The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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A single bathc of your mother resipe for slalsa call for 3 tomatos. 1/4 cup cilantro,1/2 onion, and spices. you are having a party and need 5 batches of salsa how many cups of onions do you need?
To produce five constructive batches of salsa, 2.5 cups of onion will be needed.
What is unitary method of problem solving?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Given, the number of onions required to produce one batch = 0.5 cup(s)
∴ The number of onions required to produce five batches = 0.5×5
= 2.5 cup(s)
Thus, to produce five constructive batches of salsa, 2.5 cups of onion will be needed.
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a news poll which estimated that 82% of all voters believe global warming exists had a margin of error of /- 3%. suppose an environmental group planning a follow-up survey on this issue wants to determine a 95% confidence interval with a margin of error of no more than 2%. how large a sample do they need? (for estimate of p use 0.82)
The needed sample size is 1419. Sample Size is defined as the number of observations in the study.
In the question we have ,
estimate value of all voters who believe global warming ( p) = 82% = 0.82
margin of error (M.E) = 2% = 0.02
confidence of interval is calculated by estimate point value and add or subtract margin of error .
here,we have the value of confidence of interval is 95% = 0.95
Margin of error formula is
M.E = Z × √(p(1-p)/n)
where, p --> is estimated value
n---> sample size , which we required
Z ----> is z-value for observation
for the confidence of interval level 95% , the Z-value is 1.96 exist.
put all value in above formula we get,
0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)
=> 0.02 = 1.96× √(0.82×0.18/n)
= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n
=> n = 1419
So, sample size is large and it is 1419.
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PLS HELP!!!
30 = y/2 + 8
y = ____
Answer:
y = 44
Step-by-step explanation:
y = 300
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Steps are in the attached picture!
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Joke: What runs around a farm but doesn’t move?
Answer: A fence.
Have a great day and God bless! :D
a box has a width of 15 inches and a length of 16 inches. the volume of the box is increasing at a rate of 569 cubic inches per second, with the width and length being held constant. what is the rate of change, in inches per second, of the height when the height is 6 inches?
The rate of change in height when height is 6 inches is 2.37 inches per second approximately.
We know that the volume of cube with length L, width W and height H is given by,
V = L*B*H
So given that the length is 15 inches
the width is 16 inches
Let the height be h inches.
So now the volume is given by,
V = 15*16*h
Differentiating the volume with respect to time 't' we get,
dV/dt = 15*16 dh/dt
Now given that the rate of change in volume per second is 569 cubic inches.
So, dV/dt = 569
So, 15*16 dh/dt = 569
dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)
So the rate of change in height is 2.37 inches approximately.
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how many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row? a) 70 b) 604,800 c) 120 d) 3,628,800 e) 17 f) none of the above.
The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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I need help asap… Is this relation a function or no ?
Answer:
Step-by-step explanation:
yes, it is a function
Answer: no
Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.
the two-way relative frequency table given shows the results from the lunch orders from an upperclassman picnic. 11th grade 12th grade total salad 12% 6% 18% sandwich 20% 24% 44% soup 8% 30% 38% total 40% 60% 100% a segmented bar chart was created showing the lunch preference by grade. what percentage would the bar for 11th graders show for preferring salad? 67% 40% 30%
The bar for 11th graders show 30% for preferring Salad.
Given, that the lunch orders from an upperclassman picnic.
11th Grade 12th Grade Total
Salad 12% 6% 18%
Sandwich 20% 24% 44%
Soup 8% 30% 38%
Total 40% 60% 100%
To find the relative frequency we divide the frequency by the total.
hence, to find the relative frequency for 11th graders preferring Salad
12/40 = 0.3 = 30%
Hence, the bar for 11th graders show 30% for preferring Salad.
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Apply the distributive property to
create an equivalent expression.
(-7c + 8d)0.6
Answer: -4.2c + 4.8d
Step-by-step explanation:
Multiply each number by 0.6 to get -4.2c + 4.8d.
-34, -21, -8.5 Complete the recursively defined function to describe this sequence.
The recursive definition of the arithmetic sequence -34, -21, -8 is:
f(1) = -34.f(n + 1) = f(n) + 13.What is an arithmetic sequence?It is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.
The nth term of an arithmetic sequence is given by the rule presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
An arithmetic sequence can also be defined recursively, as follows:
[tex]f(1) = a_1[/tex]f(n + 1) = f(n) + d.In this problem, the sequence is given as follows:
-34, -21, -8.
Hence the first term and the common ratio are given as follows:
First term: -34.Common ratio: 13, as each term is the previous term added to 13.Hence the recursive definition of the sequence is:
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In a circle, the length of an arc intercepted by a central angle is 12 mm, and the radius of the circle
8 is 8 mm. What is the measure, in radians, of the angle?
Answer:
1.5
Step-by-step explanation:
we calculate the circumference of this circle.
circumference of a circle=2πr
data:
r=8 mm
circumference=2(8 mm)π=16π mm
2)we calculate the measure, in radians of the angle.
We know that:
circumference of a circle=2π radians
therefore:
16π mm=2π radians.
16 π mm--------------------------2π radians
12 mm----------------------------- x
x=(12 mm * 2π radians) / 16π mm=1.5 radians.
what is the best point estimate for the population's standard deviation if the sample variance is 49.7? round your answer to one decimal place, if necessary.
Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1
What is the relation between standard deviation and sample variance?In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.
The square root of the variance yields the standard deviation, i.e.
Standard deviation = [tex]\sqrt{variance[/tex]
Given that sample, the variance is 49.7 and we have to calculate the standard deviation.
Standard deviation (σ) = [tex]\sqrt{variance[/tex]
= [tex]\sqrt{49.7}[/tex]
= 7.0498
=7.1
Hence, the standard deviation for the population for the given variance is 7.1
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Heather is planning her birthday party at the rink. the graph below shows the total cost including the fee to rent the party room and the price for each guest.
130 for 2
140 for 4
150 for 6
how much for the party room
how much for each guest
what's the equation for the total cost for the party
how much for 15 people and the party room
Step-by-step explanation:
I skipped the answer line because they are pasted below.
Since there is a ten dollar difference for two people, each guest is 5 dollars. If each guest is 5 dollars, the party room is 120. If we want to create an equation, we have:
y=5x(each guest is 5 dollars)+120(the basic fee).
If we use 15 here, we have that it will be $195.
ANSWERS DOWN HERE:
1. $120
2. $5
3. y=5x+120
4. $195
I need help please because I am failing in math
Answer:
what do you need help with?
Answer:
Step-by-step explanation:
You need a picture of the item.
What is the value of y in the equation 2(2y − 16) = 0? (5 points)
a 4
b 6
c 8
d 9
Answer:
the options are wrong
Step-by-step explanation:
open the bracket2(2y)2(-16)=04y-32=0make y the subject of formulary=-32÷4y=-8Answer:
C. 8
Step-by-step explanation:
2 x 8 = 16
16 - 16 = 0
2 x 0 = 0
Can anyone write the equation of the graph?
The equation of given graph is y = |x - 3| + 5.
The graph of a absolute or modulus function is a V- shape graph. The function of absolute is f(x) = |x|. The general form of absolute function is f(x)=a |x - h| + k. Where (h,k) is the vertex of graph.
Here, we can see that graph is in the form of V shape, so the function will be absolute function. Now, we have to find the vertex of graph.
As seen from the graph the minimum point on the graph is located at the point (3, 5) and the value of a should be 1.
So, by putting the value of vertex in general equation we get the equation of the graph,
y = |x - 3| + 5
Therefore, the equation of given graph is y = |x - 3| + 5.
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750 people go on a coach trip
each coach can hold 55 people
How many coaches are needed
Step-by-step explanation:
750 people go on a coach trip each coach can hold 55 people How many coaches are needed?
750/55 = 13.636 coaches are needed.
Because you cannot have a partial coach, you round up to needing 14 coaches.
Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked how much is Nick share of the money. Nick and Pam are paid ?
Nick got a total of $33.25 for his part of work.
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.
Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -
y₁/x₁ = y₂/x₂
We can write -
x/3.5 = (52.25 - x)/2
2x = 3.5(52.25 - x)
2x = 182.875 - 3.5x
x = 33.25
Therefore, Nick got a total of $33.25 for his part of work.
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One type of plant root splits 4 times while growing in the ground. The number of new roots after each split can be modeled by the function f(x)=3x, where x is the number of times the root splits. What is the domain of f(x)? CLEAR CHECK All positive integers All positive integers less than or equal to 4 All integers All positive integers greater than or equal to 4
The domain of the function represented as .f(x) is (b) All positive integers less than or equal to 4
How to determine the representation of the domain?The equation of the function is given as
f(x) = 3x
Where
x = Number of splits
f(x) = number of new roots in each split
From the question, we have
Splits = 4
This means that the maximum value of x is 4
The other values of x would be
x = 1, 2, 3, 4
This can be represented as
0 ≤ x ≤ 4
The interpretation of the above notation is all positive values less than or equal to 4
Hence, the domain value is option (b)
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Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
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Find the perimeter of a rectangle with a diagonal of 20 inches that make angle measure 30 and 60 using trigonometric function (sine, cosine, tangent)
The perimeter of the rectangle is 20 + 20√3 inches.
How to find the perimeter of a rectangle?The perimeter of a rectangle is sum of the whole side of the rectangle. The side bounded by the rectangle is the perimeter of the rectangle.
Therefore, the diagonal of the rectangle is given as 20 inches.
Using trigonometric ratios, let's find the sides of the rectangle.
sin 30 = opposite / hypotenuse
sin 30 = x / 20
x = 20 sin 30
x = 20 × 0.5
x = 10 inches
Therefore, using Pythagoras theorem,
20² - 10² = b²
b² = 400 - 100
b = √300
b = √100 × 3
b = 10√3
Hence,
perimeter of the rectangle = 2(l + w)
perimeter of the rectangle = 2(10 + 10√3)
perimeter of the rectangle = 20 + 20√3
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J is the midpoint of segment CT.
CJ = 9x + 1
JT = 2x + 15
Find CT.
The length CT of the line segment is 38 units
How to determine the length of CT?From the question, we have the following parameters
CJ = 9x + 1
JT = 2x + 15
Also, we understand that:
Point J is the midpoint of segment CT.
This means that
CJ = CT
So, we have
9x + 1 = 2x + 15
Evaluate the like terms
7x = 14
So, we have
x = 2
Length CT is calculated as
CT = 9x + 1 + 2x + 15
So, we have
CT = 9 x 2 + 1 + 2 x 2 + 15
Evaluate
CT = 38
Hence, the length is 38 units
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30 point reward if you help ! find the volume of each shape and then compare. do not reduce your fractions.
The volume of the cuboid is [tex]\frac{6}{125}[/tex] and The volume of the cube is [tex]\frac{8}{27}[/tex]
The comparison of both a cube and a cuboid have six faces,a cube has six faces which are all squares and on the other hand, the cuboid is but a cuboid has rectangular faces.
What is a Cube?
A cube is a symmetrical three-dimensional shape which has all six sides equal.
To find the volume of cube is addition of all seen sides or the given sides all squared.
i.e volume of a cube= [tex]a^{3}[/tex]
volume of the cube=([tex]\frac{2}{3}[/tex])^3
Volume= [tex]\frac{8}{27}[/tex] cubic inches
How to dertermine the volume of a cuboid
Whar is a Cuboid?
A Cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices, and 12 edges which the volume can be measured by multiplying the length by the breadth by the height .
Volume of a cuboid = L×B×H
Volume of a cuboid=[tex]\frac{2}{3}[/tex]×[tex]\frac{1}{5}[/tex]×[tex]\frac{3}{5}[/tex]
Volume of a cuboid=[tex]\frac{6}{125}[/tex] cubic inches.
To compare,
A cube has shapes of equal sides six faces and a cuboid faces are non-equal with six faces, 8 vertices and 12 edges.
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help pls thank you ( i need 2 answers )
Answer:
a. 111.5 / 100
b. 1.15 feet
Step-by-step explanation:
a. if Eloise's statue is 1/100th of the height, it means that for every 100 cm of height of the actual statue, Eloise will have 1cm on hers.
Therefore the division problem 111.5 / 100 can be used to calculate the height of her statue in feet.
b. 111.5 feet / 100 = 1.15 feet
y=4x^2-8x+3
find the vertex form
The vertex of the quadratic equations is at (1, -1), then the vertex form will be:
y = 4*(x - 1)^2 - 1
How to find the vertex form?For a quadratic equation with leading coefficient a and a vertex (h, k), the vertex form is:
y = a*(x - h)^2 + k
And for a equation: y = a*x^2 + b*x + c
The x-value of the vertex is at:
h = -b/2a
In this case, we have:
y = 4x^2 - 8x + 3
So the x-value of the vertex is at:
h = -(-8)/2*4 = 1
To get the y-value we evaluate in x = 1
y = 4*1^2 - 8*1 + 3
y = 4 - 8 + 3 = -1
The vertex is at (1, -1) and the leading coefficient is 4, then the vertex form is:
y = 4*(x - 1)^2 - 1
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the recursive formula for the height above the ground on the nth step of the stairs show is an=an-1+4 with a1=7 what explicit formula finds the height above the ground of the nth step?
The explicit formula is a_n = 3+4n
From the question, we have
a1 = 7
We know that,
a_n = a_1 +(n-1)d
a_n = 7 +(n-1)4
a_n = 7+4n-4
a_n = 3+4n
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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Type the correct answer in the box. use numerals instead of words. the weight of a bag of golf balls varies directly as the number of golf balls in the bag. if a bag of 69 golf balls weighs 2,553 grams, how many golf balls are in a bag that weighs 1,110 grams? number of golf balls:
A total of 30 golf balls are there in the bag that weighs 1110 grams.
A total of 69 golf balls weights 2553 grams in a bag.
It is asked that how much golf balls does make 1110 grams of weight.
Let us say that the weight of one ball is X.
So, Using unitary method,
We can write,
69 times mass of one golf ball = 2553 grams.
69X = 2553
X = 2553/69
X = 37 grams.
Hence, the weight of one ball is 37 grams.
Now, let us say that Y balls weights 1110 grams,
So, we can write,
Y time weight of one ball = 1110
37Y = 1110
Y = 1110/37
Y = 30.
Hence, 30 golf balls will weight 1110 grams.
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Answer:
30
Step-by-step explanation:
Mariyah wants to enlarge a triangle with sides of 3 inches, 6 inches, and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be?
The other sides of the new triangle are 13, 26 and 26 inches as calculated by the properties of similarity.
We know that when two triangles are similar then the ratio of the sides are also equal.
Let the original triangle be ΔABC and the new triangle be ΔXYZ
So from the property of similarity.
AB/XY = BC /YZ = CA/ ZX
Now it is given AB = 3 inches
XY = 13 inches
Hence AB/XY = 13/3
Hence YZ = 13 / 3 × 6 =26 inches
Again ZX = 26 inches
Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.
Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.
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helen buys two pineapples she pays with a £5 note and gets £3.60 change work out the cost of one pineapple
Answer:
Each pineapple costs £0.70.
Step-by-step explanation:
Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.
Helen's total cost would be: P*C = total cost.
The total cost is the difference between £5 and £3.60, which is £1.40.
We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:
P*C = total cost
2*C = £1.40
C = £0.70
Find x
35°
100°
X
algebra 1
Answer:
X would be 135 degrees
Step-by-step explanation:
35 is a vertical angle
180-(100+35) = 45
By supplements, 180-45 = 135 which would be your answer
hope this helps
the value o f x is 135, it mean x=135°
7. What number multiplied by 2/3 has a product
of 1? (Example 2) it's saying 4/6 is wrong what do i do
Answer:
3/2
Step-by-step explanation:
To multiply fraction×fraction, you multiply top×top and bottom×bottom.
2/3 × 3/2
= 6/6
= 1
The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.