According to the given data we have the following:
Javier exercises for 2 1/2 hours every Saturday, hence, he exercises for 2.5 hours.
In order to calculate the amount of time he spend weightlifting we would make the following calculation:
amount of time he spend weightlifting=total training per day/2
amount of time he spend weightlifting=2.5 hours/2
amount of time he spend weightlifting=1.25 hours
Therefore, he spends weightlifting 1 hour and 25 minutes every saturday
A radar unit is used to measure speeds of a car on a motorway. Speeds are normal distributed with a mean of 90 km an hour and a standard deviation of 10 km an hour. What is the probability that a car picked at random is traveling out more than 100 km an hour
let x is the random variable that represents the speed of car.
[tex]\begin{gathered} \mu(\operatorname{mean})=90 \\ \sigma=10 \end{gathered}[/tex]probability that x is higher than 100 :
[tex]P(x>100)[/tex]for x=100:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ z=\frac{100-90}{10} \\ z=1 \end{gathered}[/tex]so,
[tex]p(x>100)=p(z=1)[/tex]probability =total area - area of the left of (z=1)
[tex]\begin{gathered} \text{probability}=1-0.8413 \\ p(x>100)=0.1587 \end{gathered}[/tex]and the area of the left of z=1 is 0.8413 (from normal distribution)
Nolan is deciding between two truck rental companies. Company A charges an initialfee of $90 for the rental plus $2 per mile driven. Company B charges an initial fee of$50 for the rental plus $3 per mile driven. Let A represent the amount Company Awould charge if Nolan drives I miles, and let B represent the amount Company Bwould charge if Nolan drives a miles. Write an equation for each situation, in termsof 2, and determine the number miles driven, , that would make the cost of eachcompany the same.
first we writte the information they are giving to us:
For company A:
initial fee = $90
rent per mile = $2
For combany B:
initial fee = $50
rent per mile = $3
Now for company A the equation that represent the charge in one mile will be: (where n is the number of miles)
[tex]\begin{gathered} A=90+2(n) \\ A=90+2(1) \\ A=90 \end{gathered}[/tex]And for company B:
[tex]\begin{gathered} B=50+3n \\ B=50+3(1) \\ B=53 \end{gathered}[/tex]Now to determine the number miles driven, that would make the cost of each company the same, we have to make A = B
[tex]\begin{gathered} A=B \\ 90+2n=50+3n \\ \end{gathered}[/tex]and finaly we can solve for n
[tex]\begin{gathered} 90-50=3n-2n \\ 40=n \end{gathered}[/tex]so if they drive for 40 miles the will pay the same
Victoria's speedboat can travel 105 miles upstream against a 4-mph current in the same amount of time it travels 125 miles downstream with a 4-mph current. Find the speed of Victoria's boat.
Recall that:
[tex]\text{ time }=\frac{\text{ distance}}{\text{ speed}}[/tex]Let Victoria's speed be v.
Therefore, Victoria's resultant speed upstream is v - 4 and her resultant speed downstream is v + 4.
Hence the time of journey upstream is given by:
[tex]\frac{105}{v-4}[/tex]And the time of journey downstream is given by:
[tex]\frac{125}{v+4}[/tex]Since the time of journey upstream is the same as the time of journey downstream, it follows that:
[tex]\begin{gathered} \frac{105}{v-4}=\frac{125}{v+4} \\ \text{ Divide both sides by }5: \\ \frac{21}{v-4}=\frac{25}{v+4} \\ \text{ Cross-multiplying, we have:} \\ 21(v+4)=25(v-4) \\ \text{ Expanding the expressions, we have:} \\ 21v+84=25v-100 \\ 25v-21v=100+84 \\ 4v=184 \\ v=\frac{184}{4}=46 \end{gathered}[/tex]Therefore, Victoria's speed is 46 mph
Use the graph of the function to estimate the intervals on which the function is increasing or decreasing. (Enter your answers using interval notation.)
The intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)
What is the graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Increased or decreased functions are two categories of functions. Consequently, a function increases when the y-values grow, while a function decreases when the y-values decrease.
The graph indicates the y-values increase in the x-intervals from -∞ to 0 and from 3.5 to ∞. You can express that a function is increasing in the following ways using interval notation: (-∞, 0) U (3.5, ∞).
The graph, on the other hand, is decreasing: (0, 3.5)
Hence, the intervals on which the graph is increasing at (-∞, 0) U (3.5, ∞). On the other hand, the graph is decreasing at (0, 3.5)
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I only need the answer
THANK YOU!!
Answers:
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}} = -\frac{2\sqrt{5}}{15}\\\\\csc(\theta) = \frac{7}{2}\\\\\sec(\theta) = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\\cot(\theta) = \frac{-3\sqrt{5}}{2}\\\\[/tex]
=================================================
Explanation:
We're given that [tex]\sin(\theta) = \frac{2}{7}\\\\[/tex]
Plug that into the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\[/tex] and solve for cosine to find that [tex]\cos(\theta) = \frac{-3\sqrt{5}}{7}\\\\[/tex]
I skipped steps in solving so let me know if you need to see them.
Keep in mind that cosine is negative in quadrant 2
------------------
Once you've determined cosine, divide sine over cosine to get tangent
[tex]\tan(\theta) = \sin(\theta) \div \cos(\theta)\\\\\tan(\theta) = \frac{2}{7} \div \frac{-3\sqrt{5}}{7}\\\\\tan(\theta) = \frac{2}{7} \times -\frac{7}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2*7}{7*3\sqrt{5}}\\\\\tan(\theta) = -\frac{2}{3\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3\sqrt{5}*\sqrt{5}}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{3*5}\\\\\tan(\theta) = -\frac{2\sqrt{5}}{15}\\\\[/tex]
------------------
To determine cosecant, we apply the reciprocal to sine.
[tex]\sin(\theta) = \frac{2}{7} \to \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{7}{2}\\\\[/tex]
Similarly, secant is the reciprocal of cosine
[tex]\cos(\theta) = \frac{-3\sqrt{5}}{7} \to \sec(\theta) = \frac{1}{\cos(\theta)} = -\frac{7}{3\sqrt{5}} = -\frac{7\sqrt{5}}{15}\\\\[/tex]
Depending on your teacher, rationalizing the denominator may be optional.
Lastly, cotangent is the reciprocal of tangent
[tex]\tan(\theta) = -\frac{2}{3\sqrt{5}}\to \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{-3\sqrt{5}}{2}[/tex]
------------------
Side notes:
Sine and cosecant are the only things positive in Q2
Everything else (cosine, tangent, secant, cotangent) are negative in Q2.
Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (8n-4)(n^2+9) This simplifies to: AnswerThe degree of our simplified answer is: Answer
Answer
[tex]\begin{gathered} \text{ Question 1:} \\ 8n^3-4n^2+72n-36 \\ \\ \text{Qusetion 2:} \\ \text{THE DEGREE OF THE POLYNOMIAL IS 3} \end{gathered}[/tex]
SOLUTION
Problem Statement
The question gives us an expression to simplify and we are to simplify by finding the product. We are also asked to find the degree of the polynomial as well
Method
We simply need to expand the bracket to solve this question. But the degree of the polynomial is gotten by assessing which term in the final expression has the highest power. If the expression has a term with its highest power being 3, then the degree of the polynomial is 3.
With this information, let us begin solving.
Implementation
1. Expanding the expression:
Expanding the polynomial, we have:
[tex]\begin{gathered} (8n-4)(n^2+9) \\ \text{ Using the FOIL method,} \\ F=8n(n^2)=8n^3 \\ O=8n(9)=72n \\ I=-4(n^2)=-4n^2 \\ L=-4(9)=-36 \\ \\ \therefore(8n-4)(n^2+9)=8n^2+72n-4n^2-36 \\ \\ \text{ Remember, we are asked to write this result in descending order of terms. Thus, we have that:} \\ 8n^3-4n^2+72n-36 \end{gathered}[/tex]2. Degree of the polynomial:
From the above result, we can see that the highest degree of n in all the terms is 3, therefore, the degree of the polynomial is 3
Final answer
[tex]\begin{gathered} \text{ Question 1:} \\ 8n^3-4n^2+72n-36 \\ \\ \text{Qusetion 2:} \\ \text{THE DEGREE OF THE POLYNOMIAL IS 3} \end{gathered}[/tex]
Express Your Answer As A Polynomial In Standard Form.
f(x)= x-7
g(x)= 3x^2-7x-10
Find (f o g)(x)
Look at photo
According to the solving the Polynomial Standard Form of the given equation is :
3x^2-7x-17.
What is Polynomial Standard Form?When expressing a polynomial in its standard form, the greatest degree of terms are written first, followed by the next degree, and so on. When x is the variable and ai are coefficients, the polynomial has the conventional form f(x) = anxn + an-1xn-1 + an-2xn-2 +... + a1x + a0.
According to the given data:f(x)= x-7
g(x)= 3x^2-7x-10
f(x)= x-7 by substituting in the value of g into f.
f(3x^2-7x-10) = (3x^2-7x-10)-7
= 3x^2-7x-17
According to the solving the slandered form of the given equation is :
3x^2-7x-17
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A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.09.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
The probability that there are fewer than 3 tornadoes in a 14-year period is 0.992333
Let x = number of tornados
n = 14
p = 0.03
There are just two outcomes that can occur in these independent, fixed trials, and the success probability is 0.03
Consequently, we may determine the probability using the binomial distribution.
Here we want to find P( X < 3) = P( X < = 3-1) = P(X <=2)
Using Excel:
P( X <=2) = "=BINOMDIST(2,14,0.03,1)" = 0.992333
Be aware that the default Excel command to find binomial probabilities that are less than or equal is "=BINOMDIST(x, n, p, 1)"
Therefore, 0.9923333 percent of the time there won't be more than 3 tornadoes in a 14-year period.
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Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (8,-4) and perpendicular to the line whose equation is x-6y-5=0
Answer:
y + 4 = -6 (x - 8)
Step-by-step explanation:
Change the equation to the slope intercept form for a line
x - 6y 5 = 0 Add 5 to both sides
x - 6y = 5 Subtract x from both sides
-6y = -x + 5 Divide both sides by -6
y = [tex]\frac{1}{6}[/tex] c - [tex]\frac{5}{-6}[/tex] Your slope is [tex]\frac{1}{6}[/tex]
A perpendicular slope is the opposite reciprocal of [tex]\frac{1}{6}[/tex], that would be -6
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex]) Plug is -4 for [tex]y_{1}[/tex] and 8 for [tex]y_{1}[/tex]
y - -4) -6(x-8)
y + 4= -6 (x -8)
Find the area of
8 in
3 in
10 in
4.5
Answer:
Step-by-step explanation:
square kilometre (km 2): 1,000,000 hectare: 10,000
Unit: Area in m 2 square meter: SI Unit
There exist more distinctions and classifications for different types of
trapezoids, but their areas are still calculated in the same manner using the
following equation: area = b 1 + b 2 2 × h where b1 and b2 are the bases. h is the height, or perpendicular distance between the bases The Farmer and his Daughter – Ramping Endeavors
y+ 4X=0 linear or nonlinear
Answer:
linear
Step-by-step explanation:
y+4x=0
-4x -4x
=y=-4x+0
it is in the y=mx+b form so it is linear
Given the Frequency Distribution: (SHOW WORK)
Find the:
(A) Range
(B) Mean
(C) Mode
(D) Median
(E) Variance
(F) Standard Deviation of This Sample
The measures of the frequency distribution is;
(A) Range = 7
(B) Mean = 29
(C) Mode = 12
(D) Median = 29
(E) Variance = 7.612
(F) Standard Deviation = 2.759
How to solve frequency distribution?
A) The range of a frequency distribution is;
Range = Highest Value - Lowest Value
Thus;
Range = 32 - 25
Range = 7
B) Mean is expressed as;
x' = ∑fx/∑f
x' = [(25 * 4) + (26 * 6) + (28 * 6) + (30 * 4) + (32 * 12)]
x' = 928/32
x' = 29
C) Mode is the value with the highest frequency and so in this case;
Mode = 12
D) Median is the middle term when arranged from lowest to highest. In this case, it is the 16.5th term. Thus; Median = (28 + 30)/2 = 29
E) Variance = 7.612
F) The standard deviation is;
σ = √Variance
σ = 2.759
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You pick a card at random, put it back, and then pick another card at random.
4 5 6 7
What is the probability of picking a 7 and then picking an odd number?
Simplify your answer and write it as a fraction or whole number.
=======================================================
Explanation:
A = probability of picking a 7
A = 1/4 since one card is labeled "7" out of four cards total
B = probability of picking an odd number
B = 2/4 = 1/2 because there are 2 cards that are odd (5 and 7) out of 4 cards total.
C = A*B = probability events A and B happen
C = (1/4)*(1/2)
C = 1/8
This only works when we put the first card back, which means each event is independent.
Log z 2 + log 2x
pahelp po
Tell how many tens & onesWrite the number and the word name
Every column have 7 bricks
There are 8 columns,
Then there are
8x7 = 56 bricks + another 7 bricks = 63 bricks
Divide now 63 between 10
63/10 = 6 tens + 3 ones
ANSWER IS
6 TENS 3 ONES
PLS HELP ME WITH THIS
you need to use the y=mx+b
Hello!
What is a slope-intercept line:
[tex]y = mx + b[/tex]
m: slope[tex]slope = \dfrac{y_2-y_1}{x_2-x_1} =\frac{-4--2}{3-0} =-\dfrac{2}{3}[/tex]
y-intercept or point whose x-coordinate is '0'==> value of y-intercept is '-2'
Thus the equation is [tex]y=-\dfrac{2}{3}x-2[/tex]
Hope that helps!
Answer: y=-2/3x-2
Step-by-step explanation:
1) Draw a triangle from one point to the next point.
For this example, I will use (-3,0) and (0,-2).
You can see that the number goes down 2 and right 3. From this, you can conclude that the rate is -2/3 using the equation rise/run.
2) Find the y-intercept
Looking at the graph, you can find that the y-intercept is (0,-2).
3) Fill in the y=mx+b
y=-2/3x-2
This graph shows the height in inches, `h`, of a bamboo plant `t` months after it has been planted.
Write an equation that describes the relationship between `t` and `h`.
Drag the movable point to trace along the line if that helps you with your thinking.
The graph that shows the relationship between the height of the bamboo and months planted is given as h = 5t + 10
How to solve an equation?Given that the graph shows the relationship between the height (h) of a bamboo plant after months it has been planted.
Let us assume that h is plotted on the vertical axis and months (t) is planted on the horizontal axis.
If the graph passes through the points (0, 0) and (2, 10), hence:
h - 10 = [(10 - 0)/(2 - 0)](t - 0)
h - 10 = 5(t)
h = 5t + 10
The graph is given as h = 5t + 10
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What is the equation of the line that passes through the point (5, 0) and has a slope of 6/5?
Answer:
[tex]y=\frac{6}{5}(x-5)[/tex]
Step-by-step explanation:
Use point-slope form.
What value is equivalent to (8+2)2 + (6 − 4) × 3?
Answer:
26
Step-by-step explanation:
PEMDAS
8 + 2 = 10
6 - 4 = 2
10 x 2 = 20
2 x 3 = 6
20 + 6 = 26
The number of classified documents has increased approximately linear from 8.2 million documents in 2001 to 17. 4 million documents in 2005. let in be the number of documents in millions labeled as classified in the year that is years since 2000 find the equation of the linear model to describe the data
Knowing that
- The number of classified documents has increased linearly.
- In 2001 there were 8.2 million documents.
- In 2005 there were 17.4 million documents.
- The variable "n" represents the number of documents (in millions) labeled as classified.
- The variable "t" represents the number of years since 2000.
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept.
The slope of a line can be found using this formula:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]Where these two points are on the line:
[tex](x_1,y_1),(x_2,y_2)[/tex]In this case, you know these two points:
[tex](1,8.2),(5,17.4)[/tex]Then, you can substitute values into the formula and find the slope of the line:
[tex]m=\frac{17.4-8.2}{5-1}=\frac{9.2}{4}=2.3[/tex]Now you know that the form of the equation is:
[tex]n=2.3t+b[/tex]In order to find "b", you need to:
- Choose one of the points on the line:
[tex]\mleft(1,8.2\mright)[/tex]- Identify the value of each variable. Notice that:
[tex]\begin{gathered} n=8.2 \\ t=2001 \end{gathered}[/tex]- Substitute those values of "n" and "t", and the slope into the equation:
[tex]8.2=2.3(1)+b[/tex]- Solve for "b":
[tex]\begin{gathered} 8.2=2.3+b \\ 8.2-2.3=b \\ b=5.9 \end{gathered}[/tex]Therefore the equation of the Linear Model is:
[tex]n=2.3t+5.9[/tex]Hence, the answer is: Option D.
What is the quotient in simplest form? State any restrictions on the variable.see image
we have the expression
[tex]\frac{z^2-4}{z-3}\div\frac{z+2}{z^2+z-12}[/tex]Multiply in cross
[tex]\frac{(z^2-4)(z^2+z-12)}{(z-3)(z+2)}[/tex]Simplify
z^2-4=(z+2)(z-2) -----> difference of squares
z^2+z-12=(z+4)(z-3)
substitute in the above expression
[tex]\frac{\mleft(z+2\mright)\mleft(z-2\mright)\mleft(z+4\mright)\mleft(z-3\mright)}{(z-3)(z+2)}[/tex]Simplify
[tex](z-2)(z+4)[/tex]The function is defined by h(x) = (4 + x)/(- 3 + 3x) Find h(4x) .
Given h(x), find h(4x) as shown below
[tex]h(4x)=\frac{4+(4x)}{-3+3(4x)}=\frac{4+4x}{-3+12x}[/tex]Thus, the expanded form of h(4x) is (4+4x)/(-3+12x)What’s the correct answer answer asap for brainlist
Answer:
B. radio stations stopped advertising
Answer:
As televisions became more affordable and advertisers flocked to the new medium, radio stations had to quickly adapt to the changing field. Stations stopped using live in-studio performances, instead playing less expensive recordings.
Step-by-step explanation:
In the 1950s, television surpassed radio as the most popular broadcast medium, and commercial radio programming shifted to narrower formats of news, talk, sports and music. Religious broadcasters, listener-supported public radio and college stations provide their own distinctive formats.
Solve these problems.
The solutions will be (x-2)(x+1), (3x+5)(5x+2) and (x+1)(x-1) respectively using factorization.
What is factorization?A number or other mathematical object is factorized or factored in mathematics by writing it as the product of numerous factors, typically smaller or simpler things of the same kind.
18) 8x³-8x²-16x = 0
Taking 8x common we get,
8x(x²-x-2) = 0
x²-x-2 = 0×8x
x²-(2-1)x-2 = 0
x²-2x+x-2 = 0
x(x-2)+1(x-2) = 0
(x-2)(x+1) = 0
Hence, the factors are (x-2)(x+1).
19) 15x³+31x²+10x = 0
Taking x as common as we get,
x(15x²+31x+10) = 0
Factorize 15x²+31x+10=0
15x²+(25+6)x+10=0
15x²+25x+6x+10=0
5x(3x+5)+2(3x+5)=0
(3x+5)(5x+2)=0
Hence the factors are (3x+5)(5x+2).
20) x³-x=0
Taking x as common as we get,
x(x²-1)=0
x²-1=0
(x+1)(x-1)=0
Hence the factors are (x+1)(x-1).
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3. An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
What is the probability of selecting four packages that are underweight?
If an automatic machine inserts mixed vegetables into a plastic bag. the probability of selecting four packages that are underweight is: 0.000000390625
ProbabilityProbability can be defined as the tendency or likelihood that an event will happen.
We would be making use of multiplication rule to determine the probabiliy that four packages are underweight.
Given :
Underweight = 2.5 % or 0.025
Hence,
Now let find the probability that P (all four underweight) :
P(all four underweight) = ( 0.025 ) ( 0.025 ) ( 0.025 ) ( 0.025 )
P(all four underweight) = 0.000000390625
Therefore we can conclude that the probability is 0.000000390625.
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Yvonne wants to use a dissection argument to justify the formula for the area of a circle. She dissects the circle into congruent sectors and reassembles the sectors as a parallelogram-like figure. The diagram below shows the arrangement for a circle dissected into 8 sectors. M Height Base Yvonne knows that as the number of sectors of the circle increases, the reassembled figure becomes closer and closer to an actual parallelogram so that it can be used to determine the area of the circle. Determine the value of each characteristic of the parallelogram in the table below. Select the best value for each characteristic.base of the parallelogram height of the parallelogram area of the parallelogram
Each sector is formed like a triangle with a circle base. The sum of all the bases should be equal to half the length of the circle's circumference, this is calculated with the following expression:
[tex]\text{base}=\frac{2\pi r}{2}=\pi r[/tex]This is the base of the parallelogram.
The height of each triangle is the radius of the circle, therefore:
[tex]\text{height}=r[/tex]The area of the parallelogram is the product of the base and the height.
[tex]\text{Area =}\pi r^2[/tex]So the base is pi*r;
The height is r;
The area is pi*r².
Describe a series of transformations Matt can perform to device if the two windows are congruent
Answer:
the transformation matt can from A
What is the product of
(5+2i) and (-3 - 4i)?
Answer:
-7 - 26i
Step-by-step explanation:
(5+2i)(-3 - 4i)
take this and distribute them to each other
-15 -20i -6i -8i^2
then combine like terms
-15-26i-8i^2
i^2 is always equal to -1, so replace i^2 with -1 in the problem
-15-26i-8(-1)
now solve
-15-26i+8
now combine like terms and you have your answer
-7-26i
You put together allowance money and head toward a distant planet forsome routine experiments on alien life forms. You abduct 12 aliens from thestrange planet, and you capture the internal body temperature of each(harmlessly of course). That data is presented above. Does this species ofaliens have an average internal body temperature less than that of the humanaverage of 98.6°F?
Solution
The mean of the internal body temperature of the 12 abducted aliens is given by;
[tex]\frac{96.8+98.3+97.6+98.5+97.5+97.5+98.5+65.6+95.4+98+97.4}{12}=87.14<98.6[/tex]Danielle earns $36.80 for 4 hours of yardwork. How much does Danielle earn for 10 hours of yardwork?