Answer:
147 sodas88 hot dogsStep-by-step explanation:
This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.
SetupLet s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...
s +h = 235 . . . . . combined totals -h = 59 . . . . . . difference in the quantitiesSolutionAdding the two equations eliminates one variable.
(s +h) +(s -h) = (235) +(59)
2s = 294 . . . . simplify
s = 147 . . . . . .divide by 2
h = 147 -59 = 88 . . . . h is 59 less
147 sodas and 88 hot dogs were sold.
__
Additional comment
The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)
Find the area of this triangle.
Round to the nearest tenth.
10 cm
55°
12 cm
[? ]cm²
Enter
Answer:
Area = 49.15
Step-by-step explanation:
area = 0.5 * side a * side b * sin(Angle)
area = 0.5 * 10 * 12 * sin(55)
area = 60 * 0.8192
49.15
Simplify the following.
7² =
4⁰ =
6-¹=
Answer:
49
1
1/6
Step-by-step explanation:
7^2 is just 7 * 7 = 49
4^0 = 1, since anything to the power of 0, is 1.
[tex]6^{-1}[/tex] is equal to [tex]\frac{1}{6}[/tex] since [tex](\frac{a}{b})^{-x}=(\frac{b}{a})^x=\frac{b^x}{a^x}[/tex]. Whenever you have a negative exponent, you flip the fraction, in this case the fraction is 6/1 so it becomes 1/6. then distribute the exponent across the division and you get 1^1/6^1 which is just 1/6
Answer:
491Step-by-step explanation:
hey
please like my question
In the video, the water level was 15 milliliters before adding the chain, and 20 milliliters after adding the chain. When I weighed the chain, its mass was 73.5 grams.
I believe the chain is solid metal (not gold plated), but is probably a blend of gold and other metals. I looked up that gold has a density of 19.3 g/ml, while the other metals like silver and copper usually blended with gold have a combined density of about 9.7 g/ml.
Determine what percentage of the chain is gold, by mass, to at least 1 decimal place?
%
The population f(x), in millions, of State A of a country after x years is represented by the function shown below:
f(x) = 4(1.08)x
The graph shows the population g(x), in millions, of State B of the country after x years:
graph of exponential function g of x that curves up from left to right and goes through points 0 comma 2 and 9 comma 4
Which conclusion is correct about the populations of State A and State B?
Option 1 is correct. The correct solution about these functions is that The original population of State A was double of the original population of State B.
How to solve for the solutionThe function in the question is given as
For A:
[tex]F(x) = 4*(1.08)^x[/tex]
For B
[tex]g(x) = 2*(1.08)^x[/tex]
The exponential growth equation that is used to solve this is
[tex]h(x) = A(r)^x[/tex]
such that A is the initial and r is the rate of growth.
f(x) and g(x) are at the same rate but the exponential function is known to grow faster.
Hence the correct option is The original population of State A was double of the original population of State B.
Complete question:Which conclusion is correct about the population of State A and State B? 1. The original population of State A was double of the original population of State B.
2. The original population of State A was half of the original population of State B.
3. The original population of State B was one-fourth of the original population of State A.
4. The original population of State A was one-fourth of the original population of State B.
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Answer:
Step-by-step explanation:
honestly thats what it is
what is the probability of getting a number less than 5 and a head when rolling a die and tossing, help someone quickly
A simple random sample of 50 items from a population with 7 resulted in a sample mean of 35.
The 90% , 99% confidence interval for the population mean is 32.145 < [tex]\rm \mu[/tex] < 35.855 and 31.093 < [tex]\rm \mu[/tex] < 36.907
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
Total Population = 50
Mean = 35
The confidence interval is given by
[tex]\rm CI = \mu + z \dfrac{s}{\sqrt n}[/tex]
[tex]\rm \mu[/tex] is the mean
z is the confidence level value
s is the standard deviation
n is the population width
(a) The 90% confidence interval for the population mean
90% [tex]\rm \alpha / 2[/tex] = 0.05
Z = 1.64
34 [tex]\rm \pm[/tex] 1.64 * 8 / √50
34 [tex]\rm \pm[/tex] 1.855
32.145 < [tex]\rm \mu[/tex] < 35.855
(b) The 99% confidence interval for the population mean
99% [tex]\rm \alpha / 2[/tex] = 0.005
Z=2.57
34 [tex]\rm \pm[/tex] 2.57 * 8 / √50
34 [tex]\rm \pm[/tex] 2.907
31.093 < [tex]\rm \mu[/tex] < 36.907
Therefore the confidence interval for population mean has been determined.
The complete question is
A simple random sample of 50 items from a population width =7 resulted in a sample mean of 35. If required, round your answers to two decimal places.
a. Provide a 90% confidence interval for the population mean
b. Provide a 99% confidence interval for the population mean
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A body of mass 50 kg explodes and splits into three pieces. The first piece has a mass of 10 kg and a velocity of [-3,2] m/s, the second piece has a mass of 18 kg and a velocity of [5,-4]m/s. What is the velocity of the third piece?
Step-by-step explanation:
From the conversation of angular momentum
Initial momentum=final momentum
Here,
Since body is initially resting, it's momentum must be zero.
Let v be velocity of third piece. Then
0= 10(-3i+2j) + 18(5i-4j) + 22v
Solving this we get,
v= 4/22(15i+13j).
The velocity of third piece is 2/11(13 j - 15i)
What is velocity?Velocity defines the direction of the movement of the body or the object.
Given:
As the body is at rest so the initial momentum is zero.
Let v be velocity of third piece.
so,
0= 10(-3i+2j) + 18(5i-4j) + 22v
0= -30i + 20j + 90i -72j + 22 v
0= 60i - 52j + 22 v
-60i +52j = 22v
v= 2/11( 13j - 15 i)
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How do you do 56 through 58? Thanks to anyone who awnsers!
Hello !
56)
[tex]5 {x}^{2} + 8x = - 1 \\ 5 {x}^{2} + 8x + 1 = 0[/tex]
[tex]\Delta = {b}^{2} - 4ac \\ = {8}^{2} - 4 \times 5 \times 1 \\ = 64 - 20 \\ = 44[/tex]
The value of the discriminant is 44.
57) ∆>0 : there are two solutions.
58)
[tex]x_1 = \frac{ - b + \sqrt{\Delta} }{2a} \\ = \frac{ - 8 + \sqrt{44} }{2 \times 5} \\ = \frac{ \sqrt{11} - 4 }{5} [/tex]
[tex] x_2 = \frac{ - b - \sqrt{\Delta} }{2a} \\ = \frac{ - 8 - \sqrt{44} }{2 \times 5} \\ = \frac{ - \sqrt{11} - 4 }{5} [/tex]
Have a nice day
56. 44
57. 2
58. Image attached.
First, let's simplify some things. Let's make this a quadratic equation.
Moving the -1 (by adding 1 to both sides) gives us 5x^2 + 8x + 1 = 0. Note that this is the standard form of a quadratic, which is ax^2 + bx + c = 0.
Now, the discriminant. The discriminant is helpful because it tells us if we have 2 real solutions, 1 real solution, or if this equation is imaginary and thus impossible to solve using elementary techniques. If the discriminant is greater (>) than 0, then it has 2 solutions. If the discriminant equals (=) 0, it has 1 solution. If the discriminant is less than (<) 0, then it is imaginary.
The discriminant of a quadratic equation is defined as b^2 - 4ac (from the quadratic formula.) We just plug in b, a and c. b will be 8, a will be 5, and c will be 1. Now we just solve. (8)^2 - 4 * 5 * 1 = 64 - 20 = 44. Since 44 is greater than 0, we have 2 solutions for this. 44 is the discriminant. (Answer to 56.) We also have 2 solutions (answer to 57.)
Now, I'll solve the quadratic equation using the quadratic formula. I'll attach my work in an image (answer to 58.)
Hope this helped!
The actual length of the ship is 575 feet. The scale of the model is 1 inch: 25 feet. What will be the length of the model?
The length of the model as described in the task content would be; 23 inches.
What is the length of the model?According to the task content, it follows that for every 25 feet measure of the actual ship length, the representation is 1 inch on the model.
On this note, for 575 feet length of the actual ship, the length of the model is; 575/25 = 23 inch.
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Please solve this❣️
Answer:
f⁻¹(1/5) = 2
Explanation:
If f(x) = (2x -3)/5
To find inverse of f(x), make x the subject.
[tex]f(x) = \dfrac{2x - 3}{5}[/tex]
[tex]5 f(x) = 2x - 3[/tex]
[tex]2x = 5 f(x) + 3[/tex]
[tex]x = \dfrac{5 f(x) + 3}{2}[/tex]
Then,
[tex]f^{-1}(x) = \dfrac{5x+3}{2}[/tex]
To find f⁻¹(1/5), simplify insert [x = 1/5 or 0.2]
[tex]f^{-1}(0.2) = \dfrac{5(0.2)+3}{2}[/tex]
which yields
[tex]f^{-1}(0.2) = 2[/tex]
Which of the following shows the simplified form of sin x/1+cos x
O sin x- tan x
O sin x-cot x
O csc x-cot x
01
Answer:
csc x - cot x
Step-by-step explanation:
(sinx)/(1+cos x)
Multiplying the numerator and denominator by (1-cos x),
((sinx)(1-cos x))/(1-cos² x)
((sinx)(1-cosx))(sin²x)
(1-cosx)/(sinx)
cscx - cot x
Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2
The solution of the linear equations will be ( -2, 4).
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given equations are:-
2x +3y = 8 and 3x+y= -2Solving the equations by elimination method:-
2x +3y = 8
3x+y= -2
Multiply the second equation by 3 and subtract from the first equation.
2x +3y = 8
-9x -3y = 6
----------------
-7x = 14
x = -2
Out of the value of x in any one equation, we will get the value of y.
3x+y= -2
3 ( -2) + y = -2
-6 + y = -2
y = 4
The graph of the equations is also attached with the answer below.
Therefore the solution of the linear equations will be ( -2, 4).
The complete question is given below:-
Exploring Systems of Linear Equations 2x +3y =8 and 3x+y= -2. Find the value of x and y and draw a graph for the system of linear equations.
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Can someone help me with this step by step with explanation im confused need help
The construction is to draw a parallel line to a given line AB passing through point P. To fix the error, the 3rd arc must be reconstructed. Thus the correct option is D. The third arc should be drawn centered at F.
The given construction involves drawing a parallel line through a given point P to a given line AB.
From the construction shown, drawing a straight line through P and G would not be parallel to the given line AB. Thus there is an error in the construction of the 3rd arc. To draw the required corresponding angle, the 3rd arc has to be reconstructed.
Therefore to fix the error the correct step to follow is: Option D. The third arc should be drawn centered at F.
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Kindly contact a 1-on-1 tutor if more explanations are needed.
ch circle shows AB that measures 60°?
O
60⁰ -0
A
60°
B
60°
.0
Mark this and return
B
B
Save and Exit
Next
Submit
Step-by-step explanation:
there are a lot of typos and missing info in your problem and answer option definition.
based on what I understood the answer should be
"the second answer option".
this is where A and B have an arc angle (or inner angle at the center of the circle) of 60°.
one could see the 3rd answer to be right too, as the angle between A and B at Y is also 60°.
but I don't think this is really the meaning of this question here.
Write the number in numerical form-twenty-six thousandths
9. The measure of each exterior angle of a regular pentagon is
the measure of each exterior
angle of a regular nonagon.
Answer:
55,55
Step-by-step explanation:
hereakaigdidjuwjapwwjshd
14. Find the value of X round the nearest degree 12 15
The measure of the angle x is 53.13 degrees after applying the sin ratio.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Applying sin ratio:
sinx = 12/15
sinx = 0.8
x = 53.13 degrees
Thus, the measure of the angle x is 53.13 degrees after applying the sin ratio.
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Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60 and from a second position L=30 farther along this path it is B=50 What is the height of the tree?
The height of the tree based on the information is 229.23.
How to calculate the height?Based on the information given,
tan 50 = h/x + 60
h = (x + 60)tan 50°
x tan 60 = (x + 60)tan 50°
x(tan 60° - ta 50°) = 60 ta 60
x = 132.34
Therefore, the height will be:
= x tan60°
= 132.34 × tan 60
= 229.23
Therefore, the height is 229.23.
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The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and administrative support are $349,200 per year. Chimneysweep averages 200 service calls per month. What is the average cost per cleaning service call?
The average cost per cleaning service call charge by the company is $184.5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the total cost for x number of service calls in a year. Hence:
y = 39x + 349200
For 200 service call, in a year, x = 200 * 12 = 2400
y = 39(2400) + 349200 = $442800
Average cost = $442800 / 2400 = 184.5
The average cost per cleaning service call charge by the company is $184.5.
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Solution
We are given two endpoints here
Point 1: (−1, Answer
)
Point 2: ( Answer
,4)
We know our rise between the two points is 1. So
12= Answer
And our run between the two points is 4. So
42= Answer
We now have rise2+run2=distance2, so we have
1+16=distance2
Answer
=distance2
So once we take the square root of both sides we have
distance=√ Answer
We could also use the actual distance formula we developed to get the same answer.
d=(4−3)2+(−5−(−1)2)−−−−−−−−−−−−−−−−−−−√
d=(12+(−4)2)−−−−−−−−−−√
d=(1+16)−−−−−−−√
d=√ Answer
The distance between the two points on the plane is √17
Distance between two pointsThe formula for calculating the distance between two points is expressed as;
D = √(x2-x1)²+(y2-y1)²
From the given plane, we have the following coordinates
(-5, 4) and (-1, 3)
Substitute
D = √(3-4)²+(-1-(-5))²
D = √(-1)²+(4)²
D= √1+16
D=√17
Hence the distance between the two points on the plane is √17
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Question 1 of 10
The Quadratic Formula gives which roots for the equation 2x²+x-6=0?
Answer:
x=-3/2 or-2
Step-by-step explanation:
hope this helps
I can't figure this out
The equation of the function g(x) will be g(x) = - ln (x + 2).
What is a logarithm?Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.
Let the equation of the function f will be
f(x) = ln x
If the function is multiplied with negative sign, then the function gets flipped about the x-axis.
And if we add 2 in the variable of the function, then the function gets shifted towards left.
Then the equation of the function g(x) will be
g(x) = - ln (x + 2)
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Whats the correct answer answer asap for brainlist
Answer:
option C: Asian
explanation:
Asian countries, such as China, produce goods like the European products, but for much cheaper prices.
The sum of two numbers is 32. One number is 3 times the other. Find the numbers.
The numbers whose sum is 32 in which one number is 3 times the other is 8 and 24 respectively.
Equation of the unknownLet
x = one of the unknowns3x = second unknownx + 3x = 32
4x = 32
x = 32/4
x = 8
So,
3x = second unknown
= 3(8)
= 24
Check:
x + 3x = 32
8 + 24 = 32
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Mr. Parks begins to fill a large container with water for the dunk tank at the school
fair before asking Brian to finish the job. The container has 25 gallons of water in it
before Brian uses a hose to finish filling it up. The container fills at a rate of 10
gallons per minute. Suppose that y is the amount of water in the tank after x
minutes. Which equation could be graphed to help Brian find out how much water is
in the tank at any time?
y = 25x + 10
y= 10x + 25
y= 10x - 25
y = 10x
Answer:
The answer is B / y= 10x+25
Step-by-step explanation:
your welcome
A 4-sided dice is rolled. The set of equally likely outcomes is {1,2,3,4}. Find the probability of rolling a number less than 14
The probability of rolling a number less than 14 is?
The probability of rolling a number less than 14 among {1,2,3,4} is 1.
Given The dice is 4 sided. Likely outcomes is {1,2,3,4} and we have to find the probability of rolling a number less than 4.
Probability is the likeliness of happening an event among all the events possible. The value of probability cannot be negative or greater than 1. It lies between 0 to 1. The formula of calculating probability is:
Probability= number of events/ total number of events.
Total likely outcomes=4 {1,2,3,4}
Numbers less than 14 = 4
Probability of rolling a number less than 14=1/4
=0.25 because all number less than 14 is present.
1,2,3,4 are all less than 14.
and because all numbers are included that's why the value of probability is 1.
Hence the probability of rolling a number less than 14 is 1.
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I put what I thought but came out wrong, please help
Answer:
Sir, as for as I can tell that is the correct answer. Maybe you put it in wrong or added a space but that’s correct 100%.
Unless it’s not supposed to be in y = mx + b format?
Step-by-step explanation:
Answer:
y = -x - 1
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
number that describes both the direction and the steepness of the line
slope = rise/run
b represents the y-intercept
point where crosses the y-axis
The y-intercept is -1rise = -1, run = 1 so rise / run = -1 / 1 = -1line is downward slopey = mx + b → y = -1x + (-1)
this can be simplified by -x - 1
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The average student loan debt for college graduates is $25,150.
Suppose that that distribution is normal and that the standard deviation
is $12,050. Let X = the student loan debt of a randomly selected college
graduate. Round all probabilities to 4 decimal places and all dollar
answers to the nearest dollar.
a. What is the distribution of X? X - N
b Find the probability that the college graduate has between $14,200
and $33,950 in student loan debt.
c. The middle 10% of college graduates' loan debt lies between what
two numbers?
Low: $
High: $
Using the normal distribution, it is found that:
a) [tex]X \approx N(25150, 12050)[/tex]
b) There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
c) Low: $23,519.65, High: $26,580.35.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 25150, \sigma = 12050[/tex].
Hence the distribution of X can be described as follows:
[tex]X \approx N(25150, 12050)[/tex]
The probability that the college graduate has between $14,200 and $33,950 in student loan debt is the p-value of Z when X = 33950 subtracted by the p-value of Z when X = 14200, hence:
X = 33950:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33950 - 25150}{12050}[/tex]
Z = 0.73
Z = 0.73 has a p-value of 0.7673.
X = 14200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14200 - 25150}{12050}[/tex]
Z = -0.91
Z = -0.91 has a p-value of 0.1814.
0.7673 - 0.1814 = 0.5859.
There is a 0.5859 = 58.59% probability that the college graduate has between $14,200 and $33,950 in student loan debt.
Considering the symmetry of the normal distribution, the middle 10% is between the 45th percentile(X when Z = -0.127) and the 55th percentile(X when Z = 0.127), hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = -0.127(12050)
X = $23,519.65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.127 = \frac{X - 25150}{12050}[/tex]
X - 25150 = 0.127(12050)
X = $26,580.35.
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mark: 3,2,0,1,9,12,3,5
if the pass mark is 5, how many students failed the text
Answer:
5
Step-by-step explanation:
Anything below 5 is a fail:
3, 2, 0, 1, 3
That's 5 students.
Halfway through the season, a soccer player has made 12 penalty kicks in 18 attempts.
Based on her performance to date, what is the relative frequency probability that she will miss
her next penalty kick?
Answer:
21
Step-by-step explanation:
18÷6=3 attemps
13÷6=2 makes
she will probably missed I next 3rd pe alty kick
21st attempts