Data:
Total distance: 450 miles
Total time: 8 h
Average 60 mi/h before noon
Average 50 mi/h afternoon
The relationship between the time, speed (average) and distance is drescribed in the next equations:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ d=s\times t \\ \\ \end{gathered}[/tex]Then, if you multiply the speed and the time you get the distance:
time before noon: b
time afternoon: a
[tex](60\times b)+(50\times a)=450[/tex]The sum of a and b is the total time:
[tex]a+b=8[/tex]Use the next system of equations to find a and b:
[tex]\begin{gathered} 60b+50a=450 \\ a+b=8 \end{gathered}[/tex]1. Solve a in the second equation:
[tex]\begin{gathered} \text{Subtract b in both sides of the equation:} \\ a+b-b=8-b \\ \\ a=8-b \end{gathered}[/tex]2. Substitute the a in first equation by the value you get in first step:
[tex]60b+50(8-b)=450[/tex]3. Solve b:
[tex]\begin{gathered} 60b+400-50b=450 \\ 10b+400=450 \\ \\ \text{Subtract 400 in both sides of the equation:} \\ 10b+400-400=450-400 \\ 10b=50 \\ \\ \text{Divide both sides of the equation into 10:} \\ \frac{10}{10}b=\frac{50}{10} \\ \\ b=5 \end{gathered}[/tex]4. Use the value of b=5 to solve a:
[tex]\begin{gathered} a=8-b \\ a=8-5 \\ a=3 \end{gathered}[/tex]Then, Jaron begin his trip 5 hours before noon ( at 7:00) and end it 3 hours afternoon (at 15:00)In the rectangle below, SU= 4x – 2, RT = 5x-10, and m Z VSR=26°.Find RV and m ZVTS.Rm
SU and RT are the diagonals of the rectangle and are thus equal.
We the equate them to find x
SU = RT = 4x - 2 = 5x - 10
subtracting 4x from both sides gives:
4x - 2 - 4x = 5x - 10 - 4x
-2 = x - 10
Adding 10 to both sides give:
10 - 2 = x - 10 + 10
x = 8
RV is half of RT
where = RT = 4(8) - 2 = 32 - 2 = 40
Therefore, RV = 40/2 = 20
To calculate angle VTS, we consider that it is in an isosceles triangle with its angle equal to angle VST. Same angle VST is complementary with angle VSR
Therefore, angle VTS = VST = 90 - 26 = 64 degrees (sum of angles in a right angle)
VTS = 64 degrees
choose correct word name for the number below. 51,104
To write the word name of a number, we start from left to right. in the thousands place, we have 51, so this is "fifty-one thousand". The rest is 104, we is "one hundred four". All together, we have:
"Fifty-one thousand one hundred four"
You have to deliver medicines 1 mile away. In order to do that, you have to which drone to use depending on the size of the blade in the drone. The equation that gives the relationship between the size of the blade (b) in inches and speed (miles/hour) is as follows: Speed = 50-2b In order to deliver the medicine in time, the drone must travel faster than 37 miles/hour. Check the box underneath the blade that you would like to use. Then write the speed of the drone using this blade.
From the information given,
The equation representing the relationship between the size of the blade (b) in inches and speed (miles/hour) is given as
Speed = 50-2b
Also, the required drone must travel faster than 37 miles/hour.
For the small blade, b = 4 inches
speed = 50 - 2 * 4 = 50 - 8
speed = 42 miles/hour
For the medium blade, b = 6 inches
speed = 50 - 2 * 6 = 50 - 12
speed = 38 miles per hour
For the large blade, b = 8
speed = 50 - 2 * 8 = 50 - 16
speed = 34 miles per hour
Since the speed of the drone with small blade is greater than 37 miles per hour and it is the greatest among the three drones,
The speed of the drone will be 42 miles per hour
The birth weights of the 908 babies born at Valley Hospital in 2019 were normally
distributed with a mean of 7.2 pounds with a standard deviation of 1.5. Use the Z-
Score Table from the book to determine the number of babies that weighed more
than 10 pounds.
The number of babies that weighed more than 10 pounds is 43 using Z-
Score Table.
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a "bell curve."
Given that total number of babies is 908.
The mean of the normal distribution is 7.2 pound.
The standard deviation of the normal distribution is 1.5 pound.
The formula of z score is z = (x - μ)/σ
In the given question x = 10, μ = 1.5, σ = 7.2
z score = (10 - 7.2)/1.5 = 1.86667
P-value from Z-Table:
P(x<10) = 0.96903
P(x>10) = 1 - P(x<10) = 0.030974
The number of babies that weighed more than 10 pounds is ( 0.030974 × 908) = 43.39 = 43 (approx.)
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Identify whether the set of ordered pairs represent an exponential. Explain your answer. x −2 0 2 4 y 4 12 36 108A. exponential functionAs the x-values are increased by a constant amount, the y-values increase by the same amount.B. not an exponential functionAs the x-values are increased by a constant amount, the y-values increase by the same amount.C. not an exponential functionAs the x-values are increased by a constant amount, the y-values are not multiplied by a constant amount.D. exponential functionAs the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
Answer:
D. exponential function
As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
Explanation:
From the table of values:
x-values
[tex]\begin{gathered} 0-(-2)=2 \\ 2-0=2 \\ 4-2=2 \end{gathered}[/tex]The x-values increase by a constant amount, 2.
y-values
[tex]\begin{gathered} \frac{12}{4}=3 \\ \frac{36}{12}=3 \\ \frac{108}{36}=3 \end{gathered}[/tex]The y-values are multiplied by a constant amount, 3.
From these, we conclude that the set of ordered pairs represents an exponential function.
As the x-values are increased by a constant amount, the y-values are multiplied by a constant amount.
The correct option is D.
Is (2,-2) a solution to the system of equations.9x = 10 - 4yу = 3х - 8-
Solution;
Given the system of equations below
[tex]\begin{gathered} 9x=10-4y...(1) \\ y=3x-8...(2) \end{gathered}[/tex]To find out if (2, -2) is the solution to the given system of equations, we solve for x and y
Applying the substitution method to solve the system of equations
Substitute for y in equation (1)
[tex]undefined[/tex]The polar equation r=8sin(4θ) graphs as a rose.What is the length of the petals of this rose?
Polar equations of rose curves follow the pattern:
[tex]r=a\text{ }sin\text{ }n\theta\text{ }[/tex]where:
a = represents the length of the petals
n = represents the number of petals.
Based on the given polar equation, the value of "a" is 8. Since "a" represents the length of the petals, then the length of the petals of this rose is 8 units.
how do u solve 6=×+3_2
To solve the equation, we should isolate x on one side and the numerical term on the other side
So we have to multiply both sides by 2 to cancel the denominator 2 from the right side
[tex]\begin{gathered} 6\times2=\frac{(x+3)}{2}\times2 \\ 12=x+3 \end{gathered}[/tex]Now want to move 3 from the right side to the left side
Subtract 3 from both sides
[tex]\begin{gathered} 12-3=x+3-3 \\ 9=x \end{gathered}[/tex]The solution is x = 9
Can I get an answer please?
the rule is reflextive
here(x, y) is changing into (x , -y)
the process is called translation
Find the radius and area of a circle with a circumference of 62.8.Round your answer to the nearest tenth. Use 3.14
Given:
circumference of 62.8
Required:
circumference of 62.8
Explanation:
Let r be the radius of the circle
Since the circumference of the circle is 62.8
[tex]\begin{gathered} 2\pi r=62.8 \\ \\ 2\times3.14\times r=62.8 \\ \\ 6.28r=62.8 \\ \\ r=\frac{62.8}{6.28} \\ \\ r=10 \end{gathered}[/tex]area of circle is
[tex]\begin{gathered} \pi r^2 \\ \\ 3.14\times10\times10 \\ \\ =314 \end{gathered}[/tex]Required answer:
10, 314
when you compare the 2016-2017 season with the 2017-2018 season, what was the percent increase in the number of games that the Lakers won ? show your work.
In order to calculate the percent increase in the number of games that the Lakers won from the 2016-2017 season with the 2017-2018 season we would have to make the following calculation:
percentage of increase=100* (games won 2017-2018-games won 2016-2017)/ (games won 2016-2017)
percentage of increase=100*(35-26)/(26)
percentage of increase=100*0.34615
percentage of increase=34.615%
The percent increase in the number of games that the Lakers won from the 2016-2017 season with the 2017-2018 was 34.615%
Solve: -2y ≥ 10y ≤ -5y ≤ 5y ≥ -5y ≥ 5
Given
[tex]-2y\ge10[/tex]Solution
Recall: Dividing by a negative number means you reverse the inequality symbol
[tex]\begin{gathered} -2y\ge10 \\ divide\text{ both sides by -2} \\ -\frac{2y}{-2}\ge\frac{10}{-2} \\ \\ y\leq-5 \end{gathered}[/tex]The final answer
[tex]y\leq-5[/tex]QuestionThe width of a rectangle is 6 less than the length, let L represent the length of the rectangle, Write an expression for thewidth of the rectangle
Since L represents the length and the width is 6 less the length, if w denotes the width, we have
[tex]w=L-6[/tex]that is, the width measures L-6
A psychologist is interested in constructing a 90% confidence interval for the proportion of
people who accept the theory that a person's spirit is no more than the complicated network of
neurons in the brain. Of those randomly selected, 50 of the 722 people agreed with this theory.
a. With 90% confidence the proportion of all people who accept the theory that a person's spirit
is no more than the complicated network of neurons in the brain is between ____ and ____.
Round to 3 decimal places.
b. If many groups of 722 randomly selected people are surveyed, then a different confidence
interval would be produced from each group. About ___ percent of these confidence
intervals will contain the true population proportion of all people who accept the theory that a
person's spirit is no more than the complicated network of neurons in the brain and about ____
percent will not contain the true population proportion.
a. The 90% confidence interval for the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between 0.053 and 0.085.
b. About 90% of the intervals will contain and about 10% of the intervals will not contain.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
The meaning of the 90% confidence level is given as follows:
90% of the intervals contain the true population proportion.10% of the intervals do not contain the true population proportion.The sample size and the estimate are given as follows:
[tex]n = 722, \pi = \frac{50}{722} = 0.069[/tex]
Hence the lower bound of the interval is given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 - 1.645\sqrt{\frac{0.069(0.931)}{722}} = 0.053[/tex]
The upper bound of the interval is given by:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.069 + 1.645\sqrt{\frac{0.069(0.931)}{722}} = 0.085[/tex]
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Find the slope between the points:(1,7)(-2,3)
Using the formula,
[tex]m=\frac{7-3}{1-(-2)}\rightarrow m=\frac{4}{1+2}\rightarrow m=\frac{4}{3}[/tex]Answer:
slope = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 7 ) and (x₂, y₂ ) = (- 2, 3 )
m = [tex]\frac{3-7}{-2-1}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex]
J and K are independent events. P(J | K) = 0.43. Find P(J)P(J) =
Explanation
We are given the following:
[tex]P(J|K)=0.43[/tex]We are required to determine P(J).
We know that since j and K are independent events, then:
[tex]P(J|K)=P(J)[/tex]Hence, the answer is:
[tex]P(J)=0.43[/tex]given : f(x) = x2 - 5 and g(x) = 3x - 1 Find 2g (f(-5))
The given functions are
f(x) = x^2 - 5
g(x) = 3x - 1
To find 2g(f(- 5)), we would first find f(- 5)
To find f(- 5), we would substitute x = - 5 into f(x) = x2 - 5. It becomes
f(- 5) = (- 5)^2 - 5
f(- 5) = 25 - 5
f(- 5) = 20
Then, we would substitute f(- 5) = 20 into g(x) = 3x - 1
Thus,
g(f(- 5) = 3*20 - 1
g(f(- 5) = 60 - 1
g(f(- 5) = 59
Therefore,
2g(f(- 5)) = 2 * 59 = 118
(3x+30) line p and q are parallel solve for x
The two angles are alternate external, because they are on the external side of the parallel lines and on alternate sides of the transversal one. This means that they are congruent. So we can find the value of x by making their expressions equal and solving for x.
[tex]\begin{gathered} 4x=3x+30 \\ 4x-3x=30 \\ x=30 \end{gathered}[/tex]The value of x is 30°
Meredith did some research on the ages of the male U.S. Olympic swimmers. She made a dot plot for the data . 20 21 22 23 24 25 26 27 28 29 Age of male US. Olymple swimmers years) According to Meredith's data, what is the typical age of a male U.S. Olympic swimmer? O A. 21 years O B. 26 years O C. 20 years OD. 29 years
Solution
we have the following set of data from the table given
21,24,25,25,25,26,26,26,26,27,29
The typical age = (21+24+25+25+25+26+26+26+26+27+29)/10
= 255/10
= 25.5 approximately = 26
Final Answer = 26
For a given set of rectangles, the length is inversely proportional to the width. In one
of these rectangles, the length is 25 and the width is 3. For this set of rectangles,
calculate the width of a rectangle whose length is 5.
Answer:
Step-by-step explanation:
Answer:
The width is 8 units
Step-by-step explanation:
This is a variation problem we are to work with.
Length is inversely proportional to width, let length be l and width be w
modeling the statement mathematically, we have lw = k where k is the proportionality constant
Now let’s get k from l = 12 and w = 6
k = 12 * 6 = 72
Now for the second rectangle also;
lw = k given l = 9
9w = 72
w = 72/9
w = 8
f(x) = log x + 2 and g(x) = log (1/x). Find (f – g) (x).log x -2 – log (1/x)22 log x + 2(2/log x) + 1
We have to find (f-g)(x) given that f(x) = log x + 2 and g(x) = log(1/x).
We can find it as:
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x) \\ (f-g)(x)=\log x+2-\log(\frac{1}{x}) \\ (f-g)(x)=\log x+2-(\log1-\log x) \\ (f-g)(x)=\log x+2-0+\log x \\ (f-g)(x)=2\log x+2 \end{gathered}[/tex]Answer: 2log(x) + 2
balloon 670 meters away angle 42degrees the higher balloon is 945 away angle 36 degrees how much higher is the balloon on the right than the left
Answer:
[tex]h1-h2=686.582689-603.2707097=83.31198832m[/tex]match the property to the correct step in the problemA.) addition property of equality. B.) subtraction property of equalityC.) distributive property
In the first step
It is distributive property because we multiplied 10 by 2x and 10 by 4
1. C
In the second step
We add 6x to both sides, then
It is addition property of equality
2. A
In the third step
We subtract 40 from both sides, then
It is the subtraction property of equality
3. B
I need to know what goes in the boxes for this practice question.
From the question given;
5 = 2/5 m
25 = 2m
Divide both-side by 2
25 /2 = m
m = 25/2
Now to solve for H
( H + [ 1 4 -2 ] ) + [ 3 2 -6 ] = [-2 3 -1] + ( [1 4 -2] + [ 3 2 -6] )
( H + [ 4 6 - 8 ] )= [ -2 3 - 1] + [ 4 6 - 8 ]
( H + [ 4 6 - 8 ] = [ 2 9 -9 ]
Subtract [4 6 -8] from both-side
H = [ 2 9 -9 ] - [ 4 6 -8 ]
= [-2 3 - 1]
m x H = [ 25/2 * -2 25/2 * 3 25/2 * -1 ]
m x H = [ -25 75/2 -25/2 ]
For each equation state the number of complex roots, the possible number of positive real roots,and the possible rational roots x^4+8x^2+2=0
The given equation is,
[tex]x^4+8x^2+2=0[/tex]Fundamental Theorem of Algebra says that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial). A straightforward corollary of this (often stated as part of the FTOA) is that a polynomial of degree n with Complex (possibly Real) coefficients has exactly n Complex (possibly Real) zeros counting multiplicity.
Therefore, the equation will have 4 roots.
Descartes’s rule of signs says the number of positive roots is equal to changes in sign of f(x), therefore, the given equation does not have positive real roots.
Therefore, the equation will have 4 complex rooots.
9+9x=10x+2 Solve for x
This problem is about linear equations.
To solve it, we need to find the value of x.
[tex]9+9x=10x+2[/tex]First, we need to organize the equation, all terms without variables at the right side, and all terms with variables at the left side
[tex]9x-10x=2-9\text{ }\rightarrow-x=-7[/tex]Finally, we multiply the equation by -1 to get the proper answer
[tex]x=7[/tex]Therefore, the answer is 7.Use the graph of the function F shown here to find f(1), f(2), f(3).
The value of f(x) is reflected over the y-axis.
Obtain f(1) as follows,
Draw a vertical line at x=1 to intersect the curve.
From this point of intersection, draw a horizontal line to intersect the y-axis at y=3.
Therefore, the value of f(1) is 3.
Obtain f(2) as follows,
Draw a vertical line at x=2 to intersect the curve.
From this point of intersection, draw a horizontal line to intersect the y-axis at y=8.
Therefore, the value of f(2) is 8.
Obtain f(3) as follows,
Draw a vertical line at x=3 to intersect the curve.
From this point of intersection, draw a horizontal line to intersect the y-axis at y=7.
Therefore, the value of f(3) is 7.
experimental and theoretical
Spinning a three:
experimental = 11/50
theoretical = 1/5
Spinning an even number:
experimental = 21/50
theoretical = 2/5
Spinning an odd number:
experimental: 29/50
theoretical: 3/5
Spinning a number less than 5:
experimental: 21/25
theoretical: 4/5
Solve for y.2x – 8y = 24
Answer:
[tex]y=\frac{1}{4}x-3[/tex]Explanation:
Given the equation:
[tex]2x-8y=24[/tex]To solve for y, we follow the steps below:
Step 1: Rearrange to Isolate the term containing y.
[tex]8y=2x-24[/tex]Step 2: Divide both sides by 8.
[tex]\begin{gathered} \frac{8y}{8}=\frac{2x-24}{8} \\ y=\frac{2x-24}{8} \end{gathered}[/tex]Step 3: Simplify
[tex]\begin{gathered} y=\frac{2x}{8}-\frac{24}{8} \\ y=\frac{1}{4}x-3 \end{gathered}[/tex]what is the surface area of a rectangular prism if the measures are 13, 9, 4