There are 70 cars altogether in the lot.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of domestic cars to imported cars = 3 : 2,
Domestic cars = 42
Since, the number of domestic cars in the shop is 42,
Therefore,
3x = 42
x = 14
Therefore, the number of total cars = 14×5 = 70
Hence, there are 70 cars altogether in the lot.
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Determine the more basic function that has been shifted, reflected, stretched, or compressed q(x) = -1/x + 1
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
What do you understand by the team function?The transformation applied to f(x) to obtain q(x) is divided into several steps:
Reflection: The negative sign in front of 1/x reflects the graph of f(x) across the x-axis, causing the y-values to change sign.
Vertical shift: Adding "+1" to -1/x raises the graph of f(x) by one unit.
Horizontal shift: Although there is no explicit horizontal shift in q(x), we can see that the graph of q(x) has a vertical asymptote at x=0, whereas the graph of f(x) does not. This means that the graph of q(x) has been shifted to the right by one unit.
The more basic function that has been shifted, reflected, stretched, or compressed to create q(x) = -1/x + 1 is the function f(x) = 1/x.
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The vet says that raise puppy will grow to be at most 28 inches tall raise. Puppy is currently 1 foot tall how much more will the puppy grow?
Write an inequality to solve the problem
Answer:
16 inches
Step-by-step explanation:
28 - 12 = 16 inches
1 foot = 12 inches
You are interested in the development of language in bilinguals. You are able to locate five families in the word with 18-month-old toddlers who are learning both Swahili and Vietnamese simultaneously. Given that these are the only families that fit this qualification, therefore, these five families are your study population. You test the children to see how many words they can speak in Swahili. The results are listed in the following table: Calculate the mean for this population. Complete the following table. Calculate the variance and standard deviation for this population.
The mean for this population is 55. The variance and standard deviation for this population are 94.8 and 9.74
The data is given for five families and their children are tested to see how many words they can speak in Swahili.
Toddler Number of words(X) X - M (X - M)²
A 47 - 8 64
B 73 18 324
C 56 1 1
D 46 -9 81
E 53 -2 4
424
Mean of the population(M) = (∑X)/n
= (47 + 73 + 56 + 46 + 53)/5
= 275/5 = 55
Variance f population (σ²) = (X - M)²/n = 474/5 = 94.8
Standard deviation of population(σ) = √94.8 = 9.74
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Help!!! Drag and drop an answer into each box to correctly complete the statement.
The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.
What precisely is dilation?
Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:
Properties of Rotation, Translation, Reflection, and Resizing
Dilation properties
The following are some features of shapes that remain constant with dilation changes:
The angles in the illustration are all the same.The figure's side midpoints remain the same as the dilated form's midpoint.The parallel and perpendicular lines in the illustration remain unchanged.Now,
As The image of A is made on line XY and the image will be A'
then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and
P is the midpoint of AA' because we know that AP and A'P are same in a image formation.
Hence,
Point P is midpoint of AA' and XY⊥AA'.
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Can you please tell me the graphing points for this equation?
y = 2^(x+5) +1
The graphing points of the equation is given in the table.
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Given equation is [tex]y=2^{x+5} +1[/tex].
To find the graphing points of the functions:
By assuming the value for x and substitute in the given function to find the values of y.
[tex]if x=-2,y=2^{-2+5} +1=9\\ifx=-1, y=2^{-1+5} +1=17\\if x=0,y=2^{0+5} +1=33\\if x=1,y=2^{1+5} +1=65\\ifx=2,y=2^{2+5} +1=129[/tex]
It is given the table format as,
x [tex]y=2^{x+5} +1[/tex]
-2 9
-1 17
0 33
1 65
2 129
Hence, these are all the graphing points of the equation.
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3. What is the volume of this complex figure?
3 m
4 m
6 m
4 m
7m
The volume of the rectangular prism is 140 cubic meters
What is the volume of the figureThe volume of a figure is a measure of the amount of space it occupies in three-dimensional space. It is a scalar quantity, meaning that it is a single numerical value with no direction.
The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height.
This problem is a two rectangular prism joined together.
The volume can be calculated as;
V = l * w * h
v = (4 * 7 * 3) + (2 * 7 * 4)
v = 140m³
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Please help me with this question
Answer:
m∠2=12°
Step-by-step explanation:
some of two angles is 90
90 -78=12
An urn contains 3 white balls and 7 red balls. A second urn contains 7 white balls and 3 red balls. An urn is selected, and the probability of selecting the first urn is 0.3. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
Answer: the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
Step-by-step explanation:
Let's call the event of selecting the first urn "A" and the event of drawing two white balls from the selected urn "B". The probability we want to find is P(A and B), which can be found using the formula for the intersection of two events:
P(A and B) = P(A) * P(B|A)
where P(B|A) is the probability of drawing two white balls from the first urn given that the first urn was selected.
First, let's find P(A):
P(A) = 0.3
Next, let's find P(B|A):
P(B|A) = (3/10) * (3/10) = 9/100
Finally, let's find P(A and B):
P(A and B) = P(A) * P(B|A) = 0.3 * 9/100 = 0.027
So the probability of selecting the first urn and then drawing two white balls from the first urn is 0.027.
The accompanying table shows the results of a survey in which 250 mail and 250 female workers ages 25 to 64 or asked if they contribute to retirement savings plan at work find the probability that a randomly selected worker contribute to a retirement savings plan at work given the worker is male
Answer:
The answer to your question is, 0.484
Step-by-step explanation:
The actual chances of an event occurring are defined by a probability. Probability has several uses in games, and in business to create probability-based forecasts which bascially how it works.
Lets graph it out:
Let A signify that the selected employee participates to a workplace retirement savings plan. Let P stand for the male employes.
P(A∩P) the intersection of male & female.
P(A\P) is the probability that a randomly picked worker participates to a workplace retirement savings plan is the option male
The probability that a randomly selected worker contributes to a retirement savings plan at work is male is found in this formula :
P(A\P)=P(A∩P)/A(P)
P(A\P)=(121/500)/(250/500)
P(A\P)=0.484
Thus, the probability that a randomly selected worker contributes to a retirement savings plan at work that is male will be,
0.484.
a square law has area 128ft squared what is the radius of the circle
Answer: 6.38
.................
Mr. Lopez surveyed some of the students in the after-school program to figure out whether he should buy jumbo chocolate chip cookies or cinnamon twists for dessert. The circle graph shows the results. Cinnamon twists were chosen by 12 students. How students said he should buy jumbo chocolate chips cookies?
68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
What is a circle graph?
A pie chart, often known as a circle chart, is a visual representation of the various values of a specific variable or a means to summarise a set of nominal data (e.g. percentage distribution). This kind of chart consists of a circle with numerous segments.
Let's say the total number of students = X.
From the circle graph, we can say that 15% of students chose cinnamon twists and their count is 12.
Which means that
[tex]X*\frac{15}{100}=12\\ X=80[/tex]
Therefore the total number of students is 80.
Among the 80 students except for 12 students, the remaining students asked for jumbo chocolate chip cookies.
Which is equal to 80-12=68.
Therefore 68 students said that Mr.Lopez should buy jumbo chocolate chip cookies.
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A curve is defined by the implicit equation X³ + X²Y + 4Y² = 6.
Find the value of day/dx when X = 1 and when Y = 1.
Find the value of day/dx when X = 1 and when Y = 1. I would like to answer correct but Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.
20. A line passes through (4, 6) and (9, 9).
a. Write an equation for the line in slope-intercept
form.
y=3/5x+18/5?
b. Rewrite the equation in standard form using
integers.
Its 10/29 so its answers this
3/4 minus what equals 1/2
Answer:
W =1 1/4Step-by-step explanation: Let W = what. W - 1/2 = 3/4. Add 1/2 to each side. W -1/2 +1/2 = 3/4+1/2. W = 3/4+1/2.
Step-by-step explanation:
The radius of a circle is 14 meters. What is the circle's circumference?
Answer: 87.96m
Step-by-step explanation:
Circumference of a circle = 2[tex]\pi[/tex][tex]r^{2}[/tex] --> 2[tex]\pi[/tex]14² = 87.96m
Five people will share a roll of ribbon equally. The roll has 32 feet of ribbon. How much ribbon, in feet, will each person get?
A. 5/32
B. 1/32
C. 6 2/5
D. 1/5
Answer:
C
Step-by-step explanation:
In this equation, you would need to do 32/5 to figure out how much each person will get. 32/5=6.4 feet
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Isaac made all these rectangles with 24cm lengths of string. This implies that the perimeter of all these rectangles are equal. What do you observe about the sun of the length and the width, give a reason for your answer?
Answer: Since the perimeter of all the rectangles is equal (24 cm), the sum of the length and width of each rectangle must be equal for each rectangle. This is because the perimeter of a rectangle is equal to the sum of its lengths plus the sum of its widths, multiplied by 2.
For example, if the length of one rectangle is "l" cm and its width is "w" cm, then its perimeter would be 2l + 2w = 24 cm.
So, in general, we can write the equation: l + w = P/2, where P is the perimeter of the rectangle (in this case, P = 24 cm).
Therefore, the sum of the length and width of each rectangle is equal and constant, regardless of the individual values of the length and width. This means that as the length of a rectangle increases, its width must decrease by an equal amount to keep the sum constant. And vice versa.
In conclusion, the sum of the length and width of each rectangle is equal, and it is equal to half of the perimeter of the rectangle.
Step-by-step explanation:
What should be added to -7 mm + 2m ²+ 3n² to obtain 5m² +2mn-9n².
The expression to be added is 9mn +3m² - 12n²
What are algebraic expressions?These are expressions having terms, variables, coefficients, factors and constants.
They are also known to be composed of arithmetic operations, such as;
AdditionMultiplicationDivisionSubstraction BracketParenthesesFrom the information given, we have the expression;
-7 mm + 2m ²+ 3n²
To make it up to 5m² +2mn-9n²., we have
-7mn + 9mn + 2m² + 3m² + 3n² - 12n²
Hence, the expression is 9mn +3m² - 12n²
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Use a graphing utility to graph the cost and revenue functions in the same viewing window. Find the sales x necessary to break even (R = C) and the corresponding revenue R obtained by selling x units. (Round to the nearest whole unit.)
Cost Revenue
C = 7.8 √x + 22,000 R = 13.82x
The revenue corresponding to break even condition for selling x units is $4.28.
What is a cost function?An evaluation of the model's accuracy in estimating the link between X and y is done using a cost function. In most cases, this is represented as a difference or distance between the projected value and the actual value. The price element (you may also see this referred to as loss or error.)
To break even (R = C) we have:
7.8 √x + 22,000 = 13.82x
Substitute the value of x = u² thus:
7.8u +22000 = 13.8u²
13.8u² - 7.8u - 22000 = 0
The quadratic formula is given as:
u = -b ± √b² - 4ac / 2a
u = -(-7.8) ± √(-7.8)²- (4)(13.82)(22000) / 2(13.82)
u = 7.8 ± 7.8 / 27.64
u = 7.8 + 7.8 / 27.64
u = 0.56
Back substituting the value of u:
x = u²
x = (0.56)²
x = 0.31
Substituting the value of x is R:
R = 13.82 (0.31)
R = 4.28
Hence, the revenue corresponding to break even condition for selling x units is $4.28.
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Step 1: 3 - 5 = √√4x + 6
Step 2: 3x - 5-6 = √4x+6-6
Step 3: 3x 11 = √/4x
Step 4: (3x - 11)² =(√4x)
What is the next step in the solution to this equation?
The next step in the solution to this equation is to evaluate the exponents
How to determine the next step in the solution to this equationFrom the question, we have the following parameters that can be used in our computation:
The steps 1 to 4
Using the above as a guide, we have the following:
Step 4: (3x - 11)² =(√4x)²
At this point,, we open the bracket
This is done by evaluating the exponents
So, we have
9x² - 66x + 121 = 4x
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Wendy and Roger camped out at a state park, and then hiked back to their cars, which were
parked on opposite ends of the park. Wendy headed due north at 3 miles per hour, and Roger
hiked due south at 6 miles per hour. In how long were the two friends 2 miles apart?
If necessary, round your answer to the nearest minute.
In 30 minutes the two friends 2 miles apart.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
Given that, Wendy headed due north at 3 miles per hour, and Roger hiked due south at 6 miles per hour.
We know that, Time= Distance/Speed
Now, T₁= 2/3
T₂= 2/6 =1/3
T=T₁-T₂
T=2/3+1/3
T=1/3
T=0.33 hours
= 30 minutes
Therefore, in 30 minutes the two friends 2 miles apart.
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What is the rate of change for the equation y= 4x +40?
Answer:
4 would be the rate of change
Step-by-step explanation:
y=mx+b mx = slope
The slope represents the rate of change. Then the rate of change will be 4.
Arturo purchased the tank below for his aquatic turtle. The tank has a length of 5.5 feet, a width of 4 feet, and a height of h feet. Arturo poured in 74.8 cubic feet of water in the tank to fill it half way. What is the value of h, the height of the tank, in feet?
Answer:
6.8 ft
Step-by-step explanation:
You want the height of a tank with a base of 5.5 ft by 4 ft if adding 74.8 ft³ of water fills it halfway.
VolumeThe volume of a rectangular prism is given by the formula ...
V = LWH
The filled volume of the tank h feet high is ...
74.8 ft³ = (5.5 ft)(4 ft)(h/2) . . . . . . the filled height is h/2
74.8 ft³/(11 ft²) = h ≈ 6.8 ft . . . . . . divide by the coefficient of h
The height of the tank is 6.8 feet.
Help with these questions pls?
Answer:
£76
Step-by-step explanation:
[tex]28+16(1.5/0.5)=28+16(3)=28+48=76[/tex]
A boat heading out to sea starts out at Point A, at a horizontal distance of 1246 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 14°. At some later
time, the crew measures the angle of elevation from point B to be 5°. Find the
distance from point A to point B. Round your answer to the nearest tenth of a foot if
necessary.
Answer:2304.9
Step-by-step explanation:
Answer:
2304.9 ft
Step-by-step explanation:
You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.
TangentThe tangent relation for sides in a right triangle is ...
Tan = Opposite/Adjacent
In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:
tan(14°) = h/1246
tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B
SolutionSolving these equations for d, we have ...
h = 1246·tan(14°) = (1246+d)·tan(5°)
d·tan(5°) = 1246·(tan(14°) -tan(5°))
d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet
The distance from point A to point B is about 2304.9 feet.
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Find the 52nd term of the arithmetic sequence
−
3
,
12
,
27
The 52nd term of the arithmetic sequence -3, 12, 27, ..... is equal to 762.
How to calculate an arithmetic sequence?Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:
aₙ = a₁ + (n - 1)d
Where:
d represents the common difference.a₁ represents the first term of an arithmetic sequence.n represents the total number of terms.Next, we would determine the common difference as follows.
Common difference, d = a₂ - a₁
Common difference, d = 12 - (-3)
Common difference, d = 12 + 3
Common difference, d = 15
Substituting the given parameters into the formula, the 52nd term of this arithmetic sequence is given by;
a₅₂ = a₁ + (52 - 1)d
a₅₂ = -3 + (51)(15)
a₅₂ = -3 + 765
a₅₂ = 762.
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Graphing Quadratic Functions 1. List a, b, and c. 4. What is the y-intercept? 5. Create a table and graph. X f(x) Quadratic Function f(x) = x² - 2x + 6 2. Find the axis of symmetry. F Y 10 9 8 7 6 5 4 3 2 1 -9-8-7-6-5-4-3 -2 -1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 3. Find the vertex. tx 1 2 3 4 5 6 7 8 9 10 X
The value of a, b, and c are 1, -2, and 6 respectively.
The y-intercept of this quadratic function is 6.
The axis of symmetry of this quadratic function is 1.
The vertex of this quadratic function is (1, 5).
How to calculate the axis of symmetry of a quadratic function?Mathematically, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = x² - 2x + 6, we have:
Axis of symmetry, Xmax = -b/2a
Axis of symmetry, Xmax = -(-2)/2(1)
Axis of symmetry, Xmax = 2/2 = 1.
Vertex (h, k) = (1, 5).
In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).
y-intercept = 6.
Lastly, we would create a table and then graph the quadratic function as follows;
x y
0 6
2 2
5 11
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For the function
f(x)
given in the table, find the average rate of change over each specified interval.
x
0 2 2.5 3 3.8 4 5
f(x)
24 13 17 18 16 13 29
(a) [2, 5]
Incorrect: Your answer is incorrect.
(b) [3.8, 4]
The average rate of change over each specified interval is 8/3 and -10.
What is an average rate?The average rate shows the change in the function per unit, over an interval.
Given that, find the average rate of change over each specified interval.
The average rate of change is given by
f(b)-f(a) / b-a
a) [2, 5] :-
To find the average rate of change we will take the change in the function over the change in x,
f(5)-f(2) / 5-2 = 24-16 / 3 = 8/3
Therefore, the average rate of change in interval [2, 5] is 8/3
b) [3.8, 4] :-
Similarly,
f(4)-f(3.8) / 4-3.8 = 17-19 / 0.2 = -2/0.2
= -10
Therefore, the average rate of change in interval [3.8, 4] is -10
Hence, the average rate of change over each specified interval is 8/3 and -10.
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Let A, B, and C be events relative to the sample space S. Using Venndiagrams, shade the areas representing events:
a.) (A∩B)′
b.) (A∪B)′
c.) (A∩C)∪B
If A, B and C be events relative to the sample space S, then the Venn diagram of the representing event has been plotted
Let A, B and C be events relative to the sample space S.
The sample space is the set of all possible outcomes of the experiment.
The Venn diagram is the pictorial representation of the sample space of the experiment by using the circles and the overlapping of the circles.
Here we have to plot the each representing events using the Venn diagram representation
Part a
The event is (A ∩ B)'
Plot the Venn diagram
Part b
The event is (A ∪ B)'
Plot Venn diagram
Part c
The event is (A ∩ C) ∪ B
Plot the Venn diagram
Therefore, the Venn diagram of the each event has been plotted
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Use the commutative and/or associative properties to simplify (17)(0.25)(4).
The solution is, (17)(0.25)(4) = 17.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
(17)(0.25)(4)
=(17)*1
=17
at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.
Hence, The solution is, (17)(0.25)(4) = 17.
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