Answer:
There are 13 tricycles, 26 bicycles, and 7 unicycles.
Step-by-step explanation:
Let t=the number of tricycles, b=the number of bicycles, and u=the number of unicycles.
Equation to find the number of wheels:
3t+2b+u=98
This can be found because we know that each tricycle has 3 wheels, so we multiply the number of tricycles by 3. This can be done with bicycles and unicycles as well.
Equation to find the number of seats:
t+b+u=46
We know that there are two times as many bicycles as there are tricycles, this can be represented by the equation b=2t.
We can plug this into our number to wheels equation to get:
3t+2(2t)+u=98
3t+4t+u=98
7t+u=98
u=-7t+98
We can also put this into out number of seats equation to get:
t+2t+u=46
3t+u=46
u=-3t+46
Set the equations equal to each other to get:
-7t+98=-3t+46
-4t+98=46
-4t=-52
t=13
b=2t
b=2(13)
b=26
b+t+u=46
26+13+u=46
39+u=46
u=7
There are 13 tricycles, 26 bicycles, and 7 unicycles.
What is the domain of f(x)=
F(X). 4)*
?
A. x>0
B. All real numbers
C. y> 0
D. x<0
Answer: All real numbers
Step-by-step explanation:
The domain is the set of inputs.
An account pays 8% per year simple interest. in year 1, the amount in the account is $850. how much is in the account in year 6?
Answer:
Step-by-step explanation:
$1,248.92
Help needed
65. Solve for in the logarithmic equation 3 log x = 2.
O * = 1,000,000
O * = 150
O * = 56.423
O * = 4.642
Triangle M N O maps to triangle M prime N prime O prime.
In the diagram, triangle MNO maps to triangle M'N'O'.
Complete the statements.
Angle M corresponds to angle
Side
is the image of side NO.
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.
Here it is given that Triangle MNO maps to triangle M'N'O'
We need to find that Angle M corresponds to which angle and the image of side NO
By one to one correspondence we get that
Angle M corresponds to angle M' and
Side N'O' is the image of side NO
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Ellen has a bag with 3 red marbles and 2 blue marbles in it. she is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw. how many times do you predict that the marble picked will be blue using the theoretical probability?
The blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.
The theoretical probability of any event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.
If we have an event A, the number of favorable outcomes to event A as n, and the total number of possible outcomes in the experiment as S, then the theoretical probability of event A is given as:
P(A) = n/S.
In the question, we are given that Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw.
We are asked the predict the number of times that the marble picked will be blue using the theoretical probability.
Let the event of picking a blue marble be A.
The number of favorable outcomes to event A (n) = 2 {The total number of blue marbles in the bag}.
The total number of possible outcomes in the experiment of picking a ball (S) = 5 {The total number of marbles in the bag}.
Thus, the theoretical probability of event A is,
P(A) = n/S = 2/5 = 0.4.
To predict the number of times marble picked was blue, we multiply the time's the experiment was performed by the theoretical probability of picking a blue ball.
Thus, the predicted number of times = 300 * 0.4 = 120.
Thus, the blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.
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WILL GIVE BRAINLEST!!!
I. The diagonals in a trapezoid are always equal in length.
II. The diagonals in a trapezoid always bisect each other.
III. The diagonals in a trapezoid always intersect at the median.
Which of the above statements are NOT true for all trapezoids?
I only
I, II, and III
I and III
I and II only
Answer:
I and II only
4. For a camping trip, each person packs 1.5 lb of food per day. Let p represent the number of people on the trip, and let f represent the total weight of food packed for each day. What is the independent variable in this relationship? Explain. I need this with explanation please:(
The polygon circumscribes the circle. Which of the following is the perimeter of the polygon?
A. 39 cm
B. 56 cm
C. 61 cm
D. 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:
The missing lengths are 8, 6, 9 and 16.
Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
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An advertising company charges $60 per half-page advertisement and $100 per full-page advertisement. michael has a budget of $1340 to purchase 15 advertisements. define a variable for each unknown. write a system of equations to represent the situation. how many half-page advertisements does michael purchase? show your work. how many full-page advertisements does michael purchase? show your work.4
The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Let the number of half page ads be represented by h
Let the number of full page ads be represented by f.
Total number of advertisements = 15
h + f = 15 ....... (i)
h = 15 - f
Therefore, the system of equations to represent the situation will be:
60h + 100f = 1340 ........ (ii)
Put the value of h into equation (ii)
60(15 - f) + 100f = 1340
[tex]\Rightarrow[/tex] 900 - 60f + 100f = 1340
Collect like terms
100f-60f = 1340-900
[tex]\Rightarrow[/tex] 40f = 440
[tex]\Rightarrow[/tex] f = 11
The number of full-page advertisements that Michael purchased is 11.
Since h + f = 15
[tex]\Rightarrow[/tex] h + 11 = 15
[tex]\Rightarrow[/tex] h = 15 - 11
[tex]\Rightarrow[/tex] h = 4
The number of half page advertisements that Michael purchased is 5.
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I don’t get this either please save me from this ahhhhhh
Answer:
y=
[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]
Step-by-step explanation:
calculate the product, use (a+b)^2=a^2+2ab+b^2
Graph the rational function
by identifying its key features.
The graph of the rational function is shown below
Graph of rational functionsFrom the question, we are to graph the given rational function
To determine the graph that corresponds to the given rational function,
First, we will graph the given rational function.
The given rational function is
x²+3x-1/x+1
The graph of the rational function is shown below
Now, we will compare each of the rational graphs in the provided options with the attached graph
The graph that corresponds to the given rational graph in the attachment below is the graph that represents the given rational function.
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A certificate of deposit offers a nominal interest rate of 5.5 percent annually.If inflation is 2.5 percent, what is the real rate of return?
The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The real rate of return exists at 2.926%.
How to estimate the real rate of return?The real rate of return formula exists utilized, and we use the data given in the exercise to the formula to estimate the real rate of return.
The formula for the real rate of return:
R = (1+N)/(1+i) - 1
Where, N exists the nominal rate and i exists the inflation rate, as decimals.
A certificate of deposit offers a nominal interest rate of 5.5 percent annually.
This means that N = 0.055
Inflation exists 2.5 percent
i = 0.025
Substitute the values in the above equation, we get
[tex]$R = [(1+0.055)/(1+0.025)] -1[/tex]
= [1.055/1.025] - 1
= 1.02926 - 1
= 0.02926
0.02926 [tex]*[/tex] 100% = 2.926% ~ 3%
The real rate of return exists at 2.926%.
Therefore, the correct answer is option D. 3%.
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What is the rule of -3,18,-108,—,—,—
Hi! ❄
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The rule for this sequence is 'multiply by -6'.
Verification ↓
-3*(-6)[tex]\stackrel\checkmark{=}[/tex]18
18*(-6)[tex]\stackrel\checkmark{=}[/tex]-108
So the rule for the sequence is 'multiply by -6'
And the Common ratio is -6.
Hope that made sense !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[tex]\star\tiny\pmb{calligraphy}\star[/tex]
[tex]\textbf{Heya !}[/tex]
✏✏[tex]\large\textsf{Given:-}[/tex]
The first 3 terms of a sequence :- [tex]\large\textsf{-3, 18, -108}[/tex]✏✏ [tex]\large\textsf{To Find:-}}[/tex]
The rule for the sequence = ?✏✏ [tex]\large\textsf{Solution Steps:-}[/tex]
What do we multiply each term of the sequence by to arrive at the next one ? we can find that by dividing the last term of the sequence, -108, by the middle term, 18:-
[tex]\large{\sf{\longmapsto{-108\div18=-6}[/tex]
Now divide 18 by the first term (-3) :-
[tex]\longmapsto\sf{18\div-3=-6}[/tex]
we arrived at -6 twice, So the rule for this sequence is:- "Multiply by -6, And you'll arrive at the next term"
`hope it helped ~ :D
The water park charges a $45 fee plus $5 per student for a field trip. The
bowling alley charges a $35 fee plus $7 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Cost ($)
100
90
80
70
60
50
40
30
20
10
Field Trip Costs
y = 35+ 7x
y = 45 + 5x
1 2 3 4 5 6 7 8 9 10
Number of students
Using linear functions, the cost will be the same, of $70, when there are 5 students.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the functions are:
y = 45 + 5x.y = 35 + 7x.The costs are the same when:
45 + 5x = 35 + 7x
2x = 10
x = 5.
The cost is:
y = 45 + 5 x 5 = $70.
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Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. for a sample of 45 orders, the mean weight is 66 ounces and the standard deviation is 10.2 ounces. what is the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight?
a. note that the correct answer will be evaluated based on the z-values in the summary table in the teaching materials section.
please round your answer to the nearest tenth.
b. note that the correct answer will be evaluated based on the full-precision result you would obtain using excel.
Using the t-distribution, the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight is of 69.06 ounces.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.For this problem, the parameters are:
[tex]\voerline{x} = 66, t = 2.0154, s = 10.2, n = 45[/tex]
Hence the upper bound of the interval is:
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 66 + 2.0154\frac{10.2}{\sqrt{45}} = 69.06[/tex]
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The organizers of a community fair set up a small Ferris wheel for young children. The table shows the heights of one of the cars above the ground for different rotations of the wheel. The function below, where a
and b are constants, models the height of the Ferris wheel car at a rotation of x radians. What are the values of a and b?
The value of a is 6 and the value of b is 7
How to determine the values of a and b?The function is given as:
h(x) = a . sin(x - π/2) + b
From the table of values, we have:
x = π/2 when y = 7
So, we have:
a . sin(π/2 - π/2) + b = 7
Evaluate the difference
a . sin(0) + b = 7
Evaluate the value of sin(0)
a . 0 + b = 7
Evaluate the product of a and 0
b = 7
Substitute b = 7 in h(x) = a . sin(x - π/2) + b
h(x) = a . sin(x - π/2) + 7
From the table of values, we have:
x = π when y = 13
So, we have:
a . sin(π - π/2) + 7 = 13
Evaluate the difference
a . sin(π/2) + 7 = 13
Subtract 7 from both sides
a . sin(π/2) = 6
Evaluate sin(π/2)
a . 1 = 6
Divide both sides by 1
a = 6
Hence, the value of a is 6 and the value of b is 7
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Which search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
The wide-area search method employs the use of markers such as knots at regular intervals along the search line.
Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.
In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.
Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line
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Safety guidelines specify that a ladder should form an angle between 70° and 80° with the ground. If a ladder is 4 m long, determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines?
Answer:
Step-by-step explanation:
70 = x/4
x = 4 cos 70 = 1.37m
x = 4 cos 80 = 0.69m
The range is ( 0.69m, 1.37m)
The range of distances from the wall (x) that the foot of the ladder placed to fall within the safety guidelines is between 0.7052 meters and 1.456 meters.
To determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines, use trigonometry.
Let's assume the distance from the wall to the foot of the ladder is x meters the ladder is 4 meters long.
The angle between the ladder and the ground is given to be between 70° and 80°. Let's consider the extreme cases for each angle:
When the ladder makes an angle of 70° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 70° = 20°.
When the ladder makes an angle of 80° with the ground:
In this case, the angle between the wall and the ladder (θ) will be 90° - 80° = 10°.
Now, use trigonometry to calculate the range of distances (x) from the wall:
For the first case (θ = 20°):
tan(20°) = Opposite / Adjacent
tan(20°) = x / 4
x = 4 × tan(20°)
For the second case (θ = 10°):
tan(10°) = Opposite / Adjacent
tan(10°) = x / 4
x = 4 × tan(10°)
Now, let's calculate the values:
x ≈ 4 × 0.3640 ≈ 1.456 meters (rounded to three decimal places) - for the first case.
x ≈ 4 × 0.1763 ≈ 0.7052 meters (rounded to four decimal places) - for the second case.
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The number of jobs for nurses is expected to increase by 711,900 between 2010 and 2020. during the same decade, the number of jobs for physicians is expected to increase by 168,300. find the ratio of the increase in jobs for physicians to the increase in jobs for nurses.
The Ratio would be 43:100.
Lets simplify the problem,
Expected increase of nurses = 711900
Expected increase of physicians = 168300
Ratio = Expected increase of nurses / Expected increase of physicians
Ratio = 711900 / 168300
= 43/100
Ratio = 43:100
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Which statement is correct when a scatterplot is constructed?
The correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
Steps in constructing a scatterplotChoose independent and dependent variableDraw a known x-axis for the independent variableAdd y-axis for the dependent variableMake all the points in the scatterplotLabel graph and axesFrom the given steps, we can see that when a scatter plot is constructed, the independent variable is the input variable and should be represented by the x-axis.
Hence, the correct statement about when a scatterplot is constructed is the independent variable is the input variable and should be represented by the x-axis. Option A
The complete question is;
Which statement is correct when a scatterplot is constructed? The independent variable is the input variable and should be represented by the x-axis.
The independent variable is the input variable and should be represented by the y-axis.
The dependent variable is the input variable and should be represented by the x-axis.
The dependent variable is the input variable and should be represented by the y-axis.
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Answer: A; The independent variable is the input variable and should be represented by the x-axis.
Step-by-step explanation:
I just know
What is the approximate number of minutes that avery spends in extra circular activities
The approximate number of minutes that Avery spends on the extra curricular activities are 122 minutes.
Given that Avery spent 10 minutes outside, 64 minutes in riding her bike, 48 minutes on the trampoline.
We have to calculate the approximate time that Avery spends on extra curricular activities.
Time spent by Avery outside=10 minutes
Time spent by Avery in riding her bike=64 minutes
Time spent by Avery on trampoline=48 minutes
Total time spent by Avery on extra curricular activities is equal to 10+64+48
=122 minutes
Hence the total time spent by Avery on extra curricular activities is 122 minutes.
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Question is incomplete as the question should include that Avery spent 10 minutes outside,64 minutes in riding her bike, 48 minutes on trampoline and rest of the time in swimming.
What is the perimeter of the contest area on the judo mat?
(please be quick)
The perimeter of the contest area on the judo mat will be 32 meters.
What is the perimeter of the square?For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The side length of square is 8 m.
Then the perimeter of the contest area on the judo mat will be
P = 4 x 8
P = 32 m
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According to the weather report, there is a 25% chance of snow in the mountains tomorrow. how likely is it to snow tomorrow in the mountains?
It is likely is it to snow tomorrow in the mountains is 1/4
A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment
We need to find that what is the chance that it will snow tomorrow in the mountains
According to the weather report, there is a 25% chance of snow in the mountains tomorrow.
Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4
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Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as large; those from $50 to $100 million as medium size; and those between $25 and $50 million, and so on. Samples were then selected from each of these groups. What is this type of sampling called
Stratified random sampling is used to subdivided into groups by volume of sales.
According to the statements
Manufacturers are subdivided into groups by volume of sales. and for this Stratified random sampling is used.
Stratified random sampling is the technique used divide the population can be partitioned into subpopulations.
Thus, Stratified random sampling is used to subdivided into groups by volume of sales.
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2. Find the area of the circle. Round to the nearest tenth.
A.113.1
B.37.7
C.18.8
D.28.3
The answer is D.
The formula to find area of a circle is : πr²
Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.
Let's find the area.
A = π × r²A = 3.14 × (3)²A = 3.14 × 9A = 28.26A ≈ 28.3Please help
The area of a circle is 354 cm². Find in degrees and minutes, the angle subtended at the centre of the circle by a 2.9cm arc.
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
What is the measure of the central angle of a circular section?
In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:
r = √ (A / π) (1)
r = √ (354 / π)
r ≈ 10.615 cm
Then, the measure of the central angle in radians is found by the equation of circular arc:
θ = s/r
θ = 2.9 cm / 10.615 cm
θ = 0.273 radians
Finally, we convert the angle into DMS system:
θ = 0.273 rad × 180°/π
θ = 15.641°
Degrees: 15°
Minutes and seconds: 0.641° (38.46')
Minutes: 38'
Seconds: (0.46' = 27.6'')
The angle subtended at the centre of the circle by a 2.9 centimeter arc is equal to 15° 38.46'/15° 38' 27.6''.
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PLEASE HELP
If BC DA, then which segment is the shortest side?
The length of the shortest side is DC
How to determine the shortest side?As a general rule in triangle;
The smallest angle in a triangle is opposite the shortest side.
Similarly, the largest angle in a triangle is opposite the largest side.
From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.
The side opposite this angle is side length DC
Hence, the length of the shortest side is DC
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A sample of workers exhibit the following production rates before and after a workshop. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 The point estimate for the difference between the means of the two populations is: Group of answer choices
The point estimate here is 0.
Calculating the Mean of Each Set
The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}
The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}
The mean of set S1 = (20+25+27+23+22+20+17)/7
= 154/7
= 22
The mean of set S2 = (22+23+37+20+25+19+18)/7
= 154/7
=22
Calculating the Point Estimate
The formula for point estimate is given as,
Point Estimate = The mean of set S1 - The mean of set S2
Point Estimate = 22-22
Point Estimate = 0
Therefore, the point estimate for the difference between the means of the two populations or sets is 0
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A scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, what is the area of the actual building lot?
The area of the actual building lot is 5040 square ft
Scale factorsThis factors are used to enlarge or diminish the given figure. Given the scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, the new length and width is expressed as:
Length = 12 * 7 = 84ft
Width = 5*12=60 ft
Determine the area
Area = 84 * 60
Area = 5040 square feet
Hence the area of the actual building lot is 5040 square ft
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Enter the degree of the polynomial below.
5,5 + 8,2 + 2x - 319 - 8x1 -4,5
Based on the given polynomial, the degree of the polynomial can be calculated to be 1.
what is the degree of the polynomial?the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.
from the above, we see that the highest power is 1 from 8x¹.
the degree of the polynomial is therefore 1.
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