) can be rephrased into P(-2 < z < 1)
We do this because we can then use the Empirical rule as shown in the diagram below.
We'll focus on the regions between z = -2 and z = 1. This consists of the blue 13.5% on the left, and the two pink 34% portions. So we will say 13.5% + 34% + 34% = 81.5%
Approximately 81.5% of the the population sends between 68 and 158 text messages per day. This value is approximate because the percentages listed in the Empirical rule below are approximate.
Answer:
C. 81.5%
Step-by-step explanation:
PLSSS HELP IM STRUGGLING SO HARD !!! ———————
Answer:
C)
Step-by-step explanation:
Just see the length of the R line, A and B are almost the same large when you add them.
Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?
Answer:
The equation of the parabola is,
x²+4y-12=0
Find the length of BC
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.
sin(51) = BC / 58
BC = 58 x sin(51)
BC = 45.1 units
Hope this helps!
Step-by-step explanation:
Hey there!
From the above given figure;
Angle CAB = 51°
AB = 58
Taking Angle CAB as reference angle we get;
Perpendicular (p) = BC= ?
Hypotenuse (h) = 58
Now;
Taking the ratio of sin we get;
[tex] \sin( \alpha ) = \frac{p}{h} [/tex]
[tex] \sin(51) = \frac{bc}{58} [/tex]
Simplify it;
0.7771459*58 = BC
Therefore, BC = 45.0744.
Hope it helps!
Which of the following sets are equal to {x|x < 9 and x> 2}
{3,4,5,6,7,8}
{2,3,4,5,6,7,8,9}
{}
{2,3,4,5,6,7}
Answer:
{3, 4, 5, 6, 7, 8}Step-by-step explanation:
{x|x < 9 and x > 2}= {3, 4, 5, 6, 7, 8}[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Tay-Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately 0.25. Suppose that a husband and wife are both carriers and that they have four children. If the outcomes of the four pregnancies are mutually independent, what are the probabilities of the following events?
a. All three children will develop Tay–Sachs disease.
b. Only one child will develop Tay–Sachs disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Lo siento mucho, necesito los puntos porque estoy en una prueba.
Reflect the given triangle over
the y-axis.
[3 6 3 ]
[-3 3 3]
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex] ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]
how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right.how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of each shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right. plz answer the question steps by step.
Answer:
4 walls in my room. The shape of my room is square and my ceiling in square. By looking at it and measuring it. Thats how I found my answer.
I believe this is correct if it is can you mark brainliest? Hope I helped!!!! :)
Answer:
8 walls etc....
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y= -6x-6, I think, hope it helped
Step-by-step explanation:
Integers are sometimes whole numbers
true or false
Answer:
True
Step-by-step explanation:
Integers are always whole numbers
negative, 0, positive:: whole numbers
Help me please guys thanks
Answer:
A is correct
Step-by-step explanation:
Which expression is equivalent to
ху^2/9
The expression equivalent to x(y)^(2/9) is option D. x [tex]\sqrt[9]{y^{2} }[/tex].
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is x(y)^(2/9).
We have to find the equivalent expressions of this.
We can write the exponent 2/9 as 2 × 1/9.
So, x(y)^(2/9) = x(y)^(2 × 1/9)
We have the power of a power rule,
(xᵃ)ᵇ = xᵃᵇ
Using this rule,
(y)^(2 × 1/9) = (y²)^(1/9)
So, x(y)^(2/9) = x (y²)^(1/9)
Also, we have,
[tex]\sqrt[n]{x}[/tex] = [tex](x)^{\frac{1}{n}}[/tex]
So, (y²)^(1/9) = [tex]\sqrt[9]{y^{2} }[/tex]
x(y)^(2/9) = x [tex]\sqrt[9]{y^{2} }[/tex]
Hence the equivalent expression is x [tex]\sqrt[9]{y^{2} }[/tex].
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Your question is incomplete. The complete question is as follows.
Consider a political discussion group consisting of 6 Democrats, 6 Republicans, and 4 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting an Independent and then a Republican.
___.
(Type an integer or a simplified fraction.)
Answer:
10/16=5/8
6+6+4=16
The probability is 5/8
The surface areas of two similar solids are 16m2 and 100 m2. The volume of the larger one is 750m3. What is the volume of the smaller one?
Answer:
48 m^3
Step-by-step explanation:
If the scale factor of linear dimensions between two solids is k, then the scale factor for areas is k^2, and the scale factor of volumes is k^3.
Let's call the solid with 16 m^2 of area solid A, and the other one solid B.
The scale factor of areas from, A to B is (100 m^2)/(16 m^2) = 25/4
In other words, multiply the area of the solid A by 25/4 to get the area of solid B.
Let's check: 16 m^2 * 25/4 = 16 * 25/4 m^2 = 4 * 25 m^2 = 100 m^2
We do get 100 m^2 for solid B, so the area scale factor of 25/4 is correct.
The area scale factor is k^2, so we have:
k^2 = 25/4
We solve for k:
k = 5/2
Now we cube both sides to get k^3, the scale factor of volumes.
k^3 = 5^3/2^3
k^3 = 125/8
Let V = volume of smaller solid, solid A.
V * 125/8 = 750 m^3
V = 750 * 8/125 m^3
V = 48 m^3
please give me correct answer
Answer:
answer of question number 1 is 2400, 2880, 3600 respectively.
answer of question number 2 is 1384 and 1680.
Step-by-step explanation:
100×24=2400
120×24=2880
150×24=3600
692×2=1384
420×4=1680
9.) Ezri earns $10 per day plus $25 for every lawn she mows. How many lawns does she need to mow today to earn $135? First, write the equation that fits this model. Let x be the amount of yards she mows. Hurry please
Answer:
5 lawns
Step-by-step explanation:
Firstly, the equation is 25x + 10 = 135
Ezri makes $25 for every lawn she mows (25x) and has an automatic $10 per day (10). In order to make $135 we take what she makes each day and set it equal to 135.
To solve, we subtract 10 from both sides to create 25x = 125. We then divide 25 from both sides to get x=5. This means that Ezri needs to mow 5 lawns in order to make $135.
I hope this is helpful to you!
**To anyone out there seeing this - let me know if you think I made a mistake and I will fix it.**
You will need _____ml of the 95% solution
70 mL=25% alcohol
?mL=90% alcohol
90×70÷25
=252 mL
I think do like this....I'm not sure
Hope this help you
9514 1404 393
Answer:
420 mL
Step-by-step explanation:
Let x represent the amount of the 95% solution needed in the mixture. The the total amount of alcohol in the mixture is ...
0.25×70 + 0.95(x) = 0.85(70 +x)
0.10x = 42 . . . . . . . . subtract 17.5+0.85x
x = 420 . . . . . . . . divide by 0.10
You will need 420 mL of the 95% solution.
__
Additional comment
There will be 70+420 = 490 mL of solution, of which 85%, or 0.85×490 = 416.5 ml is alcohol. That alcohol is the total of 0.25×70 = 17.5 mL of alcohol from the 25% solution and 0.95×420 = 399 mL of alcohol from the added 95% solution. (17.5 +399 = 416.5)
estimate the value of -50 by plotting it on a number line
[tex] - \sqrt{50} [/tex]
how to plot -50 on a number line
Answer:
Step-by-step explanation:
Never mind the minus for a second. What is the approximate value of sqrt(50)?
Isn't it about 7 or just a tiny bit over?
That's the answer here. Find the square root first, and then add the minus.
<o==o==o==o==o==o==o==o
-7 -6 -5 -4 - 3 - 2 - 1 0
Use the Unit Circle to find the exact value of the trig function. Cos(45)
1/2
√2/2
√3/-2
1
In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.
A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].
In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].
In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.
As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].
Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].
Hope this helps :)
You can work a total of no more than 35 hours each week at your two jobs. Housecleaning pays $7 per hour and your sales job pays $9 per hour. You need to earn at least $314 each week to pay your bills. Write a system of inequalities that shows the various numbers of hours you can work at each job.
Answer: 7x + 9y >_ (more or equal) 314
X + Y <_ ( less or equal) 35
Step-by-step explanation:
Answer:
h+s≤35 and 7h + 9s >_314
Step-by-step explanation:
Students apply for admission to different academic programs within a college. Because of space, each program can only accept a limited number of students. The table below shows the acceptance data for a selection of majors in the college.
Acceptance Status
Accepted Rejected Total
College Major Chemistry 72 18 90
Business 65 35 100
Spanish 45 15 60
Total 182 68 250
What is the probability that a student was accepted, given that the student applied to the business program?
26.0%
35.0%
35.7%
65.0%
I think the answer is (A). 26%. Can someone check?
Answer:
Your wrong, it's 65%.
Step-by-step explanation:
The reason why: You can calculate the percentage by dividing the number of accepted students by the total of business students, 65/100 which equals 65%.
yw :)
The probability that a student was accepted is 5.0% since option b be the correct answer.
ProbabilityProbability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,
How to find probability?We have to find out the probability of the selection of a student applied for the business program.
We know that, Probability= Total number of events occurred÷ Total number of possible outcomes/events
So, Probability that a student applying to the business program got selected= No of accepted students for business program÷Total number of students applied for business program=65÷100=0.65For converting a number into percentage we multiply the number by 100 that is 0.65*100=65%So, probability that a student applying for business program gets selected is 65%.
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(−x3+26x2−7x−13)+(6x4−x3+8x+27)
Express the answer in standard form.
Enter your answer in the box.
Answer:
6x^4−2x^3+26x^2+x+14
Step-by-step explanation:
−x^3+26x^2−7x−13+6x^4−x^3+8x+27
= 6x^4−x^3−x^3+26x^2−7x+8x−13+27
= 6x^4−2x^3+26x^2+x+14
Answer:
Step-by-step explanation:
= -x3+ 26x2- 7x-13+6x4-x3+8x+27
=6x4-2x3+26x2+x+14
A rectangle has an area of 616 m² and a width of 22m. What is its length?
Answer:
l=28m
w Width
22
m
A Area
616
m²
Using the formula
A=wl
Solving forl
l=A
w=616
22=28m
hope this will help you
make me brainliest
Answer:
Solve for length
l=28m
W= Width
22
m
A= Area
616
m²
Using the formula
A=wl
Solving formula
l=A
W=616
22=28m
If a right circular cone has radius 4 cm and slant height 5cm then what is its volume?
Answer:
V≈50.27cm³
Step-by-step explanation:
Using the formulas
V=πr2h
3
l=r2+h2
Solving forV
V=1
3πr2l2﹣r2=1
3·π·42·52﹣42≈50.26548cm³
Tenisha solved the equation below by graphing a system of equations.
log35x = log (2x+8)
Which point approximates the solution for Tenisha's system of equations?
0 (0.9, 0.8)
O (1.0, 1.4)
O (2.3, 1.1)
O (2.7, 13.3)
Answer:
Option B.)
Step-by-step explanation:
Just took the test and got 100% :]
The system of logarithmic equation is graphed and the point of intersection of the equation is log₃ ( 5x ) = log₅ ( 2x + 8 ) is A ( 1.0 , 1.4 )
What is Equation of Graph of Polynomials?Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.
Identify the even and odd multiplicities of the polynomial functions' zeros.
Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.
The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities
Given data ,
Let the solution to the logarithmic equation be represented as A
Now , the value of A is
log₃ ( 5x ) = log₅ ( 2x + 8 )
On simplifying , we get
log₃ ( 5x ) = log₁₀ ( 5x ) / log₁₀ ( 3 )
log₅ ( 2x + 8 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )
Substituting the logarithmic quantities , we get
log₁₀ ( 5x ) / log₁₀ ( 3 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )
On cross multiplying , we get
log₁₀ ( 5x ) / log₁₀ ( 2x + 8 ) = log₁₀ ( 3 ) / log₁₀ ( 5 )
( 5x ) / ( 2x + 8 ) = 3/5
On cross multiplying , we get
25x = 6x + 24
Subtracting 6x on both sides , we get
19x = 24
Divide by 19 on both sides , we get
x = 1.26
Therefore , the approximate values of the function on graphing is A ( 1.0 , 1.4 )
Hence , the solution of function from graphing is A ( 1.0 , 1.4 )
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Please help ASAP please help me
9514 1404 393
Answer:
C) 12 cm
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratios of side lengths are ...
1 : √3 : 2
This means the hypotenuse (AC) is 2/√3 times the length of the long side (AB).
(10 cm)(2/√3) = 20/√3 cm ≈ 11.55 cm
Rounded to the nearest cm, the length of AC is 12 cm.
How many different 5-digit numbers can be written using only numbers 0, 1, 2, 3, and 4, if number should contain each of these numbers: only once?
Answer:
3125
Step-by-step explanation:
5* 5* 5* 5 = 3125
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.06 0.20 0.07 2 0.05 0.14 0.33 (a) What is P(X
Answer:
[tex]P(x = 1) = 0.33[/tex]
[tex]P(y = 2) = 0.42[/tex]
Step-by-step explanation:
Given
y
x [tex]\begin{array}{cccc}P(x,y) & {0} & {1} & {2} & {0} & {0.10} & {0.03} & {0.02} & {1} & {0.06} & {0.20} & {0.07} & {2} & {0.05} & {0.14} & {0.33}\ \end{array}[/tex]
Solving (a)
[tex]P(x = 1)[/tex]
To do this, we simply add all data where x = 1
So, we have:
[tex]P(x = 1) = P(x=1|y=0) + P(x=1|y=1) + P(x=1|y=2)[/tex]
[tex]P(x = 1) = 0.06 + 0.20 + 0.07[/tex]
[tex]P(x = 1) = 0.33[/tex]
Solving (b)
[tex]P(y = 2)[/tex]
To do this, we simply add all data where y = 2
So, we have:
[tex]P(y = 2) = P(x=0|y=2) + P(x=1|y=2) + P(x=2|y=2)[/tex]
[tex]P(y = 2) = 0.02 + 0.07 + 0.33[/tex]
[tex]P(y = 2) = 0.42[/tex]
